Abstract

Lately, the integration of two-dimensional materials into semiconductor devices has allowed the modification of their effective index by simply applying a modest voltage (between 0 and 3 volts). In this work, we present a device composed of two evanescently coupled silicon microring resonators where both rings have a graphene layer on top. This design is aimed to produce frequency combs with transmission characteristics controlled upon voltage application to the graphene layer. We numerically analyze the device response as a function of the incident wavelength and applied voltage. The results showed a low input intensity (0.6 GW/cm2) needed and a rapid response time (0.1 μs), in comparison to devices controlled by heat injection.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Two-dimensional materials are well known for their electronic and mechanical properties [1,2] leading to a vast number of applications. Among them, graphene is the most popular and studied specimen due to several features, e.g. its peculiar band structure [3–12]. The conduction and valence bands, touch at particular points named Dirac points. Around them, the density of states of carriers is low and consequently, graphene’s Fermi energy can be significantly modified by applying a relatively low voltage. The possibility of tuning the Fermi level allows the variation of graphene’s refractive index. Another extraordinary property is that the optical absorption of graphene does not depend on the wavelength in a wide range of photon energies, including the traditional optical communications bands extending from mid to far infrared [13,14].

By applying an oxide layer on top of a waveguide and a graphene sheet above, a MOS (metal-oxide-semiconductor) capacitor is built. In this way, the effective index of the complete waveguide can be varied by applying voltage to the graphene layer. This effect has been experimentally confirmed [15] and can be used to modify the optical properties of several applications [16,17], among which, we can find frequency combs.

An optical frequency comb is an optical signal whose spectrum consists of equidistant spectral lines, i.e., on equally spaced optical frequency components. These objects have application in diverse fields as optical clocks [18], precision spectroscopy [19–22], ultraviolet and infrared spectroscopy [23–25], precision distance measurement [26], etc.

A usual method used to produce optical combs consists of a continuous wave laser coupled to a resonator which operates in the nonlinear regime. Usually, the resonator is fabricated with a third order nonlinear material which allows degenerated four-wave mixing (FWM). The frequency conversion mechanism that takes place inside the resonator’s material, lies on the intensity dependence of the refractive index. In this process, two pump photons are annihilated and a new pair of photons is created: one of an up-shifted frequency called signal, and another of a downshifted frequency called idler. Provided the momentum and energy conservation, the new born waves are equidistant in frequency from the pump wave. When the optical cavity decay rates are surpassed by the scattering rate into the signal and idler modes, the parametric process occurs, yielding to symmetric sidebands that grow in intensity with increasing pump power and the frequency comb is produced [27–30].

If the signal and idler frequencies coincide with optical microresonator modes, the parametric process is enhanced, resulting in efficient sideband generation.

The power threshold for the initiation of parametric oscillation scales with the inverse of the quality factor Q squared. From this relation, it is possible to see the advantages of using a high quality factor. Furthermore, the required power to start the parametric oscillation can be strongly reduced [30–39]. Linear and nonlinear ring resonators were extensively analyzed in different applications [16,40–42].

When building a device destined to produce frequency combs, many parameters are fixed after the fabrication process, among which we can find the resonance frequency and the coupling strength to the bus waveguide. In the case of having only one resonator, the only parameter that can be varied after building the device, is the resonance frequency. This is achieved by manipulating the resonator effective index, using different techniques [43–45]. In the case of two coupled resonators, when the effective index is changed, not only the the resonance frequency is modified, but also the overall structure coupling to the bus waveguide as it is explained, for instance, in reference [46]. This coupling strength syntonization allows a more precise manipulation of the parameters that play a role in the comb building process [47].

We propose the usage of a graphene layer to change the effective index of two coupled microrring resonators in order to control the properties of the generated frequency comb. Our design aims for the advantages of rapid response time and low power consumption in comparison with the traditional method of heat transfer [48].

In the first part of this work, we analyze the effective index in the SOI-graphene structure. Secondly, we verify that the FWM is present and it is significant in comparison to other non-linear processes. After that, we continue by describing the frequency comb generation device and how the manipulation of the extinction futures is achieved.

2. SOI-graphene effective index

To model graphene, we follow the approach schemed in [49]. The graphene sheet is modeled as an extremely thin layer with a conductivity σ(ω, μc, Γ, T), being ω the angular frequency, μc the chemical potential, Γ the scattering rate (assumed to be independent of energy [49]) and T the temperature. Starting from the Kubo formula [50] and considering no magnetic field, the intraband (σintra) and interband (σinter) contributions to the conductivity are identified:

σ=σintra+σinter

The intraband term results:

σintra=ie2kBTπ2(ωi2Γ)(μckBT+2ln(eμc/kBT+1))
where e is the electron charge, kB is the Boltzmann constant and ħ = h/2π is the reduced Planck constant. Γ can be calculated as Γ = e vF2/(μ μc) being vF the Fermi velocity in graphene and μ the electron mobility. A typical value is 1/2Γ = 5×10−13 s [51].

When analyzing the energies involved in the conductivity formula we find that thermal energy is two orders of magnitude lower than photon energy and chemical potential (kBT ≪ |μc|, ħω). In this case, the interband conductivity can be approximated as [52]:

σinterie24π(2|μc|(ωi2Γ)2|μc|+(ωi2Γ))

Provided the conductivity, the dielectric constant (g) can be calculated as:

g=1+iσ(ω)ω0Δ
where Δ = 0.34 nm is the thickness of the graphene layer and 0 is the vacuum dielectric constant. A graphene monolayer is only one carbon atom in diameter. Given g, the real (ng) and imaginary (kg) parts of graphene’s refractive index can be determined using the relation ng+ikg=g.

By applying a suitable voltage Vg between the graphene layer and the Si core, the chemical potential μc can be modified and, as a consequence, the refractive index is also varied [53]:

|μc(Vg)|=vFπ|η(VgV0)|
where V0 = 0.8 V is the offset from zero caused by natural doping and η = 9×1016 1/(Vm2) [54]. Fig. 2(a) exhibits ng and kg calculations as a function of Vg and μc. It can be observed that with a modest excursion of 1 V, ng can be varied in an order of 3.

 figure: Fig. 1

Fig. 1 Geometry utilized in the finite-elements simulations. The Si core is 200 nm with and 500 nm height. It is surrounded by SiO2 and it has a Al2O3 layer on top with a graphene sheet above. The green layer represents a doped Si region of 60nm thickness, used to apply the voltage between the Si-core and the graphene layer.

Download Full Size | PPT Slide | PDF

 figure: Fig. 2

Fig. 2 (a) Real (ng) and imaginary (kg) components of graphene’s refractive index, obtained from Eqs. (1), (2), (3) and (4) for λ = 1550 nm, as a function of chemical potential μc and applied voltage Vg. (b) Example of the field distribution in the TM0 mode for a chemical potential of 0.4 eV. The background colors represent the field normal to the surface, where the color scale is in units of V/m. The arrows show the field in the surface y–z. (c) Real (neff) and imaginary (keff) components of the effective index of the first transversal magnetic mode TM0 obtained by finite-elements simulations performed for the geometry shown in Fig. 1.

Download Full Size | PPT Slide | PDF

This variation of refractive index can be profited to modify the effective index in a semiconductor waveguide. To explore this effect, we have performed finite-element simulations using an ad-hoc software that solves the Helmholtz Eq. and including the electrical conductivity of graphene as a function of the chemical potential, i.e. the applied voltage, and the incident wavelength. The incident wavelength was 1550 nm for the complete set of calculations. Fig. 1 shows the simulation geometry. The dimensions of the waveguide were chosen in order to obtain sufficient evanescent wave so the coupling between adjacent waveguides was possible. The silicon (Si) core was 200 nm width and 500 nm high and it was surrounded by silica. The green layer in Fig. 1 represents a doped Si region used to apply the voltage between the Si-core and the graphene layer. With this transversal area the waveguide results monomode. On top of each microrring resonator an Al3O2 layer is deposited with a graphene sheet above. Finally, an air layer covered the waveguide. Scattering boundary conditions were used in the geometry limits. The employed refractive indexes were nSi = 3.47 for silicon, nSiO2=1.44 for silica and nAl2O3=1.74 for Al2O3, for a wavelength of 1550 nm. In the case of graphene, its refractive index was included as a function of applied voltage as it was explained in the previous section. An example of the field distribution in the TM0 is shown in Fig. 2(b). The results for the variation of the effective index in the TM0 mode are exhibited in Fig. 2(c). It can be seen that with a small voltage variation of 1 V the effective index can be varied in 10−3. These results agree with experimental data [15].

3. Non-linear context

Several processes occur in the non-linear medium at the same time. To quantify them we have simulated the beam propagation through the non-linear medium using the non-linear Schrödinger Eq. for the Pump, Stokes, and anti-Stokes signals inside the SOI waveguide [55,56]. We also took into account spontaneous Raman which was modeled adding a term to the Stokes and anti-Stokes modes Eqs., that depends on the pump intensity [57]. These coupled Eqs. were solved using the split-step Fourier method [28]. Since light completes several round trips before leaving the rings it becomes necessary to calculate the effective length, Leff thorough which the beam travels. Following Ref. [58], Leff = 1/(2Im(k⃗)), where k⃗ is the complex propagation wavevector and |k⃗| = 2πneff/λ. For our waveguide results Leff ≃1mm. For these simulations, there was no Stokes signal stimulated.

On the other hand, the simulations show, as it is expected in Si, losses are very high due to free carriers generated by two photon absorption. We neglect these losses since they can be avoided by removing carriers with a p-n junction in reverse bias as it is the common procedure [59]. The total linear loss calculated was 0.13 GW/cm2.

Regarding the comb stability, in [60,61] it is explained why the case of anomalous dispersion is much more suitable than normal dispersion. The FWM process is highly affected by the effects of self-phase and cross-phase modulation (SPM and XPM). These processes refer to the nonlinear phase modulation of a beam, caused by its own intensity (SPM) or by other modes intensity (XPM), via the Kerr effect. In order to overcome these phenomena, the waveguide anomalous dispersion can be used. We performed a last set of finite-element simulations to verify that this effect is possible in our waveguides. In this case, we used the geometry of Fig. 1 and implemented the Sellmeier Eqs. to provide the model with an input for the dispersion of Si and SiO2 [62]. Once the effective index was obtained as a function of the incident wave frequency, the group velocity dispersion (GVD) was calculated through [27],

GVD(ω0)=2c(nω)ω=ω0+ω0c(2nω2)ω=ω0
After the GVD is extracted, the dispersion parameter D can be derived through D = −2πc/(λ2).GVD. The results are shown in Fig. 3 for a particular chemical potential of μc = 0.8 eV. It can be seen that anomalous dispersion (D > 0) is achieved for a certain range of wavelengths including λ ≃ 1550 nm, which is our selected wavelength.

 figure: Fig. 3

Fig. 3 Group velocity dispersion parameter D as a function of wavelength λ for a chemical potential of μc = 0.8 eV. The simulations were performed for the geometry of Fig 1.

Download Full Size | PPT Slide | PDF

In recent publication [58], the effective waveguide kerr coefficient n2eff is calculated which results at least three times major than that of silicon. We have followed their procedure to calculate this coefficient for our waveguide, finding n2eff = 9.75 × 10−17 m2/W, which is one order of magnitude higher than that of silicon.

To evaluate these nonlinear effects we have calculated characteristic lengths of each process. For SPM we have LSPM = 1/(γPnorm), where γ = n2effω/c and Pnorm is the incident power normalized by the waveguide area. In our case, the selected value of Pnorm is justified with in the comb formation theory and will be explained later. We used the value Pnorm = 1.74x 103 W/cm2. The dispersion length has been calculated as LD = τ22πc/(2), where τ is typical time related to the pump. Since our model uses continuous incident wave, we have chosen τ = 2π/ω = 5×10−15s. The obtained values for both lengths were LSPM =247 m and LD =0.4 m, indicating that the effect of anomalous dispersion is stronger than the self-phase modulation one. The major conclusion is that both lengths result orders of magnitude larger than the waveguide effective length Leff ≃1 mm, meaning that there will not be a big distortion in our mode profile.

4. Frequency comb generation device

The proposed analysis consists of two microrings evanescently coupled to a bus waveguide as shown in Fig. 4. Both rings possess a straight coupling section of 0.4 μm length in order to facilitate the passage of the incident wave to the rings. We worked with two options for the radio of the circular parts: 5 μm or 30 μm. These radius were chosen from a trade-off between minimizing the device size and having enough optical path to achieve an effective index change of the order of 10−3, the one achievable with graphene, produces a significant phase shift. Given the high contrast between the refractive index of Si and SiO2, we chose a 200 nm width core in order to have some evanescent field outside the core. This condition was necessary for the coupling between the microring resonators. The width of the total microring resonators, including the silica cladding, was 4 μm. Each ring has a 10 nm thick Al2O3 layer on top of the core with a graphene sheet above. With this thickness a MOS capacitor is formed between the graphene layer and the Si core. The resulting waveguide is monomode since the incident frequency is lower than the cutoff frequency of the first TM mode.

 figure: Fig. 4

Fig. 4 Schematic of the proposed device. The geometry consists of two evanescently coupled Si microring resonators and a bus waveguide. The surrounding material is SiO2. The Si core is 0.2 μm width and the SiO2 cladding is 4 μm width.

Download Full Size | PPT Slide | PDF

Since the two cavities are evanescently coupled, the individual cavity modes hybridize and, as a result, a symmetric and an anti-symmetric supermodes exist. According to the coupled-mode theory, these supermodes eigenfrequencies are given by [63]:

ωsimantisim=ωavg±Δω24+Kω2
where ωavg is the average resonant frequency (between the two cavities), Δω is the difference between the individual cavity resonances (cavity detuning), and Kω is the inter-ring temporal coupling rate. In the case of degenerated cavities (Δω = 0), the supermode resonances are separated by 2Kω.

We performed 2D finite-elements simulations with the aim of investigating the response of our system and comparing it with the predictions of Eq. (7). We solved the Helmholtz Eq. in our domain of interest with an ad-hoc software using the beam envelopes approach, first order elements and scattering boundary conditions in every geometry limit. For the first set of simulations the refractive index of both rings was kept equal.

The resulting transmittance at the end of the bus waveguide is shown in Fig. 5, as a function of the wavelength λ. The symmetric and antisymmetric modes could be identified as described by Eq. (7). The out-of-plane field in the inter-ring coupling zone is also presented to clearly visualize the parity of the supermodes. All the presented results belong to the first transversal electric mode TE0.

 figure: Fig. 5

Fig. 5 Transmittance as a function of the wavelength for microring resonators of radius R = 5 μm. The two supermodes, symmetric (S) and antisymmetric (AS) can be observed. The distribution of the out-of-plane field component, Ez, is also shown to clearly visualize the modes parity.

Download Full Size | PPT Slide | PDF

In a second set of simulations we varied the relative refractive index of the core of the two rings. We define ε as the maximum change that can be produced in neff by applying voltage to the graphene layer. We have stated before its value being ε = 10−3 which can be achieved by changing the applied voltage in 1 V. In order to modify the relative effective index we left the first ring with a fixed index of n1=nSi + ε/2, and varied the index of the second ring as n2 = n1 + Δn with −ε/2 ≤ Δnε/2, which means to vary the applied voltage between −0.5 V and 0.5 V. In this way, positive and negative detuning between the two microring resonators was possible preserving the total excursion (1 V).

The calculated transmittance as a function of incident wave frequency is shown in Fig. 6, for rings of 5 μm radius, and in Fig. 7 for rings of 30 μm radius. In both cases the behavior predicted by (7) is observed. The supermodes intensity depends on Kω [63] and, since Kω is a function of the wavelength and refractive indexes [64], the intensity finally depends on these two parameters and also does the transmittance. Kω also depends on the radius of the rings [64] and this is the reason why the shift achieved in the case of the smallest radius is minor than the one obtained for the 30 μm radius case.

 figure: Fig. 6

Fig. 6 Symmetric and antisymmetric modes transmittance as a function of the wavelength for different detuning values. The results correspond to rings of a radius of 5 μm.

Download Full Size | PPT Slide | PDF

As a result, the transmittance of the proposed device can be significantly varied by applying a modest voltage. This tunable transmittance can be profited as an envelope for the frequency comb components that allows to diminish, as well as magnify specific spectral lines.

To exemplify this point, we have performed numeric simulations. The comb lines, can be modeled by a system of coupled Eqs. [60]:

Aμt=12ΔωμAμ+δμ,012Δω0Fei(ωpω0)tig0αβγAαAβ*Aγei(ωαωβ+ωγωμ)t
where intermodal coupling is assumed. The modes amplitude is normalized so |Aμ|2 is the instantaneous number of photons in the mode μ. Each mode μ has a frequency ωμ = ω0 + D1 μ + 0.5D2 μ2, where D1 corresponds to the free spectral range (FSR) of the resonator and D2 to the difference between two neighboring FSRs at the center frequency ω0. In Eq. (8), Aμ is the amplitude of the mode μ, t is the time, Δωμ is the modal bandwidth, F is the external pumping factor which is normalized in a way such that |F|2 represents the total number of photons that are coupled into the cavity and g0 is the FWM reference gain. ωμ is the modal frequency and ωp is the pump frequency. The second term in Eq. (8) describes the external pumping and it adds up only for μ = 0 and the last term describes the frequency mixture that occurs in the FWM process.

We solved Eq. (8), that is stated for a single resonator, using the methodology proposed in [65] and a split-step Fourier algorithm. To model the structure, i.e. two coupled resonators, we then split each obtained mode following Eq. (7) and, after that, we multiplied the result by the coupled resonators efficiency. The calculus were carried out considering Δωμ = Δω0 which is a fair assumption as can be observed in Fig. 7. Δω0 was extracted from the finite-element simulations being Δω0 = 45 GHz. The pump frequency was chosen to be ωp = 1232 rad/s and g0 = 3MHz. As it is explained in [60] there is a power threshold for the initiation of the nonlinear effects, that can be translated into a threshold number of photons |A0th|2=0.5Δω0/g0. We chose to express the parameter F in units of this quantity. Once we have the threshold number of photons we can calculate the power threshold and normalize it by the waveguide area resulting 4.31 × 10−5GW/cm2. For the simulations we used F = 3|A0|2. The selected total time for the simulations was 0.1 μs.

 figure: Fig. 7

Fig. 7 Transmittance as a function of the wavelength for different detuning values. The results correspond to rings of a radius of 30 μm.

Download Full Size | PPT Slide | PDF

Results are shown in Fig. 8. It can be observed that the same line can be suppressed or amplified depending on the value of Δn, i.e. on the applied voltage. The insets zoom in the evolution of the central modes. We can observe that for Δn = 0.5 × 10−3 the first mode has a slower intensity than the second mode. When Δn = −0.5 × 10−3 the second mode has higher intensity than the first one. This shows that the relation between the intensities of these two modes is inverted when we change Δn, that is to say when we change the applied voltage.

 figure: Fig. 8

Fig. 8 Normalized intensity as a function of the wavelength for different values of Δn. The results correspond to rings of a radius of 30 μm. The insets zoom in the evolution of the central mode for the different Δn.

Download Full Size | PPT Slide | PDF

After that, we will estimate the response time of the system in order to compare it to other methods. In [60], it is established that the difference between the pump frequency and the resonator’s resonance frequency, σ, establishes a condition for certain modes to be excited. At power threshold, for the mode μ to be stable it is necessary that σ+0.5ω¯μ<3/2Δω0 where ω̄l = ωαωβ + ωγωμ referencing the frequencies involved in the four-wave mixing process. In our case, this stability condition is achieved for the six first modes, μ ∈ {−6, ..., 6}, and this was verified in the simulations (not shown). Only the six first spectral lines were activated when the incident power was at threshold.

On the other hand, after 0.1 μs these six components had already appeared so we considered this time as representative for the response time in a single resonator. We established this time as the lower limit for the response time of the coupled resonators device. Furthermore, we need to consider the speed at which the change in the refractive index is produced. In the literature we can find modulators made of Si and graphene that reach modulations speeds ranging from 1 to 30 GHz [1]. With this information we estimate a time response for this effect of the order of 30 ps. We notice that this time is significantly minor than the time needed to stabilize the comb. So, our final estimation of the response time is 0.1 μs. This is a remarkable advantage when we compare this device with others that employ the thermo-optic effect [48] since they have slower response time, i.e. in the order of microseconds [66] and they also need to deal with issues of thermal volumetric expansion.

A word must be said concerning SPM and XPM. The processes can introduce additional detunings ΔωSPM and ΔωXPM and, as a consequence, they can limit the comb span. To investigate these effects we have calculated the detunings they produce, taking into account the graphene presence by using the kerr index n2eff calculated as explained in Ref. [58]. Since we are using a continuous incident wave, the SPM frequency shift coefficient can be calculated as 2πn2I0Leffω0/λ0 where I0 is the incident intensity and all the other parameters were defined before. Evaluating this expression we obtain ΔωSPM ≃ 23 rad/s and ΔωXPM ≃ 88 rad/s. To calculate the XPM contribution we took an extreme case were the six modes present at threshold condition contribute in the same way to XPM and each mode intensity was extracted in relation to the central mode. With the obtained values the new detuning σ was calculated. Finally, the stability condition was once more verified to find that only six modes are allowed at threshold, meaning that SPM and XPM effect do not change the comb structure.

Continuing with the comparison with the method of thermal injection, we can say that voltage can be applied much more locally than heat.

In addition to this, since the envelope of the comb components can be manipulated in-situ, the proposed system also has the property of simplifying, to certain extent, the amendment of unavoidable imperfections in the fabrication process after the device is built.

Another important advantage of the proposed device arises when looking at the consumed power. The comb simulations results show that a power 1.3 × 10−4GW/cm2 destined to the FWM process is enough to produce the comb. To achieve this situation, an input intensity of 0.6 GW/cm2 is sufficient. This is considered a low input intensity [67] and makes the device suitable for many applications.

We have also estimated the electrical power consumption. Using as starting point reference [68] we have estimated power consumption of 5 mW which results in the same order of magnitude of that needed by the electric heating method [48].

5. Conclusion

We have proposed a device for frequency comb generation that allows in-situ tunability of the comb characteristics. The geometry contains two coupled SOI microrings coupled to a bus waveguide. The inter-ring coupling can be modified through low intensity voltage applied to a graphene layer lying on top of one of the microrings. We have numerically analyzed the response of the prototype as a function of the applied voltage and incident wavelength.

In comparison to thermal heating, which is commonly used to manipulate the comb characteristics, this device has the potential of offering lower response time, low input intensity and small footprint.

In addition, the calculated power consumption resulted low which makes it suitable for many applications.

Funding

Universidad Nacional de Cuyo (C014); CONICET, Comisión Nacional de Energía Atómica (CNEA); Sofrecom Argentina; Universidad de la Empresa (Research project P17T02).

Acknowledgments

We would like to acknowledge Condensed Matter Theory Group belonging to Bariloche Atomic Center for the provision of the cluster where the calculations were performed.

References and links

1. Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10, 227–238 (2016). [CrossRef]  

2. T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017). [CrossRef]  

3. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004). [CrossRef]   [PubMed]  

4. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat Mater 6, 183 (2007). [CrossRef]   [PubMed]  

5. F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5, 487–496 (2010). [CrossRef]   [PubMed]  

6. F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010). [CrossRef]  

7. L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010). [CrossRef]   [PubMed]  

8. P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2, 605–615 (2007). [CrossRef]  

9. Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015). [CrossRef]  

10. T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014). [CrossRef]   [PubMed]  

11. Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014). [CrossRef]   [PubMed]  

12. Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016). [CrossRef]  

13. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008). [CrossRef]   [PubMed]  

14. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008). [CrossRef]   [PubMed]  

15. V. Sorianello, G. De Angelis, T. Cassese, M. Midrio, M. Romagnoli, M. Mohsin, M. Otto, D. Neumaier, I. Asselberghs, J. Van Campenhout, and C. Huyghebaert, “Complex effective index in graphene-silicon waveguides,” Opt. Express 24, 29984–29993 (2016). [CrossRef]  

16. J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene waveguide tunable broadband microwave photonics phase shifter,” Opt. Express 22, 8094–8100 (2014). [CrossRef]   [PubMed]  

17. J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene Bragg gratings,” Opt. Express 22, 5283–5290 (2014). [CrossRef]   [PubMed]  

18. S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001). [CrossRef]   [PubMed]  

19. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007). [CrossRef]  

20. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008). [CrossRef]   [PubMed]  

21. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008). [CrossRef]   [PubMed]  

22. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007). [CrossRef]   [PubMed]  

23. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005). [CrossRef]   [PubMed]  

24. R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005). [CrossRef]   [PubMed]  

25. F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004). [CrossRef]   [PubMed]  

26. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009). [CrossRef]  

27. R. W. Boyd, Nonlinear optics (Academic Press, 2003).

28. G. P. Agrawal, Nonlinear fiber optics (Academic Press, 2007).

29. T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011). [CrossRef]   [PubMed]  

30. T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012). [CrossRef]  

31. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008). [CrossRef]   [PubMed]  

32. I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a caf 2 resonator,” Opt. Lett. 34, 878–880 (2009). [CrossRef]   [PubMed]  

33. W. Liang, A. Savchenkov, A. Matsko, V. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011). [CrossRef]   [PubMed]  

34. C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

35. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-q silica microspheres,” Phys. Rev. A 76, 043837 (2007). [CrossRef]  

36. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010). [CrossRef]  

37. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010). [CrossRef]  

38. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011). [CrossRef]   [PubMed]  

39. D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett 102, 193902 (2009). [CrossRef]   [PubMed]  

40. Y. Yi, P. Pignalosa, and D. Wu, “Tunable and ultra-small graphene integrated silicon racetrack micro resonator,” IEEE IEEE J. Sel. Top. Quantum Electron. 23, 1–6 (2017).

41. P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011). [CrossRef]  

42. S. Rabal, L. A. Bulus Rossini, and P. A. Costanzo Caso, “Control strategy of true time delay lines,” Fiber Integrated Opt. 36, 38–58 (2016).

43. P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011). [CrossRef]  

44. H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013). [CrossRef]   [PubMed]  

45. X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

46. D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006). [CrossRef]  

47. C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014). [CrossRef]   [PubMed]  

48. S. A. Miller, Y. Okawachi, S. Ramelow, K. Luke, A. Dutt, A. Farsi, A. L. Gaeta, and M. Lipson, “Tunable frequency combs based on dual microring resonators,” Opt. Express 23, 21527–21540 (2015). [CrossRef]   [PubMed]  

49. G. W. Hanson, “Dyadic Green’ s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008). [CrossRef]  

50. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007). [CrossRef]  

51. L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014). [CrossRef]  

52. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007). [CrossRef]  

53. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012). [CrossRef]   [PubMed]  

54. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011). [CrossRef]   [PubMed]  

55. N. M. Abadía Calvo, “Nonlinear effects in silicon ring resonators,” Ph.D. thesis, Vrije Universiteit Brussels (2011).

56. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007). [CrossRef]   [PubMed]  

57. S. Lefrançois, “High energy pulse propagation and parametric conversion in normal-dispersion optical fibers,” Ph.D. thesis, Cornell University (2012).

58. K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015). [CrossRef]   [PubMed]  

59. G. T. Reed, Silicon photonics: the state of the art (John Wiley & Sons, 2008). [CrossRef]  

60. Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010). [CrossRef]  

61. Y. Okawachi, M. R. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014). [CrossRef]   [PubMed]  

62. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14, 4357–4362 (2006). [CrossRef]   [PubMed]  

63. H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987). [CrossRef]  

64. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997). [CrossRef]  

65. T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014). [CrossRef]  

66. F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

67. S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017). [CrossRef]  

68. G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10, 227–238 (2016).
    [Crossref]
  2. T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
    [Crossref]
  3. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [Crossref] [PubMed]
  4. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat Mater 6, 183 (2007).
    [Crossref] [PubMed]
  5. F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5, 487–496 (2010).
    [Crossref] [PubMed]
  6. F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
    [Crossref]
  7. L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
    [Crossref] [PubMed]
  8. P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2, 605–615 (2007).
    [Crossref]
  9. Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015).
    [Crossref]
  10. T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
    [Crossref] [PubMed]
  11. Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
    [Crossref] [PubMed]
  12. Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
    [Crossref]
  13. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
    [Crossref] [PubMed]
  14. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
    [Crossref] [PubMed]
  15. V. Sorianello, G. De Angelis, T. Cassese, M. Midrio, M. Romagnoli, M. Mohsin, M. Otto, D. Neumaier, I. Asselberghs, J. Van Campenhout, and C. Huyghebaert, “Complex effective index in graphene-silicon waveguides,” Opt. Express 24, 29984–29993 (2016).
    [Crossref]
  16. J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene waveguide tunable broadband microwave photonics phase shifter,” Opt. Express 22, 8094–8100 (2014).
    [Crossref] [PubMed]
  17. J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene Bragg gratings,” Opt. Express 22, 5283–5290 (2014).
    [Crossref] [PubMed]
  18. S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
    [Crossref] [PubMed]
  19. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
    [Crossref]
  20. T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
    [Crossref] [PubMed]
  21. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
    [Crossref] [PubMed]
  22. S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
    [Crossref] [PubMed]
  23. C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
    [Crossref] [PubMed]
  24. R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
    [Crossref] [PubMed]
  25. F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004).
    [Crossref] [PubMed]
  26. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009).
    [Crossref]
  27. R. W. Boyd, Nonlinear optics (Academic Press, 2003).
  28. G. P. Agrawal, Nonlinear fiber optics (Academic Press, 2007).
  29. T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
    [Crossref] [PubMed]
  30. T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
    [Crossref]
  31. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
    [Crossref] [PubMed]
  32. I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a caf 2 resonator,” Opt. Lett. 34, 878–880 (2009).
    [Crossref] [PubMed]
  33. W. Liang, A. Savchenkov, A. Matsko, V. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
    [Crossref] [PubMed]
  34. C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.
  35. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
    [Crossref]
  36. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
    [Crossref]
  37. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
    [Crossref]
  38. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
    [Crossref] [PubMed]
  39. D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett 102, 193902 (2009).
    [Crossref] [PubMed]
  40. Y. Yi, P. Pignalosa, and D. Wu, “Tunable and ultra-small graphene integrated silicon racetrack micro resonator,” IEEE IEEE J. Sel. Top. Quantum Electron. 23, 1–6 (2017).
  41. P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011).
    [Crossref]
  42. S. Rabal, L. A. Bulus Rossini, and P. A. Costanzo Caso, “Control strategy of true time delay lines,” Fiber Integrated Opt. 36, 38–58 (2016).
  43. P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
    [Crossref]
  44. H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013).
    [Crossref] [PubMed]
  45. X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.
  46. D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
    [Crossref]
  47. C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
    [Crossref] [PubMed]
  48. S. A. Miller, Y. Okawachi, S. Ramelow, K. Luke, A. Dutt, A. Farsi, A. L. Gaeta, and M. Lipson, “Tunable frequency combs based on dual microring resonators,” Opt. Express 23, 21527–21540 (2015).
    [Crossref] [PubMed]
  49. G. W. Hanson, “Dyadic Green’ s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
    [Crossref]
  50. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
    [Crossref]
  51. L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
    [Crossref]
  52. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
    [Crossref]
  53. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012).
    [Crossref] [PubMed]
  54. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
    [Crossref] [PubMed]
  55. N. M. Abadía Calvo, “Nonlinear effects in silicon ring resonators,” Ph.D. thesis, Vrije Universiteit Brussels (2011).
  56. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
    [Crossref] [PubMed]
  57. S. Lefrançois, “High energy pulse propagation and parametric conversion in normal-dispersion optical fibers,” Ph.D. thesis, Cornell University (2012).
  58. K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
    [Crossref] [PubMed]
  59. G. T. Reed, Silicon photonics: the state of the art (John Wiley & Sons, 2008).
    [Crossref]
  60. Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
    [Crossref]
  61. Y. Okawachi, M. R. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014).
    [Crossref] [PubMed]
  62. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14, 4357–4362 (2006).
    [Crossref] [PubMed]
  63. H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
    [Crossref]
  64. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
    [Crossref]
  65. T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
    [Crossref]
  66. F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.
  67. S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
    [Crossref]
  68. G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
    [Crossref]

2017 (4)

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Y. Yi, P. Pignalosa, and D. Wu, “Tunable and ultra-small graphene integrated silicon racetrack micro resonator,” IEEE IEEE J. Sel. Top. Quantum Electron. 23, 1–6 (2017).

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

2016 (4)

S. Rabal, L. A. Bulus Rossini, and P. A. Costanzo Caso, “Control strategy of true time delay lines,” Fiber Integrated Opt. 36, 38–58 (2016).

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10, 227–238 (2016).
[Crossref]

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

V. Sorianello, G. De Angelis, T. Cassese, M. Midrio, M. Romagnoli, M. Mohsin, M. Otto, D. Neumaier, I. Asselberghs, J. Van Campenhout, and C. Huyghebaert, “Complex effective index in graphene-silicon waveguides,” Opt. Express 24, 29984–29993 (2016).
[Crossref]

2015 (3)

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015).
[Crossref]

S. A. Miller, Y. Okawachi, S. Ramelow, K. Luke, A. Dutt, A. Farsi, A. L. Gaeta, and M. Lipson, “Tunable frequency combs based on dual microring resonators,” Opt. Express 23, 21527–21540 (2015).
[Crossref] [PubMed]

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

2014 (8)

Y. Okawachi, M. R. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Opt. Lett. 39, 3535–3538 (2014).
[Crossref] [PubMed]

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
[Crossref] [PubMed]

T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene waveguide tunable broadband microwave photonics phase shifter,” Opt. Express 22, 8094–8100 (2014).
[Crossref] [PubMed]

J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene Bragg gratings,” Opt. Express 22, 5283–5290 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (2)

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012).
[Crossref] [PubMed]

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

2011 (6)

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

W. Liang, A. Savchenkov, A. Matsko, V. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref] [PubMed]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011).
[Crossref]

2010 (6)

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
[Crossref]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5, 487–496 (2010).
[Crossref] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

2009 (3)

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett 102, 193902 (2009).
[Crossref] [PubMed]

I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a caf 2 resonator,” Opt. Lett. 34, 878–880 (2009).
[Crossref] [PubMed]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009).
[Crossref]

2008 (6)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

G. W. Hanson, “Dyadic Green’ s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

2007 (8)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref] [PubMed]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2, 605–615 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat Mater 6, 183 (2007).
[Crossref] [PubMed]

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref] [PubMed]

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[Crossref]

2006 (2)

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14, 4357–4362 (2006).
[Crossref] [PubMed]

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

2005 (2)

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[Crossref] [PubMed]

2004 (2)

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

2001 (1)

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

1987 (1)

H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Abadía Calvo, N. M.

N. M. Abadía Calvo, “Nonlinear effects in silicon ring resonators,” Ph.D. thesis, Vrije Universiteit Brussels (2011).

Agarwal, A. M.

Agha, I. H.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[Crossref]

Agrawal, G. P.

Arafin, S.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Asselberghs, I.

Avouris, P.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2, 605–615 (2007).
[Crossref]

Bai, J.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Bao, C.

Bao, M.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Barwicz, T.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Benedick, A. J.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Bergquist, J.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Boyd, R.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear optics (Academic Press, 2003).

Braje, D.

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett 102, 193902 (2009).
[Crossref] [PubMed]

Bulus Rossini, L. A.

S. Rabal, L. A. Bulus Rossini, and P. A. Costanzo Caso, “Control strategy of true time delay lines,” Fiber Integrated Opt. 36, 38–58 (2016).

Caldwell, J. D.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Capmany, J.

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

Carvalho, D. O.

Cassese, T.

Chang, H.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Chaves, A.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Chembo, Y. K.

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
[Crossref]

Chen, Z.

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2, 605–615 (2007).
[Crossref]

Cheng, R.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Chu, S.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Coddington, I.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009).
[Crossref]

Coldren, L.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Costanzo Caso, P. A.

S. Rabal, L. A. Bulus Rossini, and P. A. Costanzo Caso, “Control strategy of true time delay lines,” Fiber Integrated Opt. 36, 38–58 (2016).

Costanzo-Caso, P. A.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011).
[Crossref]

Curtis, E.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

D’Odorico, S.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Dahlem, M.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Dai, T.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

De Angelis, G.

Dekker, H.

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Del’ Haye, P.

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

Del’Haye, P.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Di Franco, S.

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Diddams, S.

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett 102, 193902 (2009).
[Crossref] [PubMed]

Diddams, S. A.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref] [PubMed]

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Domenech, D.

Drullinger, R.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Duan, X.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Duchesne, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Dutt, A.

Eliyahu, D.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Fan, Y.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015).
[Crossref]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Fang, N. X.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Farsi, A.

Fendel, P.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Ferrari, A.

F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Ferrera, M.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Fiorenza, P.

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Fischer, M.

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Fisichella, G.

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Fong, K. Y.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Foster, M. A.

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[Crossref] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[Crossref]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14, 4357–4362 (2006).
[Crossref] [PubMed]

Fu, Q.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Gaeta, A. L.

Gan, F.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

Gehring, G.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat Mater 6, 183 (2007).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Giannazzo, F.

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Glenday, A. G.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Gohle, C.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004).
[Crossref] [PubMed]

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Gorodetsky, M.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

Granieri, S.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011).
[Crossref]

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Grudinin, I. S.

Guinea, F.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Guo, C. C.

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Haensch, T. W.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Hänsch, T.

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Hänsch, T. W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

Hanson, G. W.

G. W. Hanson, “Dyadic Green’ s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

Hansson, T.

T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
[Crossref]

Hartinger, K.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

Hasan, T.

F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Haus, H.

H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Heinz, T. F.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

Herr, T.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Herrmann, M.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

Hollberg, L.

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett 102, 193902 (2009).
[Crossref] [PubMed]

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref] [PubMed]

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Holzwarth, C.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Holzwarth, R.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004).
[Crossref] [PubMed]

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Hu, T.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

Huang, W.

H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Huang, Y.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Huyghebaert, C.

Ilchenko, V.

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Ippen, E.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Itano, W. M.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Jackson, D.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Jiang, X.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012).
[Crossref] [PubMed]

Jin, Y.

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012).
[Crossref] [PubMed]

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011).
[Crossref]

Johansson, L.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Jones, R. J.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[Crossref] [PubMed]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Jung, H.

Kartner, F.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Kärtner, F. X.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Kawakami, S.

H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Keilmann, F.

Kentischer, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

Kim, S.-K.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Kimerling, L. C.

Kippenberg, T.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

Koppens, F.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Koschny, T.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015).
[Crossref]

Krausz, F.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

Kumar, A.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Kuzucu, O.

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Lamont, M. R.

Leaird, D. E.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Lee, W.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Lefrançois, S.

S. Lefrançois, “High energy pulse propagation and parametric conversion in normal-dispersion optical fibers,” Ph.D. thesis, Cornell University (2012).

Lepeshkin, N. N.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Levy, J. S.

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[Crossref] [PubMed]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Li, C.-H.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Li, H.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Li, X. J.

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

Li, Y.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

Liang, W.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

W. Liang, A. Savchenkov, A. Matsko, V. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref] [PubMed]

Liao, L.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Lin, Q.

Lin, Y.-C.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Lipson, M.

Little, B.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Liu, K.

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Liu, Y.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Low, T.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

Lui, C. H.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

Luke, K.

Mak, K. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

Maleki, L.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

C. Bao, L. Zhang, A. Matsko, Y. Yan, Z. Zhao, G. Xie, A. M. Agarwal, L. C. Kimerling, J. Michel, L. Maleki, and A. E. Willner, “Nonlinear conversion efficiency in Kerr frequency comb generation,” Opt. Lett. 39, 6126–6129 (2014).
[Crossref] [PubMed]

W. Liang, A. Savchenkov, A. Matsko, V. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref] [PubMed]

I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a caf 2 resonator,” Opt. Lett. 34, 878–880 (2009).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Manescau, A.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Manolatou, C.

Martinez, A.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10, 227–238 (2016).
[Crossref]

Martin-Moreno, L.

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Mashanovitch, M.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Matsko, A.

Matsko, A. B.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Mbele, V.

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref] [PubMed]

Michel, J.

Midrio, M.

Miller, S. A.

Misewich, J. A.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

Modotto, D.

T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
[Crossref]

Mohsin, M.

Moll, K. D.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[Crossref] [PubMed]

Morandotti, R.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Morrison, G.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Moss, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Muñoz, P.

Murphy, M.

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Murphy, M. T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

Nair, R. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Nenadovic, L.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009).
[Crossref]

Neumaier, D.

Newbury, N. R.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009).
[Crossref]

Nigro, R. Lo

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Novoselov, K. S.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat Mater 6, 183 (2007).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Oates, C.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Okawachi, Y.

Otto, M.

Painter, O. J.

Park, Q.-H.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Pasquini, L.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Pei, C.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

Perebeinos, V.

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2, 605–615 (2007).
[Crossref]

Peres, N. M.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Phillips, D. F.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Picqué, N.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Pignalosa, P.

Y. Yi, P. Pignalosa, and D. Wu, “Tunable and ultra-small graphene integrated silicon racetrack micro resonator,” IEEE IEEE J. Sel. Top. Quantum Electron. 23, 1–6 (2017).

Popovic, M.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Qi, M.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Qin, S. Q.

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

Qu, Y.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Rabal, S.

S. Rabal, L. A. Bulus Rossini, and P. A. Costanzo Caso, “Control strategy of true time delay lines,” Fiber Integrated Opt. 36, 38–58 (2016).

Rakich, P.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Ramelow, S.

Rauschenberger, J.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

Ravesi, S.

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Razzari, L.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Reed, G. T.

G. T. Reed, Silicon photonics: the state of the art (John Wiley & Sons, 2008).
[Crossref]

Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

Roccaforte, F.

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Rodwell, M.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Romagnoli, M.

Saha, K.

Sasselov, D.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Savchenkov, A.

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Schilirò, E.

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

Schliesser, A.

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Schmidt, B. S.

Schmidt, W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

Schuessler, H. A.

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

Schweinsberg, A.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Schwierz, F.

F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5, 487–496 (2010).
[Crossref] [PubMed]

Seidel, D.

W. Liang, A. Savchenkov, A. Matsko, V. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Sfeir, M. Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[Crossref]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14, 4357–4362 (2006).
[Crossref] [PubMed]

Shen, A.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

Shen, N.-H.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015).
[Crossref]

Siahmakoun, A.

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011).
[Crossref]

Simsek, A.

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

Sizmann, A.

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Smith, D. D.

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Smith, H.

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

Sorianello, V.

Soukoulis, C. M.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015).
[Crossref]

Stauber, T.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

Steinmetz, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

Sun, Z.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10, 227–238 (2016).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Swann, W. C.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009).
[Crossref]

Szentgyorgyi, A.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Tang, H. X.

Thorpe, M. J.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[Crossref] [PubMed]

Turner, A. C.

Turner-Foster, A. C.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Udem, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Van Campenhout, J.

Vogel, K.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Wabnitz, S.

T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
[Crossref]

Walsworth, R. L.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Wang, C.

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

Wang, F.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10, 227–238 (2016).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Wang, J.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Wang, K. L.

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Wang, P.-H.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Wei, Z.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Weiner, A. M.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Whitaker, N.

H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

Wilken, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

Willner, A. E.

Wineland, D. J.

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

Wu, D.

Y. Yi, P. Pignalosa, and D. Wu, “Tunable and ultra-small graphene integrated silicon racetrack micro resonator,” IEEE IEEE J. Sel. Top. Quantum Electron. 23, 1–6 (2017).

Wu, Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

Xie, G.

Xiong, C.

Xu, C.

Xu, W.

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

Xuan, Y.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Xue, X.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Yan, Y.

Yang, J.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012).
[Crossref] [PubMed]

Yang, L.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012).
[Crossref] [PubMed]

Ye, J.

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[Crossref] [PubMed]

Yi, Y.

Y. Yi, P. Pignalosa, and D. Wu, “Tunable and ultra-small graphene integrated silicon racetrack micro resonator,” IEEE IEEE J. Sel. Top. Quantum Electron. 23, 1–6 (2017).

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Yu, H.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

Yu, M.

Yu, N.

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
[Crossref]

I. S. Grudinin, N. Yu, and L. Maleki, “Generation of optical frequency combs with a caf 2 resonator,” Opt. Lett. 34, 878–880 (2009).
[Crossref] [PubMed]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Zhang, F.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Zhang, J. F.

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

Zhang, L.

Zhang, P.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Zhang, X.

H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Zhao, Q.

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Y. Fan, F. Zhang, Q. Zhao, Z. Wei, and H. Li, “Tunable terahertz coherent perfect absorption in a monolayer graphene,” Opt. Lett. 39, 6269–6272 (2014).
[Crossref] [PubMed]

Zhao, Z.

Zhu, Z. H.

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

ACS Appl. Mater. Inter. (1)

G. Fisichella, E. Schilirò, S. Di Franco, P. Fiorenza, R. Lo Nigro, F. Roccaforte, S. Ravesi, and F. Giannazzo, “Interface Electrical Properties of Al2O3 Thin Films on Graphene Obtained by Atomic Layer Deposition with an in Situ Seedlike Layer,” ACS Appl. Mater. Inter. 9, 7761–7771 (2017).
[Crossref]

ACS Nano (1)

T. Low and P. Avouris, “Graphene plasmonics for terahertz to mid-infrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref] [PubMed]

ACS Photonics (1)

Y. Fan, N.-H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable terahertz meta-surface with graphene cut-wires,” ACS Photonics 2, 151–156 (2015).
[Crossref]

Adv. Opt. Mater. (1)

Y. Fan, N.-H. Shen, F. Zhang, Z. Wei, H. Li, Q. Zhao, Q. Fu, P. Zhang, T. Koschny, and C. M. Soukoulis, “Electrically tunable Goos–Hänchen effect with graphene in the terahertz regime,” Adv. Opt. Mater. 4, 1824–1828 (2016).
[Crossref]

Fiber Integrated Opt. (1)

S. Rabal, L. A. Bulus Rossini, and P. A. Costanzo Caso, “Control strategy of true time delay lines,” Fiber Integrated Opt. 36, 38–58 (2016).

IEEE IEEE J. Sel. Top. Quantum Electron. (1)

Y. Yi, P. Pignalosa, and D. Wu, “Tunable and ultra-small graphene integrated silicon racetrack micro resonator,” IEEE IEEE J. Sel. Top. Quantum Electron. 23, 1–6 (2017).

IEEE Photonics J. (1)

S. Arafin, A. Simsek, S.-K. Kim, W. Liang, D. Eliyahu, G. Morrison, M. Mashanovitch, A. Matsko, L. Johansson, L. Maleki, M. Rodwell, and L. Coldren, “Power-efficient kerr frequency comb based tunable optical source,” IEEE Photonics J. 9, 1–14 (2017).
[Crossref]

IEEE Photonics Technol. Lett. (1)

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 optical switch based on graphene-silicon-waveguide microring,” IEEE Photonics Technol. Lett. 26, 235–238 (2014).
[Crossref]

J. Appl. Phys. (1)

G. W. Hanson, “Dyadic Green’ s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

J. Lightwave Technol. (2)

H. Haus, W. Huang, S. Kawakami, and N. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

J. Nonlinear Opt. Phys. Mater. (1)

P. A. Costanzo-Caso, Y. Jin, S. Granieri, and A. Siahmakoun, “Optical bistability in a nonlinear soa-based fiber ring resonator,” J. Nonlinear Opt. Phys. Mater. 20, 281–292 (2011).
[Crossref]

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19, 026222 (2007).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, T. Hänsch, and A. Manescau, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839–847 (2007).
[Crossref]

Nat Mater (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat Mater 6, 183 (2007).
[Crossref] [PubMed]

Nat. Mater. (1)

T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, “Polaritons in layered two-dimensional materials,” Nat. Mater. 16, 182 (2017).
[Crossref]

Nat. Nanotechnol. (2)

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2, 605–615 (2007).
[Crossref]

F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5, 487–496 (2010).
[Crossref] [PubMed]

Nat. Photonics (6)

F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10, 227–238 (2016).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3, 351–356 (2009).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “Cmos-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “Cmos-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

Nature (5)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

S. A. Diddams, L. Hollberg, and V. Mbele, “Molecular fingerprinting with the resolved modes of a femtosecond laser frequency comb,” Nature 445, 627–630 (2007).
[Crossref] [PubMed]

C. Gohle, T. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature 436, 234–237 (2005).
[Crossref] [PubMed]

L. Liao, Y.-C. Lin, M. Bao, R. Cheng, J. Bai, Y. Liu, Y. Qu, K. L. Wang, Y. Huang, and X. Duan, “High-speed graphene transistors with a self-aligned nanowire gate,” Nature 467, 305–308 (2010).
[Crossref] [PubMed]

Opt. Commun. (2)

T. Hansson, D. Modotto, and S. Wabnitz, “On the numerical simulation of kerr frequency combs using coupled mode equations,” Opt. Commun. 312, 134–136 (2014).
[Crossref]

D. D. Smith, N. N. Lepeshkin, A. Schweinsberg, G. Gehring, R. Boyd, Q.-H. Park, H. Chang, and D. Jackson, “Coupled-resonator-induced transparency in a fiber system,” Opt. Commun. 264, 163–168 (2006).
[Crossref]

Opt. Express (8)

S. A. Miller, Y. Okawachi, S. Ramelow, K. Luke, A. Dutt, A. Farsi, A. L. Gaeta, and M. Lipson, “Tunable frequency combs based on dual microring resonators,” Opt. Express 23, 21527–21540 (2015).
[Crossref] [PubMed]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[Crossref] [PubMed]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide,” Opt. Express 20, 22398–22405 (2012).
[Crossref] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14, 4357–4362 (2006).
[Crossref] [PubMed]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref] [PubMed]

V. Sorianello, G. De Angelis, T. Cassese, M. Midrio, M. Romagnoli, M. Mohsin, M. Otto, D. Neumaier, I. Asselberghs, J. Van Campenhout, and C. Huyghebaert, “Complex effective index in graphene-silicon waveguides,” Opt. Express 24, 29984–29993 (2016).
[Crossref]

J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene waveguide tunable broadband microwave photonics phase shifter,” Opt. Express 22, 8094–8100 (2014).
[Crossref] [PubMed]

J. Capmany, D. Domenech, and P. Muñoz, “Silicon graphene Bragg gratings,” Opt. Express 22, 5283–5290 (2014).
[Crossref] [PubMed]

Opt. Lett. (7)

Phys. Rev. A (2)

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[Crossref]

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
[Crossref]

Phys. Rev. B (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Sum rules for the optical and hall conductivity in graphene,” Phys. Rev. B 75, 165407 (2007).
[Crossref]

Phys. Rev. Lett (1)

D. Braje, L. Hollberg, and S. Diddams, “Brillouin-enhanced hyperparametric generation of an optical frequency comb in a monolithic highly nonlinear fiber cavity pumped by a cw laser,” Phys. Rev. Lett 102, 193902 (2009).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

P. Del’ Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[Crossref] [PubMed]

R. J. Jones, K. D. Moll, M. J. Thorpe, and J. Ye, “Phase-coherent frequency combs in the vacuum ultraviolet via high-harmonic generation inside a femtosecond enhancement cavity,” Phys. Rev. Lett. 94, 193201 (2005).
[Crossref] [PubMed]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref] [PubMed]

Sci. Rep. (1)

K. Liu, J. F. Zhang, W. Xu, Z. H. Zhu, C. C. Guo, X. J. Li, and S. Q. Qin, “Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide,” Sci. Rep. 5, 16734 (2015).
[Crossref] [PubMed]

Science (5)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser frequency combs for astronomical observations,” Science 321, 1335–1337 (2008).
[Crossref] [PubMed]

T. J. Kippenberg, R. Holzwarth, and S. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref] [PubMed]

S. A. Diddams, T. Udem, J. Bergquist, E. Curtis, R. Drullinger, L. Hollberg, W. M. Itano, W. Lee, C. Oates, K. Vogel, and D. J. Wineland, “An optical clock based on a single trapped 199hg+ ion,” Science 293, 825–828 (2001).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Other (8)

R. W. Boyd, Nonlinear optics (Academic Press, 2003).

G. P. Agrawal, Nonlinear fiber optics (Academic Press, 2007).

C. Wang, T. Herr, P. Del’Haye, A. Schliesser, R. Holzwarth, T. W. Haensch, N. Picqué, and T. Kippenberg, “Mid-infrared frequency combs based on microresonators,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2011), p. PDPA4.

G. T. Reed, Silicon photonics: the state of the art (John Wiley & Sons, 2008).
[Crossref]

S. Lefrançois, “High energy pulse propagation and parametric conversion in normal-dispersion optical fibers,” Ph.D. thesis, Cornell University (2012).

N. M. Abadía Calvo, “Nonlinear effects in silicon ring resonators,” Ph.D. thesis, Vrije Universiteit Brussels (2011).

F. Gan, T. Barwicz, M. Popovic, M. Dahlem, C. Holzwarth, P. Rakich, H. Smith, E. Ippen, and F. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Proceedings of IEEE Conference Photonics in Switching, 2007, (IEEE, 2007), pp. 67–68.

X. Xue, Y. Xuan, P.-H. Wang, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Tunable frequency comb generation from a microring with a thermal heater,” in Proceedings of Optical Society of America Conference CLEO: Science and Innovations (Optical Society of America, 2014), pp. SF1I-8.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 Geometry utilized in the finite-elements simulations. The Si core is 200 nm with and 500 nm height. It is surrounded by SiO2 and it has a Al2O3 layer on top with a graphene sheet above. The green layer represents a doped Si region of 60nm thickness, used to apply the voltage between the Si-core and the graphene layer.
Fig. 2
Fig. 2 (a) Real (ng) and imaginary (kg) components of graphene’s refractive index, obtained from Eqs. (1), (2), (3) and (4) for λ = 1550 nm, as a function of chemical potential μc and applied voltage Vg. (b) Example of the field distribution in the TM0 mode for a chemical potential of 0.4 eV. The background colors represent the field normal to the surface, where the color scale is in units of V/m. The arrows show the field in the surface y–z. (c) Real (neff) and imaginary (keff) components of the effective index of the first transversal magnetic mode TM0 obtained by finite-elements simulations performed for the geometry shown in Fig. 1.
Fig. 3
Fig. 3 Group velocity dispersion parameter D as a function of wavelength λ for a chemical potential of μc = 0.8 eV. The simulations were performed for the geometry of Fig 1.
Fig. 4
Fig. 4 Schematic of the proposed device. The geometry consists of two evanescently coupled Si microring resonators and a bus waveguide. The surrounding material is SiO2. The Si core is 0.2 μm width and the SiO2 cladding is 4 μm width.
Fig. 5
Fig. 5 Transmittance as a function of the wavelength for microring resonators of radius R = 5 μm. The two supermodes, symmetric (S) and antisymmetric (AS) can be observed. The distribution of the out-of-plane field component, Ez, is also shown to clearly visualize the modes parity.
Fig. 6
Fig. 6 Symmetric and antisymmetric modes transmittance as a function of the wavelength for different detuning values. The results correspond to rings of a radius of 5 μm.
Fig. 7
Fig. 7 Transmittance as a function of the wavelength for different detuning values. The results correspond to rings of a radius of 30 μm.
Fig. 8
Fig. 8 Normalized intensity as a function of the wavelength for different values of Δn. The results correspond to rings of a radius of 30 μm. The insets zoom in the evolution of the central mode for the different Δn.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

σ = σ intra + σ inter
σ intra = i e 2 k B T π 2 ( ω i 2 Γ ) ( μ c k B T + 2 ln ( e μ c / k B T + 1 ) )
σ inter i e 2 4 π ( 2 | μ c | ( ω i 2 Γ ) 2 | μ c | + ( ω i 2 Γ ) )
g = 1 + i σ ( ω ) ω 0 Δ
| μ c ( V g ) | = v F π | η ( V g V 0 ) |
GVD ( ω 0 ) = 2 c ( n ω ) ω = ω 0 + ω 0 c ( 2 n ω 2 ) ω = ω 0
ω sim antisim = ω avg ± Δ ω 2 4 + K ω 2
A μ t = 1 2 Δ ω μ A μ + δ μ , 0 1 2 Δ ω 0 F e i ( ω p ω 0 ) t i g 0 α β γ A α A β * A γ e i ( ω α ω β + ω γ ω μ ) t

Metrics