Abstract

Comb generation in different mode families via a stimulated Raman scattering (SRS) process is studied using a silica toroid microcavity. The broad gain bandwidth of SRS in silica allows us to excite longitudinal modes at long wavelengths belonging to mode families that are either the same as or different from the pump mode. We found through experiment and numerical analysis, that an SRS comb in a different mode family with a high quality factor (Q) is excited when we pump in a low-Q mode. No transverse mode interaction occurs when we excite in a high-Q mode resulting the generation of a single comb family. We studied the condition of the transverse mode interaction while varying the mode overlap and Q of the Raman mode. Our experimental results are in good agreement with the analysis and this enables us to control the generation of one- and two-mode combs.

© 2017 Optical Society of America

1. Introduction

Comb generation with microcavities has been intensively researched because it has many attractive applications such as spectroscopy, frequency metrology, and optical communication [1–13]. A high quality factor (Q) microcavity enables us to obtain Kerr comb generation, because third-order nonlinearity is proportional to Q2/V at a given input power, where V is the mode volume of the cavity. Four-wave mixing (FWM) is the principal mechanism that contributes to the generation of the Kerr comb, but other effects such as stimulated Raman scattering (SRS) also occur in the same cavity.

The use of SRS is attractive because it allows us to generate long-wavelength light, particularly in the mid-infrared (MIR) wavelength regime, where the wavelengths are useful for sensing applications. Thus, SRS was taken into account and Raman lasing was demonstrated by using high-Q cavities made of silica, calcium fluoride, diamond, polymer, and other materials [14–26], including at MIR [21,27,28] wavelengths. Recently, the generation of comb light with the SRS process using a crystalline has even been reported [29,30].

Among various materials, silica is particularly good for demonstrating Raman lasing [14–17], because it has broadband Raman gain that has a full-width half-maximum (FWHM) bandwidth of 260 cm−1 with a center Stokes spectrum shift of 450 cm−1 [31,32]. The broad bandwidth gain usually makes precise control of the frequency separation of the longitudinal modes of the microcavity unnecessary. It is therefore straightforward to imagine that a different mode family can be simultaneously excited through the SRS process.

In this paper, we study the interaction between different mode families via the SRS process in a silica toroidal microcavity. We study the energy transition via SRS between two different mode families, one with a high Q and the other with a low Q. The interaction between transverse modes has already been observed in a crystalline cavity [33], but as yet there is no clear understanding of the condition required for transverse mode coupling, particularly with systems that have a broad SRS gain such as a silica microcavity.

The paper is organized as follows. In section 2, we explain analytically the condition of the mode interaction. We discuss the occurrence of transverse mode coupling via SRS by considering the SRS threshold power as a function of the mode overlapping and Qs. Section 3 describes our experiment, and we report two different results, one with and one without transverse mode coupling. We show the relationship between Q and the mode coupling. Section 4 is a numerical analysis based on the Lugiato-Lefever equation (LLE). We developed a model, where two LLEs are coupled through a Raman scattering term. The obtained results are in good agreement with the experimental result. These results enable us to understand clearly the mechanism of mode interaction through Raman scattering. The paper finishes with a conclusion.

2. Threshold power analysis of SRS

We first consider the analytical threshold power of SRS in a silica cavity. The threshold is described as [17]

Pth=π2n2VeffλPλRgRQeP(1QTP)21QTR,
where λp and λR are the respective wavelengths of the pump and a Raman modes, gR is the nonlinear bulk Raman gain coefficient, and QeP, QTP, and QTR are the external Q factor of the pump mode, the total Q factor of the pump mode, and the total Q factor of the Raman mode, respectively. Veff is the effective mode volume contributing to this SRS conversion process. Veff is usually almost identical to the mode volume of the pump mode since SRS occurs in the same mode family. However, we rigorously calculate the effective mode volume to describe the mode interaction accurately, as follows,
Veff=|EP|2dV|ER|2dV|EP|2|ER|2dV,
where Ep and ER are the amplitudes of the electric fields of the pump and Raman modes, respectively. This includes an overlap of the mode profiles of two modes. When the Raman mode is in the same mode family as the pump mode, Veff is at its minimum value because the mode overlap is perfect.

We consider three mode families, TE00, TE01 and TE10, which are present in a silica toroidal microcavity. The major diameter, the minor diameter and the free spectral range (FSR) are 100 μm, 8 μm and 600 GHz, respectively. Figure 1(a) shows the mode profiles that we used for our analysis. The calculated effective mode areas are Aeff TE00-TE00 = 9.75 μm2, Aeff TE01-TE01 = 12.79 μm2, Aeff TE02-TE02 = 17.75 μm2, Aeff TE00-TE01 = 18.19 μm2, Aeff TE00-TE10 = 21.69 μm2, and Aeff TE01-TE10 = 29.45 μm2. The effective mode areas are given as Veff = 2πr × Aeff, where r is the radius of a cavity. To compare the ratios of different excited transverse mode families via the SRS process, we define the power ratio C as,

C=Pth_samePth_diff=Aeff_sameAeff_diffQT_diffQT_same,
where, Pth-same and Pth-diff, Aeff-same and Aeff-diff, QT-same and QT-diff are the SRS threshold powers, effective mode areas, and total Qs of the Raman mode. The subscript indicates whether the Raman mode is in the same or a different mode family. When C is higher than 1, the SRS threshold power of a Raman mode in a different mode family is lower than that for one in the same mode family, which means that the SRS to the different mode family will be dominant. Figure 1(b) shows the calculated C as a function of QT-diff/QT-same for three different mode combinations. The blue, red and black lines show the cases for TE01(pump)-TE00(different), TE10(pump)-TE00(different), and TE10(pump)-TE01(different). Since the Q of a high-order mode is usually lower than that of a lower-order mode, these three cases are sufficient to understand the influence of the mode interaction in SRS. When QT-diff/QT-same < 1, C is smaller than 1 in all cases because the mode overlapping is not perfect. However, C is larger than 1 in three cases when QT-diff/QT-same > 2. This suggests that the mode interaction will occur easily when the Q factor of one mode is only double that of the pump mode. Generally, the Q factor of the fundamental mode (TE00 mode) is much higher than that of a high-order mode (i.e. TE01) in a silica toroidal microcavity.

 

Fig. 1 (a) Cross-sectional mode profiles of a silica toroid microcavity. These results were obtained using the finite-element method (COMSOL Multiphysics). The diameter of the microcavity is 100 μm and the minor diameter is 8 μm. The results are for the TE00, TE01, and TE10 mode. (b) Calculated threshold coefficient C. The blue, red, and black lines indicate combinations of TE01(pump) -TE00(Raman), TE10(pump) -TE00(Raman), and TE10(pump) -TE01(Raman), respectively.

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3. Experimental results

To confirm the theory, we conducted experiments with a silica toroidal microcavity. Figure 2(a) shows our experimental setup. A tunable laser diode scans the input laser wavelength and an erbium-doped fiber amplifier amplifies the input power up to 1 W. A tapered fiber with a diameter of about 1 μm is used as an evanescent coupler. The output is measured with a power meter and an optical spectrum analyzer. Figure 2(b) shows a microscope image obtained from the top of our cavity. A typical Raman gain in silica is shown in Fig. 2(c).

 

Fig. 2 (a) Schematic image of our experimental setup. TLD, tunable laser diode (Santec TSL-710); EDFA, erbium-doped fiber amplifier (Pritel PMFA-30); VOA, variable optical attenuator (OZ Optics DA-100); FPC, fiber polarization controller (Thorlabs FPC560); OSA, optical spectrum analyzer (Yokogawa AQ6375); PM, power meter (Agilent 81634B). A tapered fiber is used as an evanescent coupler to couple light with a microcavity. (b) An optical microscope image of a fabricated silica toroidal microcavity obtained from the top. A tapered fiber is aligned close to the cavity. The diameter is about 100 μm. (c) Typical Raman gain in silica at 1550 nm calculated with parameters given in [38].

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First, we pumped one of the modes and observed the spectrum as shown in Fig. 3(a). A comb spectrum ranging from 1400 to 2000 nm was observed. Figure 3(c) is a magnified view of Fig. 3(a), which shows that the SRS occurs in the same mode family as the pump mode. Then, we pumped the cavity in a different mode. The result is shown in Fig. 3(b), where we observe a dual-comb-like spectrum. The magnified view in Fig. 3(b) clearly shows that a different mode family is excited via the SRS process. Please note that the transverse mode is not generated through FWM because of the energy and momentum mismatch. The frequency difference between these two mode families is about 180 GHz.

 

Fig. 3 Optical spectra pumped with different modes. We used the same cavity. Spectrum when we pumped the cavity at (a) 1548.96 nm and (b) 1543.08 nm. The pump power was about 1 W after the EDFA. (c) and (d) are magnified views of (a) and (b), respectively. The equidistant vertical gray lines in (c) show that the SRS comb is generated in the same mode family as the pump mode.

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Next, we measured the Qs of the pump and the SRS comb modes. The modes that we measured are indicated in Fig. 3 as H0 and L0 for two different pump modes and L1, L2, H1, and H2 as two different sets of mode families. We performed a conventional transmittance spectrum measurement using a tunable wavelength sweep laser, and obtained Qs of 1.1 × 107 for the 1548.96 nm mode (H0 mode) and 3.1 × 106 for the 1543.08 nm mode (L0 mode), as shown in Figs. 4(a) and (b), respectively. Figures 5(a) and 5(b) are the transmittance spectra for the H1 and H2 modes, which exhibit Qs of 1.6 × 107 and 1.9 × 107, respectively. On the other hand, the Qs for the L1 and L2 modes are 5.2 × 106 and 4.7 × 106, respectively.

 

Fig. 4 (a) Transmittance spectrum for the 1548.96 nm mode we used in Fig. 3(a). (b) Same as (a) but for 1543.08 nm. It should be noted that the resonant is at shorter wavelength for Fig. 3(a) and 3(b) due to the presence of thermo-optic effect, but we are measuring the same mode.

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Fig. 5 Transmittance spectrum of the modes where comb generates. Transmittance spectrum of (a) H1, (b) H2, (c) L1, and (d) L2 modes respectively. the obtained Q are shown in the panel.

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From this result, we confirmed that an energy transfer occurs when we pump in a low-Q mode, but no transverse mode coupling occurs when we pump the cavity in the highest Q mode. Therefore, if we want to suppress the generation of a different longitudinal mode family, we must pump the cavity at the lowest order mode with the highest Q. This transverse mode coupling even allows us to find the lowest order mode. And this experimental result is in good agreement with our theoretical understanding that SRS converts energy from a low-Q mode to a high-Q mode.

Figure 6 confirms our discussion by showing pumping performed at different wavelengths. Figure 6(a) explains the high- and low-Q values of the pump modes. The spectrum obtained when we pumped at H0 and L0 are already shown in Figs. 3(a) and 3(b). When we compare Fig. 6(b) with Fig. 3(a), which is the spectrum when we pump at mode (b), we find that they are almost identical, showing only one longitudinal mode family. This indicates that the SRS process occurs in the same mode family as the pump. Indeed, we confirmed that the anti-Stokes light is also in the same mode family. On the other hand, Fig. 6(c), when we pump at mode (c), has the same trend as Fig. 3(b) that shows a twin comb spectrum. It is noted that in Fig. 6(c) that anti-Stokes SRS light is excited at ~1450 nm and it is also in a different mode family from the pump, but in the same mode family as the SRS mode. Thus, the generation of the high-Q mode family dominates the generation of the low-Q mode in the SRS process. These results indicate that this mode interaction behavior depends solely on the relationship between the Qs of the modes used for the pump and the generated SRS light.

 

Fig. 6 (a) Explanation of the high and low Q modes of the pump. (b) Optical spectrum when we pump at mode b. (c) As (b) but when we pump the cavity at mode c.

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4. Numerical simulation with coupled LLEs

We developed a numerical model to describe the behavior of a nonlinear cavity in which FWM and SRS occur simultaneously. To obtain a full understanding, we modified the LLE [34,35] and took the nonlinear energy transition via SRS into account [36]. The equations are as follows,

tREpr={αp2κp2iδp+iLk2βp(k)k!(it)k}Ep+iL(1fR)(γp|Ep|2+2γp|Es|2)Ep+fR{γpEphR(t')|Ep(tt')|2dt'+ΓpEphR(t')|Es(tt')|2dt'+ΓpEshR(t')Ep(tt')Es*(tt')dt'}+κpSin,
tREsr={αs2κs2iL(βs(1)βp(1))(it)+iLk2βs(k)k!(it)k}Es+iL(1fR)(γs|Es|2+2γs|Ep|2)Es,+fR{γsEshR(t')|Es(tt')|2dt'+ΓsEshR(t')|Ep(tt')|2dt'+ΓsEphR(t')Es(tt')Ep*(tt')dt'}
where, Ep and Es are the electrical fields of the pump and signal (Raman) lights. r, t, tR, L, and Sin are the propagation coordinate (step), (short) time, round-trip time, cavity length, and pump light, respectively. α, κ, δ, β(k), γ, andΓ are the intrinsic cavity loss, coupling loss with the waveguide, detuning of the light frequency from the resonance (detuning from the center frequency), cavity dispersion, effective nonlinear coefficients, and effective nonlinear coefficients considering mode overlapping, respectively. The subscripts denote pump and signal lights. Cavity dispersion is calculated with a finite element method as shown Fig. 7.

 

Fig. 7 Dispersions used for numerical calculation. The cavity is the same as that shown in Fig. 1. The major diameter is 100 μm and the minor diameter is 8 μm. (a) β1 is the inverse of the group velocity. (b) β2 is the second-order dispersion including material and geometrical dispersion.

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Equation (4) shows the behavior of a pump mode that couples with a signal mode via cross phase modulation and Raman scattering. The Raman scattering terms include the response from its own intensity, the coupled light intensity, and the interaction between two modes. It is noted that only the pump mode is excited with an external source. Therefore, the signal mode receives energy only through the Raman scattering as described in Eq. (5).

Mode overlapping is considered with effective mode area Aps described as

Γ=n2ωcAps,
Aps=|Ep(x,y)|2dxdy|Es(x,y)|2dxdy|Ep(x,y)|2|Es(x,y)|2dxdy,
where, n2 is the nonlinear coefficient of a material. When calculating LL equations, we assume that Γp and Γs have the same value for simplification. The Raman scattering terms, namely the Raman contribution fR and the Raman response function hR, are well-known values where fR = 0.18 and hR is described as
hR=τ12+τ22τ1τ22exp(tτ2)sin(tτ1),
Here, τ1 = 12.2 fs and τ2 = 32 fs [32]. Although Raman scattering has gain in the orthogonal modes, the efficiency is small [37] and the conversion to orthogonal modes can be neglected. Thus, we consider Raman modes with the same polarization as a pump mode.

To explain the experimental results, we set a pump mode with a Q of 5.0 × 106. Based on the theoretical understanding, the Q factor ratio, QRaman/Qpump, is used as a parameter. Figure 8(a) shows the calculation results when TE01 and TE00 are set as the pump and Raman modes, respectively. The vertical axis is the integrated light power of the generated SRS mode. Since each calculation time is tens of thousands of round trip times, the cavity is set in a steady state. When the Q factor ratio is 2, the Raman power suddenly increases, which means that the gain overcomes the cavity loss. The value agrees with the theoretical prediction as discussed in section 2 and shown Fig. 8(b). The optical spectrum when the ratio is 3, which corresponds to our experimental values, is shown in Fig. 8(c). The spectrum has the same shape as the experimental result shown in Fig. 3(b). On the other hand, when we pump at a higher mode, we obtain the spectrum shown in Fig. 8(d). The Raman power does not increase, and this is in good agreement with Fig. 3(a).

 

Fig. 8 Simulation results with the model we used in experiments. Input power is set as 1 W. (a) Integrated power of SRS modes versus QTE00/QTE01. The Q of the TE01 mode is defined as 5.0 × 106. As QTE00/QTE01 increases and exceeds > 2, the SRS mode power increases rapidly, because the gain exceeds the threshold of SRS. (b) The theoretical threshold coefficient C mentioned in section 2. (c) Optical spectrum when QTE00/QTE01 = 3. (d) High-Q mode pumping with the same Q ratio as (c). No transverse mode coupling is observed.

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This calculation confirmed that the origin of the dual comb-like spectrum is the result of mode interaction between the pump and Raman modes via Raman scattering. And the ratio of the Q values plays an important role in determining the strength of the mode interaction.

5. Summary

In this study, we focused on the transverse mode interaction via stimulated Raman scattering in a silica toroidal microcavity. We measured a twin comb spectrum experimentally and confirmed that the Q values of the modes are key parameters as regards allowing the generation of combs in different mode families. The dual comb is only present when we pump in a low-Q mode. The experimental results are in good agreement with the theoretical understanding where the critical point for the transverse mode interaction is present at a Q ratio larger than two. We developed a numerical model based on LLE considering the mode interaction via Raman scattering and the numerical results showed the same spectrum as the experimental results. The mode interaction we discussed could be also observed in other silica microcavities such as microspheres and microdisks. Our findings contribute to both the understanding of Kerr-Raman dynamics in a silica microcavity and the generation of dual-comb spectra [39–41].

Funding

This work was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan, KAKEN #15H05429, and the Photon Frontier Network Program. The first author acknowledges to the Grant-in-Aid by the Program for Leading Graduate School for “Science for Development of Super Mature Society” from the Ministry of Education, Culture, Sport, Science, and Technology in Japan.

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References

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  1. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
    [Crossref] [PubMed]
  2. N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
    [Crossref]
  3. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
    [Crossref] [PubMed]
  4. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
    [Crossref] [PubMed]
  5. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013).
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  6. T. Kato, A. C. Jinnai, T. Nagano, T. Kobatake, R. Suzuki, W. Yoshiki, and T. Tanabe, “Hysteresis behavior of Kerr frequency comb generation in a high-quality-factor whispering-gallery-mode microcavity,” Jpn. J. Appl. Phys. 55(7), 072201 (2016).
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  7. A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, “Stabilization of a Kerr frequency comb oscillator,” Opt. Lett. 38(15), 2636–2639 (2013).
    [Crossref] [PubMed]
  8. S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1(1), 10–14 (2014).
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  9. C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
    [Crossref] [PubMed]
  10. M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3(8), 854–860 (2016).
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  15. B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett. 28(17), 1507–1509 (2003).
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  17. T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1219–1228 (2004).
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  18. A. B. Matsko, A. A. Savchenkov, R. J. Letargat, V. S. Ilchenko, and L. Maleki, “On cavity modification of stimulated Raman scattering,” J. Opt. B Quantum Semiclassical Opt. 5(3), 272–278 (2003).
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  22. B.-B. Li, Y.-F. Xiao, M.-Y. Yan, W. R. Clements, and Q. Gong, “Low-threshold Raman laser from an on-chip, high-Q, polymer-coated microcavity,” Opt. Lett. 38(11), 1802–1804 (2013).
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  23. N. Deka, A. J. Maker, and A. M. Armani, “Titanium-enhanced Raman microcavity laser,” Opt. Lett. 39(6), 1354–1357 (2014).
    [Crossref] [PubMed]
  24. H. Choi and A. M. Armani, “High Efficiency Raman Lasers Based on Zr-Doped Silica Hybrid Microcavities,” ACS Photonics 3(12), 2383–2388 (2016).
    [Crossref]
  25. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
    [Crossref] [PubMed]
  26. F. Vanier, M. Rochette, N. Godbout, and Y. A. Peter, “Raman lasing in As2S3 high-Q whispering gallery mode resonators,” Opt. Lett. 38(23), 4966–4969 (2013).
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  27. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics 2(3), 170–174 (2008).
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  28. V. M. N. Passaro and F. De Leonardis, “Investigation of SOI Raman lasers for mid-infrared gas sensing,” Sensors (Basel) 9(10), 7814–7836 (2009).
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  30. G. Lin and Y. K. Chembo, “Phase-locking transition in Raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41(16), 3718–3721 (2016).
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  39. I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016).
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  40. M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
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2016 (7)

T. Kato, A. C. Jinnai, T. Nagano, T. Kobatake, R. Suzuki, W. Yoshiki, and T. Tanabe, “Hysteresis behavior of Kerr frequency comb generation in a high-quality-factor whispering-gallery-mode microcavity,” Jpn. J. Appl. Phys. 55(7), 072201 (2016).
[Crossref]

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3(8), 854–860 (2016).
[Crossref]

H. Choi and A. M. Armani, “High Efficiency Raman Lasers Based on Zr-Doped Silica Hybrid Microcavities,” ACS Photonics 3(12), 2383–2388 (2016).
[Crossref]

G. Lin and Y. K. Chembo, “Phase-locking transition in Raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41(16), 3718–3721 (2016).
[Crossref] [PubMed]

Q.-F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Stokes solitons in optical microcavities,” Nat. Phys. 13(1), 53–57 (2016), doi:.
[Crossref]

I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
[Crossref] [PubMed]

2015 (3)

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92(4), 043818 (2015).
[Crossref]

P. Latawiec, V. Venkataraman, M. J. Burek, B. J. M. Hausmann, I. Bulu, and M. Lončar, “On-chip diamond Raman laser,” Optica 2(11), 924–928 (2015).
[Crossref]

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015).
[Crossref] [PubMed]

2014 (3)

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1(1), 10–14 (2014).
[Crossref]

N. Deka, A. J. Maker, and A. M. Armani, “Titanium-enhanced Raman microcavity laser,” Opt. Lett. 39(6), 1354–1357 (2014).
[Crossref] [PubMed]

2013 (7)

B.-B. Li, Y.-F. Xiao, M.-Y. Yan, W. R. Clements, and Q. Gong, “Low-threshold Raman laser from an on-chip, high-Q, polymer-coated microcavity,” Opt. Lett. 38(11), 1802–1804 (2013).
[Crossref] [PubMed]

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref] [PubMed]

F. Vanier, M. Rochette, N. Godbout, and Y. A. Peter, “Raman lasing in As2S3 high-Q whispering gallery mode resonators,” Opt. Lett. 38(23), 4966–4969 (2013).
[Crossref] [PubMed]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref] [PubMed]

A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, “Stabilization of a Kerr frequency comb oscillator,” Opt. Lett. 38(15), 2636–2639 (2013).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013).
[Crossref]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38(1), 37–39 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (2)

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

2009 (1)

V. M. N. Passaro and F. De Leonardis, “Investigation of SOI Raman lasers for mid-infrared gas sensing,” Sensors (Basel) 9(10), 7814–7836 (2009).
[Crossref] [PubMed]

2008 (3)

I. S. Grudinin and L. Maleki, “Efficient Raman laser based on a CaF2 resonator,” J. Opt. Soc. Am. B 25(4), 594–598 (2008).
[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(9), 093902 (2008).
[Crossref] [PubMed]

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics 2(3), 170–174 (2008).
[Crossref]

2007 (2)

I. S. Grudinin and L. Maleki, “Ultralow-threshold Raman lasing with CaF2 resonators,” Opt. Lett. 32(2), 166–168 (2007).
[Crossref] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref] [PubMed]

2006 (1)

2004 (2)

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29(11), 1224–1226 (2004).
[Crossref] [PubMed]

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1219–1228 (2004).
[Crossref]

2003 (2)

A. B. Matsko, A. A. Savchenkov, R. J. Letargat, V. S. Ilchenko, and L. Maleki, “On cavity modification of stimulated Raman scattering,” J. Opt. B Quantum Semiclassical Opt. 5(3), 272–278 (2003).
[Crossref]

B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett. 28(17), 1507–1509 (2003).
[Crossref] [PubMed]

2002 (3)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

D. Hollenbeck and C. D. Cantrell, “Multiple-vibrational-mode model for fiber-optic Raman gain spectrum and response function,” J. Opt. Soc. Am. B 19(12), 2886–2892 (2002).
[Crossref]

1989 (1)

1987 (1)

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58(21), 2209–2211 (1987).
[Crossref] [PubMed]

Agrawal, G. P.

Aksyuk, V.

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref] [PubMed]

Armani, A. M.

H. Choi and A. M. Armani, “High Efficiency Raman Lasers Based on Zr-Doped Silica Hybrid Microcavities,” ACS Photonics 3(12), 2383–2388 (2016).
[Crossref]

N. Deka, A. J. Maker, and A. M. Armani, “Titanium-enhanced Raman microcavity laser,” Opt. Lett. 39(6), 1354–1357 (2014).
[Crossref] [PubMed]

Armani, D. K.

Asano, T.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref] [PubMed]

Balakireva, I. V.

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015).
[Crossref] [PubMed]

Beha, K.

Brasch, V.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013).
[Crossref]

Bulu, I.

Burek, M. J.

Byrd, J.

Cantrell, C. D.

Chembo, Y. K.

G. Lin and Y. K. Chembo, “Phase-locking transition in Raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41(16), 3718–3721 (2016).
[Crossref] [PubMed]

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92(4), 043818 (2015).
[Crossref]

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015).
[Crossref] [PubMed]

Chen, L.

Chihara, M.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref] [PubMed]

Choi, H.

H. Choi and A. M. Armani, “High Efficiency Raman Lasers Based on Zr-Doped Silica Hybrid Microcavities,” ACS Photonics 3(12), 2383–2388 (2016).
[Crossref]

Clements, W. R.

Coddington, I.

Coen, S.

Cohen, O.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics 2(3), 170–174 (2008).
[Crossref]

Coillet, A.

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015).
[Crossref] [PubMed]

De Leonardis, F.

V. M. N. Passaro and F. De Leonardis, “Investigation of SOI Raman lasers for mid-infrared gas sensing,” Sensors (Basel) 9(10), 7814–7836 (2009).
[Crossref] [PubMed]

Deka, N.

Del’Haye, P.

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1(1), 10–14 (2014).
[Crossref]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref] [PubMed]

Diddams, S. A.

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1(1), 10–14 (2014).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

Eliyahu, D.

Erkintalo, M.

Ferdous, F.

Freude, W.

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015).
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Gaeta, A. L.

Godbout, N.

Gong, Q.

Gordon, J. P.

Gorodetsky, M. L.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013).
[Crossref]

Griffith, A. G.

Grudinin, I. S.

Hänsch, T. W.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

Hartinger, K.

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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
[Crossref] [PubMed]

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1(1), 10–14 (2014).
[Crossref]

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1219–1228 (2004).
[Crossref]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29(11), 1224–1226 (2004).
[Crossref] [PubMed]

B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett. 28(17), 1507–1509 (2003).
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

Vanier, F.

Venkataraman, V.

Wang, C. Y.

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013).
[Crossref]

Wang, J.

Wang, P.-H.

Wegner, D.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Weimann, C.

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114(9), 093902 (2015).
[Crossref] [PubMed]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

Weiner, A. M.

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref] [PubMed]

Xiao, Y.-F.

Xu, S.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics 2(3), 170–174 (2008).
[Crossref]

Yan, M.-Y.

Yang, K. Y.

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
[Crossref] [PubMed]

Q.-F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Stokes solitons in optical microcavities,” Nat. Phys. 13(1), 53–57 (2016), doi:.
[Crossref]

Yang, Q.-F.

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
[Crossref] [PubMed]

Q.-F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Stokes solitons in optical microcavities,” Nat. Phys. 13(1), 53–57 (2016), doi:.
[Crossref]

Yi, X.

Q.-F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Stokes solitons in optical microcavities,” Nat. Phys. 13(1), 53–57 (2016), doi:.
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
[Crossref] [PubMed]

Yoshiki, W.

T. Kato, A. C. Jinnai, T. Nagano, T. Kobatake, R. Suzuki, W. Yoshiki, and T. Tanabe, “Hysteresis behavior of Kerr frequency comb generation in a high-quality-factor whispering-gallery-mode microcavity,” Jpn. J. Appl. Phys. 55(7), 072201 (2016).
[Crossref]

Yu, M.

Yu, N.

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92(4), 043818 (2015).
[Crossref]

Yu, Y.

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

ACS Photonics (1)

H. Choi and A. M. Armani, “High Efficiency Raman Lasers Based on Zr-Doped Silica Hybrid Microcavities,” ACS Photonics 3(12), 2383–2388 (2016).
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IEEE J. Sel. Top. Quantum Electron. (1)

T. J. Kippenberg, S. M. Spillane, B. Min, and K. J. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1219–1228 (2004).
[Crossref]

J. Opt. B Quantum Semiclassical Opt. (1)

A. B. Matsko, A. A. Savchenkov, R. J. Letargat, V. S. Ilchenko, and L. Maleki, “On cavity modification of stimulated Raman scattering,” J. Opt. B Quantum Semiclassical Opt. 5(3), 272–278 (2003).
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J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

T. Kato, A. C. Jinnai, T. Nagano, T. Kobatake, R. Suzuki, W. Yoshiki, and T. Tanabe, “Hysteresis behavior of Kerr frequency comb generation in a high-quality-factor whispering-gallery-mode microcavity,” Jpn. J. Appl. Phys. 55(7), 072201 (2016).
[Crossref]

Nat. Commun. (1)

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref] [PubMed]

Nat. Photonics (4)

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013).
[Crossref]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014).
[Crossref] [PubMed]

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, “A cascaded silicon Raman laser,” Nat. Photonics 2(3), 170–174 (2008).
[Crossref]

Nat. Phys. (1)

Q.-F. Yang, X. Yi, K. Y. Yang, and K. Vahala, “Stokes solitons in optical microcavities,” Nat. Phys. 13(1), 53–57 (2016), doi:.
[Crossref]

Nature (4)

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013).
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (10)

F. Vanier, M. Rochette, N. Godbout, and Y. A. Peter, “Raman lasing in As2S3 high-Q whispering gallery mode resonators,” Opt. Lett. 38(23), 4966–4969 (2013).
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B.-B. Li, Y.-F. Xiao, M.-Y. Yan, W. R. Clements, and Q. Gong, “Low-threshold Raman laser from an on-chip, high-Q, polymer-coated microcavity,” Opt. Lett. 38(11), 1802–1804 (2013).
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N. Deka, A. J. Maker, and A. M. Armani, “Titanium-enhanced Raman microcavity laser,” Opt. Lett. 39(6), 1354–1357 (2014).
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G. Lin and Y. K. Chembo, “Phase-locking transition in Raman combs generated with whispering gallery mode resonators,” Opt. Lett. 41(16), 3718–3721 (2016).
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A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, “Stabilization of a Kerr frequency comb oscillator,” Opt. Lett. 38(15), 2636–2639 (2013).
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B. Min, T. J. Kippenberg, and K. J. Vahala, “Compact, fiber-compatible, cascaded Raman laser,” Opt. Lett. 28(17), 1507–1509 (2003).
[Crossref] [PubMed]

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29(11), 1224–1226 (2004).
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Optica (4)

Phys. Rev. A (1)

Y. K. Chembo, I. S. Grudinin, and N. Yu, “Spatiotemporal dynamics of Kerr-Raman optical frequency combs,” Phys. Rev. A 92(4), 043818 (2015).
[Crossref]

Phys. Rev. Lett. (3)

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(9), 093902 (2008).
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Science (2)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354(6312), 600–603 (2016).
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V. M. N. Passaro and F. De Leonardis, “Investigation of SOI Raman lasers for mid-infrared gas sensing,” Sensors (Basel) 9(10), 7814–7836 (2009).
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G. P. Agrawal, Nonlinear Optical Fiber Optics, (Academic, New York, 2001).

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” https://arxiv.org/abs/1610.01121 (2016).

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Figures (8)

Fig. 1
Fig. 1 (a) Cross-sectional mode profiles of a silica toroid microcavity. These results were obtained using the finite-element method (COMSOL Multiphysics). The diameter of the microcavity is 100 μm and the minor diameter is 8 μm. The results are for the TE00, TE01, and TE10 mode. (b) Calculated threshold coefficient C. The blue, red, and black lines indicate combinations of TE01(pump) -TE00(Raman), TE10(pump) -TE00(Raman), and TE10(pump) -TE01(Raman), respectively.
Fig. 2
Fig. 2 (a) Schematic image of our experimental setup. TLD, tunable laser diode (Santec TSL-710); EDFA, erbium-doped fiber amplifier (Pritel PMFA-30); VOA, variable optical attenuator (OZ Optics DA-100); FPC, fiber polarization controller (Thorlabs FPC560); OSA, optical spectrum analyzer (Yokogawa AQ6375); PM, power meter (Agilent 81634B). A tapered fiber is used as an evanescent coupler to couple light with a microcavity. (b) An optical microscope image of a fabricated silica toroidal microcavity obtained from the top. A tapered fiber is aligned close to the cavity. The diameter is about 100 μm. (c) Typical Raman gain in silica at 1550 nm calculated with parameters given in [38].
Fig. 3
Fig. 3 Optical spectra pumped with different modes. We used the same cavity. Spectrum when we pumped the cavity at (a) 1548.96 nm and (b) 1543.08 nm. The pump power was about 1 W after the EDFA. (c) and (d) are magnified views of (a) and (b), respectively. The equidistant vertical gray lines in (c) show that the SRS comb is generated in the same mode family as the pump mode.
Fig. 4
Fig. 4 (a) Transmittance spectrum for the 1548.96 nm mode we used in Fig. 3(a). (b) Same as (a) but for 1543.08 nm. It should be noted that the resonant is at shorter wavelength for Fig. 3(a) and 3(b) due to the presence of thermo-optic effect, but we are measuring the same mode.
Fig. 5
Fig. 5 Transmittance spectrum of the modes where comb generates. Transmittance spectrum of (a) H1, (b) H2, (c) L1, and (d) L2 modes respectively. the obtained Q are shown in the panel.
Fig. 6
Fig. 6 (a) Explanation of the high and low Q modes of the pump. (b) Optical spectrum when we pump at mode b. (c) As (b) but when we pump the cavity at mode c.
Fig. 7
Fig. 7 Dispersions used for numerical calculation. The cavity is the same as that shown in Fig. 1. The major diameter is 100 μm and the minor diameter is 8 μm. (a) β1 is the inverse of the group velocity. (b) β2 is the second-order dispersion including material and geometrical dispersion.
Fig. 8
Fig. 8 Simulation results with the model we used in experiments. Input power is set as 1 W. (a) Integrated power of SRS modes versus QTE00/QTE01. The Q of the TE01 mode is defined as 5.0 × 106. As QTE00/QTE01 increases and exceeds > 2, the SRS mode power increases rapidly, because the gain exceeds the threshold of SRS. (b) The theoretical threshold coefficient C mentioned in section 2. (c) Optical spectrum when QTE00/QTE01 = 3. (d) High-Q mode pumping with the same Q ratio as (c). No transverse mode coupling is observed.

Equations (8)

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P th = π 2 n 2 V eff λ P λ R g R Q e P ( 1 Q T P ) 2 1 Q T R ,
V eff = | E P | 2 dV | E R | 2 dV | E P | 2 | E R | 2 dV ,
C= P th_same P th_diff = A eff_same A eff_diff Q T_diff Q T_same ,
t R E p r ={ α p 2 κ p 2 i δ p +iL k2 β p (k) k! ( i t ) k } E p +iL(1 f R )( γ p | E p | 2 +2 γ p | E s | 2 ) E p + f R { γ p E p h R ( t ' ) | E p (t t ' ) | 2 d t ' + Γ p E p h R ( t ' ) | E s (t t ' ) | 2 d t ' + Γ p E s h R ( t ' ) E p (t t ' ) E s * (t t ' )d t ' }+ κ p S in ,
t R E s r ={ α s 2 κ s 2 iL( β s (1) β p (1) )( i t )+iL k2 β s (k) k! ( i t ) k } E s +iL(1 f R )( γ s | E s | 2 +2 γ s | E p | 2 ) E s , + f R { γ s E s h R ( t ' ) | E s (t t ' ) | 2 d t ' + Γ s E s h R ( t ' ) | E p (t t ' ) | 2 d t ' + Γ s E p h R ( t ' ) E s (t t ' ) E p * (t t ' )d t ' }
Γ= n 2 ω c A ps ,
A ps = | E p (x,y) | 2 dxdy | E s (x,y) | 2 dxdy | E p (x,y) | 2 | E s (x,y) | 2 dxdy ,
h R = τ 1 2 + τ 2 2 τ 1 τ 2 2 exp( t τ 2 )sin( t τ 1 ),

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