Open Access
Add to BibSonomyAbstract
We investigate a structure consisting of two parallel GaAs thin membranes with an air-slot type photonic crystal (PhC) nanocavity, which is designed to achieve highly efficient optomechanical coupling. The structure shows a large theoretical optomechanical coupling factor of ~990 GHz/nm. We designed, fabricated, and performed optical characterization of a system consisting of a grating coupler, a PhC waveguide, and a PhC nanocavity, which achieves highly efficient vertical emission using the band folding technique. The experimentally obtained overall efficiency is about 0.3% for a microscope objective lens with a moderate numerical aperture of 0.65. This waveguide coupled air-slot PhC nanocavity with efficient vertical light coupling can be useful for on-chip cavity optomechanical systems.
© 2013 Optical Society of America
1. Introduction
The optical manipulation of micro and nanomechanical structures has been intensively investigated due to interests in both the fundamental physics and a variety of potential applications, including quantum information science and highly sensitive sensors. The fact that a particular mechanical mode of a mesoscopic dielectric object can be optically cooled down to its quantum ground state with the assistance of cryogenic technology [1] is impressive. In experimental investigations, cavity-assisted schemes are used to enhance the interaction between a mechanical oscillator and a resonant electric field. Optomechanical experiments using the radiation pressure [2] or the optical gradient force [3] have been performed using a microlever with a micromirror [4, 5], a thin membrane in or molded as an optical cavity [6–8], a disk [9], a micro-toroid [10], a microsphere [11], and a photonic crystal (PhC) [1,12] structure. The optical gradient force, which is the basic operating principle of optical tweezers, can provide a much larger force per photon when strong field gradients are available. Therefore, the optical gradient force can be used for efficient manipulation of optomechanical systems. In cavity optomechanical systems with nanocavities, the strongly localized electric field leads to a large field gradient and a high optomechanical coupling factor gOM is achieved.
A PhC nanocavity is one of the best types of nanocavities for cavity optomechanics owing to its high optical quality factor (Q), modal volume (V), small effective mass, and large gOM. There are many reports of optomechanical coupling using PhC nanocavities using these advantages [1,12–15]. One of the most scientifically interesting goals of this research is cooling down a mesoscopic mechanical oscillator to its quantum ground state. Among the different types of PhC nanocavities, an air-slot type achieves extremely high values of gOM both in numerical simulations and experimentally for Si [16–18] and GaAs [19] based systems. The strong optomechanical coupling in an optomechanical system with an air-slot type PhC nanocavity stems from strong spatial localization of the electric field near the air/dielectric-object boundary. In most cases, optomechanical coupling has been observed by using a fiber-taper probe, which enables highly efficient optical coupling with a nanocavity. In addition to such an optical fiber based system, for on-chip cavity mechanical systems, a waveguide coupled PhC nanocavity with a highly efficient vertical emission is one of the essential tools. There are several possible experimental configurations to couple the input laser beam in order to investigate the performance of a waveguide coupled PhC nanocavity system: in one such configuration the input laser beam is injected from the normal direction, and diffracted into the waveguide by a grating coupler; in another configuration the input laser beam is focused onto a cleaved facet of the waveguide. We adopted the former configuration, because it requires only one microscope objective lens for input and output.
In this paper, we report the design and optical properties of a waveguide coupled GaAs air-slot type PhC nanocavity system with highly efficient vertical emission for on-chip cavity optomechanics. The directivity of the radiation was optimized by using a band folding technique for the first time to improve the coupling efficiency of the emitted cavity photons to an output channel in the normal direction, such as a microscope objective with a moderate numerical aperture (N.A.).
2. Design of the optomechanical system
2.1 Structure of the cavity optomechanical system
Figure 1 shows the schematic of the investigated cavity optomechanical system with an optical waveguide coupling. The system consists of a grating coupler, a PhC line defect waveguide, and an air-slot PhC nanocavity. The entire structure is suspended in vacuum. The grating coupler enables vertical light input by the diffraction of incident light that is normal to the in-plane direction to couple with the waveguide mode of a slab. The diffracted light is guided by the PhC waveguide and coupled to the fundamental mode of the PhC nanocavity. We designed all the optical components to function in the wavelength region of 1.5 μm. The cavity photons are emitted in various directions, which are defined by the radiation pattern of the fundamental cavity mode. The band folding technique [20], which redistributes the radiation direction by superposing the second periodicity to the PhC, was adapted to improve the coupling efficiency in the vertical direction. The target mechanical mode is the fundamental in-plane vibration mode of the two parallel membranes, which is described in the next subsection. The design of the mechanical structure is based on our previous report [19].
Fig. 1 Schematic of the investigated waveguide coupled air-slot PhC nanocavity system with a vertical input/output light coupling configuration. The system consists of a grating coupler, a PhC line defect waveguide, and a PhC nanocavity with a band folding structure.
2.2 Designs of the grating coupler, PhC waveguide, and PhC nanocavity
Figure 2 shows the optical and mechanical properties of each part of the investigated system. The investigated microstructure consists of two parallel GaAs membranes separated by an air-slot with a width s = 80 nm. These thin semiconductor membranes function as mechanical oscillators. The air-slot, which is used as the main part of a PhC nanocavity, is located at the center of a line defect of a triangular lattice of air holes. The nano-mechanical structure possesses a mode-gap type PhC cavity with a high Q [21] to enhance the optomechanical coupling by a long cavity photon lifetime. The air holes are shifted slightly outward, as indicated by arrows in the inset in Fig. 2(a), to create a mode-gap PhC nanocavity. The amounts of shift are 3δ, 2δ, and δ for the air holes as indicated by the red, blue, and green arrows, respectively, where δ = 0.0095a (a denotes the period of the PhC lattice). This cavity design was proposed by Yamamoto et al. for the study of cavity quantum electrodynamics in free space using Si-based structures [22]. We note that air-slot type cavities are also useful for optomechanics, as reported in references [16–19]. Figure 2(a) shows the electric field component in the y direction (Ey) of the cavity mode, which is found at 1.52 μm, calculated by finite-difference time-domain (FDTD) method for the structure with a = 490 nm and the radius of the air hole r = 140 nm. The thickness, length, and width of the membrane are 204 nm, 7.84 μm (16a), and 2.08 μm (), respectively. The lower right inset shows that the electric field in the air-slot is much higher than that in the semiconductor membrane. The calculated value of the cavity Q is ~4.8 × 106 and V is ~0.015λ3, where λ is the wavelength of the cavity mode. The stronger optomechanical coupling stems from the enhancement of the electric field in the narrow air-slot and it clearly indicates the advantage of an air-slot cavity for cavity optomechanics.
Fig. 2 (a) Simulated distribution of the cavity electric field in the air-slot PhC nanocavity structure. The long-term (Q = 4.8 × 106) and localized (V = 0.015λ3) electric field confinement around the air/semiconductor boundary results in extremely strong optomechanical interaction. (b) Color plot of the absolute displacement in the y direction for the investigated fundamental mechanical oscillation mode (95 MHz). (c, d) Simulated distributions of Ey around the grating coupler and the PhC line defect waveguide, respectively.
The mechanical property of the structure was studied by the finite-element-method (FEM). In the numerical simulations, the beams were clamped at both ends using fixed boundary conditions. The mechanical motions of the beam were categorized as in-plane (y direction) and out-of-plane (z direction) motions. In this study, the in-plane fundamental mode is investigated. Figure 2(b) shows a color plot of the absolute displacement in the y-direction of the mode. The deformation of the structure is exaggerated for clear visibility. The mechanical frequency of the mode is calculated to be Ωm/2π = 95 MHz.
Figure 2(c) shows the simulated distribution of Ey around the grating coupler with a period of 854 nm. This period was obtained by calculating the effective refractive index nw of the GaAs slab by using a theory for guided light in void nanostructures reported in reference [23].The value of nw becomes lower than that of GaAs = 3.374 at 1.55 μm, because some portion of the guided mode leaks in the vacuum, where the refractive index is 1. The obtained value of nw was 2.631, and the period was determined. The wavelength of the input light was 1.55 μm, and the spot size was 1.5 μm, which is defined as the beam waist of the Gaussian beam focused by a lens with an N.A. = 0.65. The obtained diffraction efficiency, which is defined as the ratio of the optical power at the entrance of the PhC waveguide to that of the input power, was ~13%. The diffraction efficiency spectrum, which will be shown in Fig. 6(a), has many sharp peaks with a half width at half maximum about 8-20 nm.
Figure 2(d) shows the simulated distribution of Ey for the waveguide mode. We performed a simulation to design a PhC waveguide with high transmittance at around 1.55 μm. The width of the line defect waveguide Wc was set as the parameter, and we found that Wc = 1.2W0 opens the transmission window between 1.45 to 1.62 μm. Here, W0 is the width of the original line defect waveguide.
2.3 Band-folding for efficient vertical emission
In general, a high-Q PhC nanocavity has weak emission in the vertical direction and the cavity Q is improved by tailoring the radiation pattern by the fine tuning of the cavity structure [24]. On the other hand, it is also important to increase the coupling efficiency in the normal direction to obtain better coupling efficiency to the output channel in the vertical direction. The band folding technique is the powerful tool used for this purpose [20]. Band folding is the superimposition of a double periodicity on the original structure, which leads to the redistribution of radiation components from the first Brillouin zone boundary to the zero point in the reciprocal space. This redistribution of radiation drastically improves the coupling efficiency of nanocavities and is especially useful for nanolasers [25].
In our structure, the radius of the air holes within the region marked by a broken line in Fig. 3(a) was reduced to introduce the band folding effect. The alternate modulation of the air-hole radius introduces the double periodicity. We investigated the amount of collected power by a microscope objective lens with an N.A. = 0.65 for various reductions of the radius Δr, the results of which are summarized in Table 1. The collected power is normalized by the value for the cavity without reduction (Δr = 0). The data in the table shows that the coupled power is increased by 32 times using the band folding technique for the case of Δr = −35 nm. The value of Δr = −35 nm was adopted for the fabrication of the structures. We also investigated the improvement in the power and efficiency of coupling to the microscope objective lens with various N.As. Here, the definition of the coupling efficiency is the ratio of the coupled power with the microscope objective to the integrated power of light, which leaks out of the semiconductor wafer. Therefore, the maximum coupling efficiency is limited to 50% due to the symmetric structure in the vertical direction. These results are plotted in Figs. 3(b) and 3(c) for the cases of Δr = 0 nm (black squares) and Δr = −35 nm (red circles). These clearly show that band folding is an effective technique to improve the output coupling for all the values of N.A. The coupling efficiency for the case for which N.A. = 0.65 is doubled and the coupled power is increased by 32 times. Here, the coupled power is defined as the integrated power of the emitted light from the PhC nanocavity to the microscope objective lens. The total amount of leaky components is increased by the radius modulation. In the case of Δr = −35 nm, the theoretical cavity Q is decreased to only 2,000. Therefore, it is important to optimize the value of Δr so that the theoretical cavity Q is larger than the experimental cavity Q, which is determined by fabrication error. Figures 3(d) and 3(e) are color plots of the calculated far-field patterns for the cavities with the radius-modulations of Δr = 0 nm and Δr = −35 nm, respectively, and a comparison of these two figures clearly shows the enhancement of the coupling efficiency in the vertical direction. The white circle marks the points at which N.A. = 0.65, and the components within the circle couple to the lens. Figure 3(e) shows that the components in the higher N.A. (larger circle) regime in Fig. 3(d) are folded into the smaller N.A. (smaller circle) regime.
Fig. 3 (a) Calculated distribution of Ey and the radius-modulated air holes for band folding. (b, c) Comparison of coupled power and coupling efficiency as a function of N.A. calculated for the cases of Δr = 0 (black squares) and −35 nm (red circles). (d, e) Color plots of the calculated far-field patterns for the cavities with the radius-modulations of Δr = 0 and −35 nm, respectively. The white circle marks points at which N.A. = 0.65.
Table 1. Comparison of the collected optical power by an objective having different values of Δr. The values are normalized by the value for the cavity without the radius modulation (Δr = 0).
3. Sample fabrication
3.1 Crystal growth and structure
The semiconductor wafer was grown by molecular beam epitaxy on an undoped (100) oriented GaAs substrate. First, a 200 nm-thick GaAs buffer layer was grown on the substrate at 595°C. Then, a 1 μm thick Al0.7Ga0.3As sacrificial layer was grown at 595°C. Finally, a 200 nm thick GaAs slab layer was grown at 595°C.
3.2 Fabrication of PhC nanostructures
The investigated GaAs microstructures were fabricated by electron beam lithography, inductively coupled plasma reactive ion etching, and a wet etching process using a hydrofluoric acid solution, which formed 200 nm thick air-bridge structures by removing the sacrificial layer. A detailed description of this fabrication method can be found in our previous paper [26]. We fabricated a sample with a period of the lattice a between 500 nm and 520 nm and radius of the air hole r ~0.3a. Triangular lattice air holes were patterned using an electron beam lithography system. An inductively coupled plasma reactive ion etching process using a Cl2/Ar mixture was used to etch air holes into the GaAs layer. Finally, the AlGaAs sacrificial layer was removed using a hydrofluoric acid solution to form free-standing 200 nm thick air bridge structures. These series of processes were used to fabricate a grating coupler and two parallel semiconductor membranes with a PhC waveguide and a PhC nanocavity, as shown in Fig. 4. All the structures are air-suspended.
Fig. 4 (a) Scanning electron micrographs of the entire structure, (b) the PhC nanocavity with a band folding structure, and (c) the PhC line defect waveguide with a width of 1.2W0.
The PhC nanocavity was fabricated based on the band folding design with a reduced radius (Δr = −35 nm) of air holes within the region indicated by a broken line in Fig. 4(b). The value of Δr measured by a scanning electron microscope (SEM) was about 35–40 nm, which is almost equal to the designed value and is only slightly larger. The PhC waveguide is a line defect waveguide with the width Wc = 1.2W0 [Fig. 4(c)]. The outer grating structures are separated to three parts for mechanical support. However, the mechanical supporting structures have little effect on the diffraction efficiency.
4. Experimental results and discussions
The optical measurements were performed at room temperature using a wavelength tunable continuous-wave semiconductor laser with a spectrum line width of 200 kHz and a wavelength resolution of 2 pm. The beam was focused to an about 1.5 μm spot in diameter on the surface of the sample using a 40 × microscope objective lens (N.A. = 0.65). The laser spot was positioned by observing the structure by a phosphor coated CCD camera for the infrared region [Fig. 5(a)]. Then, the position of the laser spot was optimized by monitoring the signal intensity. The reflectance spectra were measured by positioning the focused laser spot directly on the cavity, and the wavelength of the laser was swept. Figure 5(b) shows the measured reflectance spectra for the PhC nanocavities with a = 500, 510, and 520 nm. The reflectance is decreased at the resonant wavelength due to coupling of the input laser beam to the cavity mode. The observed spectral line shapes shown in Fig. 5(b) are asymmetric. The interference between the resonant scattering by the cavity mode and the regular reflection gave rise to the asymmetric line-shape; this phenomenon is known as Fano resonance. Figure 5(c) shows the measured wavelength of the cavity resonance for the PhC nanocavities with a = 500, 510, and 520 nm. The resonances were observed in the range between 1.5 and 1.55 μm. We calculated the resonant wavelengths of the PhC with a = 480 to 520 nm and r = 0.3a for the case of the band folding design with a reduced radius (Δr = −35 nm) of the air holes. The experimental data (red circles) and simulated data (blue squares) show good agreement.
Fig. 5 (a) Optical image of the investigated structure taken by a phosphor coated CCD camera. (b) Reflectance spectra of the PhC nanocavities for different lattice constants of 500, 510, and 520 nm. (c) Measured (red circles) and simulated (blue squares) peak wavelengths of the PhC nanocavities. The dashed line indicates the linear approximation of the simulated data.
Figure 6(a) shows the calculated spectra for the diffraction efficiency of the grating coupler (upper), transmission of the PhC waveguide (middle), and output from the PhC nanocavity with radius-modulated air holes for band folding (bottom). The main structural parameters were set at a = 520 nm, r = 0.3a, and Δr = −35 nm. The diffraction efficiency shows the periodic peaky spectrum. This relatively narrow peak leads to narrow tolerance to fabrication errors in the experiment. Therefore, different fabrication errors for each grating coupler may lead to a difference in the overall efficiency of the entire system. On the other hand, the PhC line defect waveguide shows a very flat and wide transmission window. The cavity resonance was found to be in the range of 1.55–1.56 μm with those structural parameters. The wavelength of the cavity resonance was measured by reflectivity measurement, and it was observed at 1.54 μm as shown in Fig. 6(b), which is very close to the simulated result. The Fano resonance is clearly observed in the reflection spectrum.
Fig. 6 (a) Simulated spectra for the diffraction efficiency of the grating coupler to the PhC waveguide (upper), the transmission of the PhC line defect waveguide (middle), and the output intensity from the PhC nanocavity with the optimized band folding (bottom). (b) Reflection spectrum of the PhC nanocavity. (c) Spectrum of the output light from the PhC nanocavity with an input from the grating coupler.
The input laser spot was positioned at the input position of the grating coupler shown in Fig. 5(a), while the detection spot was fixed at the nanocavity, and the output spectrum from the nanocavity was measured [Fig. 6(c)]. The cavity mode was observed at the same wavelength as observed in the reflectivity measurement. These results indicate that the input laser beam is diffracted by the grating, guided and coupled to the PhC nanocavity, and coupled to the detection system by cavity photon emission. The measured value of the cavity Q is about 1,600, which is mainly limited by the theoretical cavity Q of about 2,000 and the fabrication errors. The low theoretical Q can be improved by optimizing the parameters for band folding, which will be reported elsewhere. The spectrum shows a high noise floor, which mostly results from the scattering from the grating coupler. We measured the reflection spectrum of the grating coupler to investigate the source of undesired noise and compared it with the spectrum of the noise floor. These two spectra showed complementary wavelength dependence. Therefore, some of the diffracted and scattered components were considered to couple with the lens to form the noise floor. The diffracted electric field distribution in Fig. 2(c) shows that some components are diffracted obliquely upward. The calculated results support this speculation. Figure 2(c) also shows some amount of diffraction to the direction slightly above the horizontal, and moreover, such a high-angle beam rarely couples to the objective lens. Therefore, the signal to noise ratio can be improved by using a longer waveguide or by in-plane light injection, which is the case for on-chip configurations.
We measured the overall efficiency η of this system, which is defined by the ratio of the output power of the cavity mode coupling to the microscope objective lens with an N.A. = 0.65 to the input power measured above the grating coupler. The wavelength of the laser was set at the value that led to cavity mode resonance and injected from the grating coupler. The net output power from the nanocavity was measured after the microscope objective lens by subtracting the noise power, which is estimated by the output intensity at off resonance. We found that the value of η was about 0.3%. This value is larger than the calculated efficiency by more than one order of magnitude. This can be possibly attributed to the diffraction efficiency spectrum with many sharp peaks, scattering of the cavity photon between the cavity and waveguide, and scattering of the cavity photon by imperfections in the structure due to fabrication error, among other such factors. The results obtained indicate that the proposed waveguide coupled air-slot PhC nanocavity system can be used as a monolithic on-chip optomechanical system with a large optomechanical coupling factor.
5. Summary
We demonstrated a structure consisting of two parallel membranes with a GaAs waveguide coupled air-slot PhC nanocavity for efficient cavity optomechanical systems. The newly designed air-slot PhC nanocavity with band folding doubled the coupling efficiency to a microscope objective with a moderate N.A. of 0.65. The measured overall coupling efficiency of the system is ~0.3%. The results indicate that the proposed waveguide coupled air-slot PhC nanocavity system can be used as a monolithic on-chip cavity optomechanical system with a large optomechanical coupling factor for vertical input/output configuration.
Acknowledgments
This work was supported by the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, by JSPS through its Funding Program for World-Leading Innovation R&D on Science and Technology, by JSPS through the Core-to-Core Program as a matching fund to the EU-FP7 Project EUJO-LIMMS, by the Nippon Glass Foundation for Materials Science and Engineering, by the Mitsubishi Foundation, and by a KAKENHI (25709090).
References and links
1. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011). [CrossRef] [PubMed]
2. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008). [CrossRef] [PubMed]
3. D. Van Thourhout and J. Roels, “Optomechanical Device actuation through the optical gradient force,” Nat. Photonics 4(4), 211–217 (2010). [CrossRef]
4. D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micro-mechanical resonator,” Nature 444(7115), 75–78 (2006). [CrossRef] [PubMed]
5. C. H. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432(7020), 1002–1005 (2004). [CrossRef] [PubMed]
6. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452(7183), 72–75 (2008). [CrossRef] [PubMed]
7. O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, “Radiation-pressure cooling and optomechanical instability of a micromirror,” Nature 444(7115), 71–74 (2006). [CrossRef] [PubMed]
8. K. Usami, A. Naesby, T. Bagci, B. Melholt Nielsen, J. Liu, S. Stobbe, P. Lodahl, and E. S. Polzik, “Optical cavity cooling of mechanical modes of a semiconductor nanomembrane,” Nat. Phys. 8(2), 168–172 (2012). [CrossRef]
9. Q. Lin, J. Rosenberg, X. Jiang, K. J. Vahala, and O. Painter, “Mechanical oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103(10), 103601 (2009). [CrossRef] [PubMed]
10. G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Riviere, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, “Near-field cavity optomechanics with nanomechanical oscillators,” Nat. Phys. 5(12), 909–914 (2009). [CrossRef]
11. Y.-S. Park and H. Wang, “Resolved-sideband and cryogenic cooling of an optomechanical resonator,” Nat. Phys. 5(7), 489–493 (2009). [CrossRef]
12. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459(7246), 550–555 (2009). [CrossRef] [PubMed]
13. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009). [CrossRef] [PubMed]
14. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity,” Opt. Express 17(5), 3802–3817 (2009). [CrossRef] [PubMed]
15. E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106(20), 203902 (2011). [CrossRef] [PubMed]
16. Y. Li, J. Zheng, J. Gao, J. Shu, M. S. Aras, and C. W. Wong, “Design of dispersive optomechanical coupling and cooling in ultrahigh-Q/V slot-type photonic crystal cavities,” Opt. Express 18(23), 23844–23856 (2010). [CrossRef] [PubMed]
17. J. Gao, J. F. McMillan, M.-C. Wu, J. Zheng, S. Assefa, and C. W. Wong, “Demonstration of an air-slot modegap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010). [CrossRef]
18. A. H. Safavi-Naeini, T. P. Alegre, M. Winger, and O. Painter, “Optomechanics in an ultrahigh-Q two-dimensional photonic crystal cavity,” Appl. Phys. Lett. 97(18), 181106 (2010). [CrossRef]
19. M. Nomura, “GaAs-based air-slot photonic crystal nanocavity for optomechanical oscillators,” Opt. Express 20(5), 5204–5212 (2012). [CrossRef] [PubMed]
20. N.-V.-Q. Tran, S. Combrie, and A. De Rossi, “Directive emission from high-Q photonic crystal cavities through band folding,” Phys. Rev. B 79(4), 041101(R) (2009). [CrossRef]
21. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultra-high-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006). [CrossRef]
22. T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18), 13809–13817 (2008). [CrossRef] [PubMed]
23. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]
24. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]
25. M. Narimatsu, S. Kita, H. Abe, and T. Baba, “Enhancement of vertical emission in photonic crystal nanolasers,” Appl. Phys. Lett. 100(12), 121117 (2012). [CrossRef]
26. M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single quantum dot-nanocavity system,” Nat. Phys. 6(4), 279–283 (2010). [CrossRef]
