A. Taghizadeh, J. Mørk, and I.-S. Chung, “Hybrid grating reflector with high reflectivity and broad bandwidth,” Opt. Express 22(18), 21175–21184 (2014).
[PubMed]

R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014).
[PubMed]

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38(2), 100–102 (2013).
[PubMed]

T.-T. Wu, S.-H. We, T.-C. Lu, and S.-C. Wang, “GaN-based high contrast grating surface-emitting lasers,” Appl. Phys. Lett. 102, 081111 (2013).
[Crossref]

W. Yang and C. J. Chang-Hasnain, “Physics of high contrast gratings: a band diagram insight,” Proc. SPIE 8633, 863303 (2013).

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
[PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express 19(24), 24672–24686 (2011).
[PubMed]

V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry-Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
[PubMed]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

I.-S. Chung and J. Mørk, “Silicon-photonics light source realized by III-V/Si-grating-mirror laser,” Appl. Phys. Lett. 97(15), 151113 (2010).
[Crossref]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[Crossref] [PubMed]

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Subwavelength grating-mirror VCSEL with a thin oxide gap,” IEEE Photonics Technol. Lett. 20(2), 105–107 (2008).
[Crossref]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Nano electro-mechanical optoelectronic tunable VCSEL,” Opt. Express 15(3), 1222–1227 (2007).
[Crossref] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007).
[PubMed]

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized for-malization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
[Crossref] [PubMed]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).

L. Li, “New formulation of the Fourier modal method for crossed surface relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. of Lightwave Technol. 14(5), 914–927 (1996).

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13(5), 1024–1035 (1996).

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13(4), 779–784 (1996).

G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13(5), 1019–1023 (1996).

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).

S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
[PubMed]

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).

W. Yang and C. J. Chang-Hasnain, “Physics of high contrast gratings: a band diagram insight,” Proc. SPIE 8633, 863303 (2013).

V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
[PubMed]

V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry-Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
[PubMed]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[Crossref] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Nano electro-mechanical optoelectronic tunable VCSEL,” Opt. Express 15(3), 1222–1227 (2007).
[Crossref] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry-Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
[PubMed]

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Subwavelength grating-mirror VCSEL with a thin oxide gap,” IEEE Photonics Technol. Lett. 20(2), 105–107 (2008).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Hybrid grating reflector with high reflectivity and broad bandwidth,” Opt. Express 22(18), 21175–21184 (2014).
[PubMed]

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

I.-S. Chung and J. Mørk, “Silicon-photonics light source realized by III-V/Si-grating-mirror laser,” Appl. Phys. Lett. 97(15), 151113 (2010).
[Crossref]

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Subwavelength grating-mirror VCSEL with a thin oxide gap,” IEEE Photonics Technol. Lett. 20(2), 105–107 (2008).
[Crossref]

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Comparison of Different Numerical Methods for Quality Factor Calculation of Nano and Micro Photonic Cavities.” in Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), 8th International Congress on Advanced (IEEE, 2014), pp. 277–279.

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38(2), 100–102 (2013).
[PubMed]

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Subwavelength grating-mirror VCSEL with a thin oxide gap,” IEEE Photonics Technol. Lett. 20(2), 105–107 (2008).
[Crossref]

G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13(5), 1019–1023 (1996).

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13(5), 1019–1023 (1996).

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
[Crossref] [PubMed]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[Crossref] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Nano electro-mechanical optoelectronic tunable VCSEL,” Opt. Express 15(3), 1222–1227 (2007).
[Crossref] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized for-malization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express 19(24), 24672–24686 (2011).
[PubMed]

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
[PubMed]

V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry-Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
[PubMed]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[Crossref] [PubMed]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized for-malization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13(4), 779–784 (1996).

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
[Crossref] [PubMed]

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
[Crossref] [PubMed]

L. Li, “New formulation of the Fourier modal method for crossed surface relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13(5), 1024–1035 (1996).

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express 19(24), 24672–24686 (2011).
[PubMed]

T.-T. Wu, S.-H. We, T.-C. Lu, and S.-C. Wang, “GaN-based high contrast grating surface-emitting lasers,” Appl. Phys. Lett. 102, 081111 (2013).
[Crossref]

R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014).
[PubMed]

M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007).
[PubMed]

S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
[PubMed]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[Crossref] [PubMed]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Hybrid grating reflector with high reflectivity and broad bandwidth,” Opt. Express 22(18), 21175–21184 (2014).
[PubMed]

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

I.-S. Chung and J. Mørk, “Silicon-photonics light source realized by III-V/Si-grating-mirror laser,” Appl. Phys. Lett. 97(15), 151113 (2010).
[Crossref]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Subwavelength grating-mirror VCSEL with a thin oxide gap,” IEEE Photonics Technol. Lett. 20(2), 105–107 (2008).
[Crossref]

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Comparison of Different Numerical Methods for Quality Factor Calculation of Nano and Micro Photonic Cavities.” in Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), 8th International Congress on Advanced (IEEE, 2014), pp. 277–279.

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13(4), 779–784 (1996).

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express 19(24), 24672–24686 (2011).
[PubMed]

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express 19(24), 24672–24686 (2011).
[PubMed]

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
[Crossref] [PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express 19(24), 24672–24686 (2011).
[PubMed]

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38(2), 100–102 (2013).
[PubMed]

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).

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C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
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C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
[Crossref] [PubMed]

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]

M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007).
[PubMed]

E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Hybrid grating reflector with high reflectivity and broad bandwidth,” Opt. Express 22(18), 21175–21184 (2014).
[PubMed]

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Comparison of Different Numerical Methods for Quality Factor Calculation of Nano and Micro Photonic Cavities.” in Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), 8th International Congress on Advanced (IEEE, 2014), pp. 277–279.

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. of Lightwave Technol. 14(5), 914–927 (1996).

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
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K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38(2), 100–102 (2013).
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T.-T. Wu, S.-H. We, T.-C. Lu, and S.-C. Wang, “GaN-based high contrast grating surface-emitting lasers,” Appl. Phys. Lett. 102, 081111 (2013).
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T.-T. Wu, S.-H. We, T.-C. Lu, and S.-C. Wang, “GaN-based high contrast grating surface-emitting lasers,” Appl. Phys. Lett. 102, 081111 (2013).
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N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

T.-T. Wu, S.-H. We, T.-C. Lu, and S.-C. Wang, “GaN-based high contrast grating surface-emitting lasers,” Appl. Phys. Lett. 102, 081111 (2013).
[Crossref]

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]

W. Yang and C. J. Chang-Hasnain, “Physics of high contrast gratings: a band diagram insight,” Proc. SPIE 8633, 863303 (2013).

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38(2), 100–102 (2013).
[PubMed]

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. of Lightwave Technol. 14(5), 914–927 (1996).

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[Crossref] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Nano electro-mechanical optoelectronic tunable VCSEL,” Opt. Express 15(3), 1222–1227 (2007).
[Crossref] [PubMed]

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).

S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
[PubMed]

T.-T. Wu, S.-H. We, T.-C. Lu, and S.-C. Wang, “GaN-based high contrast grating surface-emitting lasers,” Appl. Phys. Lett. 102, 081111 (2013).
[Crossref]

I.-S. Chung and J. Mørk, “Silicon-photonics light source realized by III-V/Si-grating-mirror laser,” Appl. Phys. Lett. 97(15), 151113 (2010).
[Crossref]

N. Gregersen, S. Reitzenstein, C. Kistner, M. Strauss, C. Schneider, S. Hofling, L. Worschech, A. Forchel, T. R. Nielsen, J. Mørk, and J.-M. Gerard, “Numerical and Experimental Study of the Q Factor of High-Q Micropillar Cavities,” IEEE J. Quantum Electron. 46(10), 1470–1483 (2010).

I.-S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mørk, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46(9), 1245–1253 (2010).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photonics Technol. Lett. 24(6), 455–457 (2012).
[Crossref]

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Subwavelength grating-mirror VCSEL with a thin oxide gap,” IEEE Photonics Technol. Lett. 20(2), 105–107 (2008).
[Crossref]

T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. of Lightwave Technol. 14(5), 914–927 (1996).

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13(5), 1024–1035 (1996).

P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13(4), 779–784 (1996).

G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13(5), 1019–1023 (1996).

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E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).

J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized for-malization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005).

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995).

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16(22), 17282–17287 (2008).
[Crossref] [PubMed]

H. T. Hattori, X. Letartre, C. Seassal, P. Rojo-Romeo, J. L. Leclercq, and P. Viktorovitch, “Analysis of hybrid photonic crystal vertical cavity surface emitting lasers,” Opt. Express 11(5), 1799–1808 (2003).
[Crossref] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “Nano electro-mechanical optoelectronic tunable VCSEL,” Opt. Express 15(3), 1222–1227 (2007).
[Crossref] [PubMed]

V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
[PubMed]

C. Peng, Y. Liang, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for photonic-crystal surface-emitting lasers on air-holes with arbitrary sidewalls,” Opt. Express 19(24), 24672–24686 (2011).
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A. Taghizadeh, J. Mørk, and I.-S. Chung, “Hybrid grating reflector with high reflectivity and broad bandwidth,” Opt. Express 22(18), 21175–21184 (2014).
[PubMed]

R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014).
[PubMed]

M. Shokooh-Saremi and R. Magnusson, “Particle swarm optimization and its application to the design of diffraction grating filters,” Opt. Lett. 32(8), 894–896 (2007).
[PubMed]

K. X. Wang, Z. Yu, S. Sandhu, and S. Fan, “Fundamental bounds on decay rates in asymmetric single-mode optical resonators,” Opt. Lett. 38(2), 100–102 (2013).
[PubMed]

V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry-Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36(9), 1704–1706 (2011).
[PubMed]

B. Vial, F. Zolla, A. Nicolet, and M. Commandré, “Quasimodal expansion of electromagnetic fields in open two-dimensional structures,” Phys. Rev. A 89, 023829 (2014).

W. Yang and C. J. Chang-Hasnain, “Physics of high contrast gratings: a band diagram insight,” Proc. SPIE 8633, 863303 (2013).

E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).

A. Taghizadeh, J. Mørk, and I.-S. Chung, “Comparison of Different Numerical Methods for Quality Factor Calculation of Nano and Micro Photonic Cavities.” in Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), 8th International Congress on Advanced (IEEE, 2014), pp. 277–279.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mrk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev., doi: .
[Crossref]