Abstract

A theoretical study of differences in broadband high-index-contrast grating (HCG) reflectors for TM and TE polarizations is presented, covering various grating parameters and properties of HCGs. It is shown that the HCG reflectors for TM polarization (TM HCG reflectors) have much thicker grating thicknesses and smaller grating periods than the TE HCG reflectors. This difference is found to originate from the different boundary conditions met for the electric field of each polarization. Due to this difference, the TM HCG reflectors have much shorter evanescent extension of HCG modes into low-refractive-index media surrounding the HCG. This enables to achieve a very short effective cavity length for VC-SELs, which is essential for ultrahigh speed VCSELs and MEMS-tunable VCSELs. The obtained understandings on polarization dependences will be able to serve as important design guidelines for various HCG-based devices.

© 2015 Optical Society of America

Full Article  |  PDF Article
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2015 (1)

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

2014 (1)

2013 (1)

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

2012 (2)

W. H. Hofmann, P. Moser, and D. Bimberg, “Energy-efficient VCSELs for interconnects,” IEEE Photon. J. 4(2), 652 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

2011 (1)

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

2010 (4)

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. 8(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, 151113 (2010).
[Crossref]

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of sub wavelength high contrast grating reflectors,” Opt. Express 18(16), 16973–16988 (2010).
[Crossref] [PubMed]

D. Zhao, Z. Ma, and W. Zhou, “Field penetrations in photonic crystal Fano reflectors,” Opt. Express 18(13), 14152 (2010).
[Crossref] [PubMed]

2008 (2)

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
[Crossref] [PubMed]

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

2007 (4)

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]

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Vitorovitch, “Compact and polarization controlled 1.55 μ m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror”, Appl. Phys. Lett. 91, 071105 (2007).
[Crossref]

Y. Ding and R. Magnusson, “Band gaps and leaky-wave effects in resonant photonic-crystal waveguides,” Opt. Express 15(2), 680–694 (2007).
[Crossref] [PubMed]

2004 (1)

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]

1996 (1)

1995 (1)

Bakir, B. B.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Benbakir, B.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Vitorovitch, “Compact and polarization controlled 1.55 μ m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror”, Appl. Phys. Lett. 91, 071105 (2007).
[Crossref]

Bimberg, D.

W. H. Hofmann, P. Moser, and D. Bimberg, “Energy-efficient VCSELs for interconnects,” IEEE Photon. J. 4(2), 652 (2012).
[Crossref]

Bordel, D.

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Boutami, S.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Vitorovitch, “Compact and polarization controlled 1.55 μ m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror”, Appl. Phys. Lett. 91, 071105 (2007).
[Crossref]

Caliman, A.

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. 8(9), 1245–1253 (2010).
[Crossref]

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

Chang-Hasnain, C. J.

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

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of sub wavelength high contrast grating reflectors,” Opt. Express 18(16), 16973–16988 (2010).
[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]

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]

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]

Chang-Hasnain, C. N.

H. Sano, J. Kashino, A. Gerke, A. Imamura, F. Koyama, and C. N. Chang-Hasnain, “Transverse mode control of VCSELs with high contrast sub-wavelength grating functioning as angular filter,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2012), CW3N.5.

Chelnokov, A.

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

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Broadband sub wavelength grating mirror and its application to vertical-cavity surface-emitting laser,” in International Conference on Transparent Optical Networks (2008), Tu.C2.5.

Chen, L.

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]

Chung, I.-S.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

I.-S. Chung and J. Mørk, “Silicon-photonics light source realized by III-V/Si-grating-mirror laser,” Appl. Phys. Lett. 97, 151113 (2010).
[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. 8(9), 1245–1253 (2010).
[Crossref]

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

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Broadband sub wavelength grating mirror and its application to vertical-cavity surface-emitting laser,” in International Conference on Transparent Optical Networks (2008), Tu.C2.5.

Czyszanowski, T.

Dems, M.

Ding, Y.

Fedeli, J.-M.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Gaylord, T. K.

Gebski, M.

Gerke, A.

H. Sano, J. Kashino, A. Gerke, A. Imamura, F. Koyama, and C. N. Chang-Hasnain, “Transverse mode control of VCSELs with high contrast sub-wavelength grating functioning as angular filter,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2012), CW3N.5.

Gilet, P.

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

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Broadband sub wavelength grating mirror and its application to vertical-cavity surface-emitting laser,” in International Conference on Transparent Optical Networks (2008), Tu.C2.5.

Grann, E. B.

Harduin, J.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

Hofmann, W. H.

W. H. Hofmann, P. Moser, and D. Bimberg, “Energy-efficient VCSELs for interconnects,” IEEE Photon. J. 4(2), 652 (2012).
[Crossref]

Huang, M. C. Y.

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]

Huang, M. C.Y.

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]

Iakovlev, V.

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. 8(9), 1245–1253 (2010).
[Crossref]

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

Imamura, A.

H. Sano, J. Kashino, A. Gerke, A. Imamura, F. Koyama, and C. N. Chang-Hasnain, “Transverse mode control of VCSELs with high contrast sub-wavelength grating functioning as angular filter,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2012), CW3N.5.

Kapon, E.

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. 8(9), 1245–1253 (2010).
[Crossref]

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

Karagodsky, V.

Kashino, J.

H. Sano, J. Kashino, A. Gerke, A. Imamura, F. Koyama, and C. N. Chang-Hasnain, “Transverse mode control of VCSELs with high contrast sub-wavelength grating functioning as angular filter,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2012), CW3N.5.

Koyama, F.

H. Sano, J. Kashino, A. Gerke, A. Imamura, F. Koyama, and C. N. Chang-Hasnain, “Transverse mode control of VCSELs with high contrast sub-wavelength grating functioning as angular filter,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2012), CW3N.5.

Kuzior, O.

Leclercq, J. L.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Vitorovitch, “Compact and polarization controlled 1.55 μ m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror”, Appl. Phys. Lett. 91, 071105 (2007).
[Crossref]

Letartre, X.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Li, L.

Ma, Z.

Magnusson, R.

Mateus, C. F. R.

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]

Mereuta, A.

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. 8(9), 1245–1253 (2010).
[Crossref]

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

Moharam, M. G.

Mørk, J.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

I.-S. Chung and J. Mørk, “Silicon-photonics light source realized by III-V/Si-grating-mirror laser,” Appl. Phys. Lett. 97, 151113 (2010).
[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. 8(9), 1245–1253 (2010).
[Crossref]

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

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Broadband sub wavelength grating mirror and its application to vertical-cavity surface-emitting laser,” in International Conference on Transparent Optical Networks (2008), Tu.C2.5.

Moser, P.

W. H. Hofmann, P. Moser, and D. Bimberg, “Energy-efficient VCSELs for interconnects,” IEEE Photon. J. 4(2), 652 (2012).
[Crossref]

Olivier, N.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Park, G. C.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

Pommet, D. A.

Regreny, P.

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Rojo-Romeo, P.

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Sano, H.

H. Sano, J. Kashino, A. Gerke, A. Imamura, F. Koyama, and C. N. Chang-Hasnain, “Transverse mode control of VCSELs with high contrast sub-wavelength grating functioning as angular filter,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2012), CW3N.5.

Sciancalepore, C.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Seassal, C.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Sedgwick, F. G.

Semenova, E.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

Shokooh-Saremi, M.

Sirbu, A.

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. 8(9), 1245–1253 (2010).
[Crossref]

Suzuki, Y.

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]

Syrbu, A.

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

Taghizadeh, A.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

Viktorovitch, P.

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

Vitorovitch, P.

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Vitorovitch, “Compact and polarization controlled 1.55 μ m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror”, Appl. Phys. Lett. 91, 071105 (2007).
[Crossref]

Walsiak, M.

Wang, Q. J.

Xie, Y.Y.

Xu, Z.J.

Xue, W.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

Yang, W.

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

Yvind, K.

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

Zhang, D. H.

Zhao, D.

Zhou, W.

Zhou, Y.

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]

Appl. Phys. Lett. (2)

S. Boutami, B. Benbakir, J. L. Leclercq, and P. Vitorovitch, “Compact and polarization controlled 1.55 μ m vertical-cavity surface-emitting laser using single-layer photonic crystal mirror”, Appl. Phys. Lett. 91, 071105 (2007).
[Crossref]

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

IEEE J. Quantum Electron. (1)

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. 8(9), 1245–1253 (2010).
[Crossref]

IEEE Photon. J. (2)

C. Sciancalepore, B. B. Bakir, C. Seassal, X. Letartre, J. Harduin, N. Olivier, J.-M. Fedeli, and P. Viktorovitch, “Thermal, modal, and polarization features of double photonic crystal vertical-cavity surface-emitting lasers,” IEEE Photon. J. 4(2), 399 (2012).
[Crossref]

W. H. Hofmann, P. Moser, and D. Bimberg, “Energy-efficient VCSELs for interconnects,” IEEE Photon. J. 4(2), 652 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (2)

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

J. Light. Technol. (1)

C. Sciancalepore, B. B. Bakir, X. Letartre, J.-M. Fedeli, N. Olivier, D. Bordel, C. Seassal, P. Rojo-Romeo, P. Regreny, and P. Viktorovitch, “Quasi-3D light confinement in double photonic crystal reflectors VCSELs for CMOS-compatible integration,” J. Light. Technol. 29(13), 2015–2024 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

Laser Photonics Rev. (1)

G. C. Park, W. Xue, A. Taghizadeh, E. Semenova, K. Yvind, J. Mørk, and I.-S. Chung, “Hybrid vertical-cavity laser with lateral emission into a silicon waveguide,” Laser Photonics Rev.,  9(3), L11–L15 (2015).
[Crossref]

Nat. Photonics (1)

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]

Opt. Express (6)

Proc. SPIE (1)

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

Other (3)

I.-S. Chung, J. Mørk, P. Gilet, and A. Chelnokov, “Broadband sub wavelength grating mirror and its application to vertical-cavity surface-emitting laser,” in International Conference on Transparent Optical Networks (2008), Tu.C2.5.

I.-S. Chung, V. Iakovlev, A. Mereuta, A. Caliman, A. Syrbu, E. Kapon, and J. Mørk, “Selectively-pumped grating-mirror long wavelength VCSEL,” in International Conference on Indium Phosphide and Related Materials (IEEE, 2009), ThA2.4.

H. Sano, J. Kashino, A. Gerke, A. Imamura, F. Koyama, and C. N. Chang-Hasnain, “Transverse mode control of VCSELs with high contrast sub-wavelength grating functioning as angular filter,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2012), CW3N.5.

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Figures (7)

Fig. 1
Fig. 1 Field profiles around (a, b) TM and (c, d) TE HCG reflectors with 1550-nm-wavelength TM and TE waves being incident from the bottom, respectively. (e) 3D schematic of 1D HCG and axes convention used in this paper. (f) Reflectivity spectra of TM and TE HCGs. In (b, d), the field profiles at x=0 nm (tot) are shown together with their 0th (0h) and 1st harmonic (1h) components. The TM HCG has a grating thickness of 420 nm, a grating period of 642 nm, and a grating bar width of 410 nm while the TE HCG has a thickness of 245 nm, a period of 1084 nm, and a width of 322 nm. The black dashed lines denote grating boundaries. The refractive index of the grating made of Si is 3.47 and both incident and exit media are air.
Fig. 2
Fig. 2 (a)–(c) Histograms of HCG parameters (grating thickness, grating period, and grating bar width). (d)–(f) Histograms of HCG properties (reflection phase, stopband width, and penetration depth).
Fig. 3
Fig. 3 Plots of HCG properties (stopband width, reflection phase, and penetration) as a function of HCG parameters (grating period and grating width) at a specific grating thickness. The thicknesses of TE HCGs and TM HCGs are 245 nm and 420 nm, respectively.
Fig. 4
Fig. 4 Transmittance plots of (a) TM HCGs and (b) TE HCGs as a function of wavelength and grating thickness. The grating period and width are the same as in Fig. 1.
Fig. 5
Fig. 5 Eigenmode electric-field profiles Et,m of (a, b) the TM waveguide array and (c, d) the TE waveguide array, with propagation constant, β values. The waveguide period and width are the same as given in the caption of Fig. 1. The black dashed lines designate waveguide boundaries. (e) Schematic of the waveguide array (infinite version of HCG) used to find eigenmodes of the grating layer. (f) Definitions of input and exit planes.
Fig. 6
Fig. 6 Transmittances of (a) the TM HCG and (b) the TE HCG as a function of wavevector, kx and angular frequency, ω. The green dashed lines designate 1550-nm wavelength, light line, and the 1st Brillouin zone boundary. The red dashed lines designate the guesses for the lowest guided modes below the light line.
Fig. 7
Fig. 7 Transmittance, (1 − R) of the top reflector seen from the cavity layer as a function of the airgap thickness. A TE- and a TM-polarized plane wave at a wavelength of 1550 nm are incident from the cavity layer for the TE HCG and the TM HCG cases, respectively. The same grating parameters as in Fig. 1 are assumed. The refractive index of the cavity layer made of InP is 3.1661.

Equations (6)

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t 0 m = 1 , 2 ( a m + a m ρ ) Λ 1 0 Λ E t , m ( x ) e i β m z ex d x = 0 ,
t 0 ( a 1 + a 1 ρ ) Λ 1 m = 1 , 2 e i β m t gr 0 Λ E t , m ( x ) d x = ( a 1 + a 1 ρ ) Λ 1 m = 1 , 2 e i β m t gr × 1 = ( a 1 + a 1 ρ ) Λ 1 e i β 2 t gr ( e i ( β 1 β 2 ) t gr + 1 ) ,
t gr , 0 = π β 1 β 2 .
( ω c ) 2 = k x 2 + k z 2 ~ k x 2 + ( π t gr ) 2 .
( 2 π 1550 nm ) 2 ~ ( 2 π Λ ) 2 + ( π t gr ) 2 .
k z air = ( 2 π / λ ) 2 ( 2 π m / Λ ) 2 ,

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