Abstract

2-dimensional simulations of high-contrast gratings (HCGs) of finite size are carried out, targeting at their applications in vertical-cavity surface-emitting lasers (VCSELs). Finite HCGs show a very different behavior from infinite grating ones. The reflectivity of a finite HCG strongly depends on the HCG size and the source size. Our simulation results predict finite reflectivity and transmission values, well consistent with reported experimental results. The band of high reflectivity (>99.5%) of finite HCGs is less broad as compared to the infinite case. Losses into a guided mode excited in the HCG plane are identified as being at the root. This guided mode is excited due to the nonzero angular components in the finite source size, and greatly enhances the transmission and the light leakage from the slab. In addition, the simulation results show that the details of the finite HCG can shape the output beam, whilst a Gaussian-like reflected wave is typically achieved. Our simulations can explain the current discrepancies between numerical predictions of reflectivities approaching 100% and working HCG-VCSELs showing finite reflectivities and nearly Gaussian-like output. Consequently, our analysis of finite HCGs is indispensable for HCG-VCSEL design.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (3)

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

P. Debernardi, R. Orta, W. Hofmann, “Rigorous, highly-efficient optical tools for HCG-VCSEL design,” Proc. SPIE 8633, 86330A (2013).
[CrossRef]

P. Debernardi, R. Orta, T. Gründl, M.-C. Amann, “3-D vectorial optical model for high-contrast grating vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 49(2), 137–145 (2013).
[CrossRef]

2012 (5)

P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. B. Bakir, X. Letartre, “Surface addressable photonic crystal membrane resonators: generic enablers for 3D harnessing of light,” Proc. SPIE 8270, 827003 (2012).
[CrossRef]

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

W. Hofmann, D. Bimberg, “VCSEL-based light sources—Scalability challenges for VCSEL-based multi-100-Gb/s Systems,” IEEE Photon. J. 4(5), 1831–1843 (2012).
[CrossRef]

A. Liu, F. Fu, Y. Wang, B. Jiang, W. Zheng, “Polarization-insensitive subwavelength grating reflector based on a semiconductor-insulator-metal structure,” Opt. Express 20(14), 14991–15000 (2012).
[CrossRef] [PubMed]

2011 (2)

A. Larsson, “Advances in VCSELs for communication and sensing,” J. Sel. Top. Quantum Electron. 17(6), 1552–1567 (2011).
[CrossRef]

W. Hofmann, “Evolution of high-speed long-wavelength vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 26(1), 014011 (2011).
[CrossRef]

2010 (4)

D. Bimberg, “Ultrafast VCSELs for datacom,” IEEE Photonics Journal 2(2), 273–275 (2010).
[CrossRef]

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

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

2008 (5)

2007 (2)

M. C. Y. Huang, Y. Zhou, 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, P. Viktorovitch, “Compact and polarization controlled 1.55 μm vertical-cavity surface emitting laser using single-layer photonic crystal mirror,” Appl. Phys. Lett. 91(7), 071105 (2007).
[CrossRef]

2006 (1)

2005 (1)

A. F. Benner, M. Ignatowski, J. A. Kash, D. M. Kuchta, M. B. Ritter, “Exploitation of optical interconnects in future server architectures,” IBM J. Res. Develop. 49(4.5), 755–775 (2005).
[CrossRef]

2004 (1)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

2002 (1)

N. Savage, “Linking with light,” IEEE Spectr. 39(8), 32–36 (2002).
[CrossRef]

2000 (1)

1999 (1)

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[CrossRef]

1997 (1)

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

1989 (1)

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

Amann, M.-C.

P. Debernardi, R. Orta, T. Gründl, M.-C. Amann, “3-D vectorial optical model for high-contrast grating vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 49(2), 137–145 (2013).
[CrossRef]

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

Avrutsky, I. A.

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

Bakir, B. B.

P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. B. Bakir, X. Letartre, “Surface addressable photonic crystal membrane resonators: generic enablers for 3D harnessing of light,” Proc. SPIE 8270, 827003 (2012).
[CrossRef]

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Benbakir, B.

S. Boutami, B. Benbakir, J.-L. Leclercq, P. Viktorovitch, “Compact and polarization controlled 1.55 μm vertical-cavity surface emitting laser using single-layer photonic crystal mirror,” Appl. Phys. Lett. 91(7), 071105 (2007).
[CrossRef]

Benner, A. F.

A. F. Benner, M. Ignatowski, J. A. Kash, D. M. Kuchta, M. B. Ritter, “Exploitation of optical interconnects in future server architectures,” IBM J. Res. Develop. 49(4.5), 755–775 (2005).
[CrossRef]

Benyattou, T.

P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. B. Bakir, X. Letartre, “Surface addressable photonic crystal membrane resonators: generic enablers for 3D harnessing of light,” Proc. SPIE 8270, 827003 (2012).
[CrossRef]

Bimberg, D.

W. Hofmann, D. Bimberg, “VCSEL-based light sources—Scalability challenges for VCSEL-based multi-100-Gb/s Systems,” IEEE Photon. J. 4(5), 1831–1843 (2012).
[CrossRef]

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

D. Bimberg, “Ultrafast VCSELs for datacom,” IEEE Photonics Journal 2(2), 273–275 (2010).
[CrossRef]

Böhm, G.

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

Boutami, S.

S. Boutami, B. Benbakir, J.-L. Leclercq, P. Viktorovitch, “Compact and polarization controlled 1.55 μm vertical-cavity surface emitting laser using single-layer photonic crystal mirror,” Appl. Phys. Lett. 91(7), 071105 (2007).
[CrossRef]

Boye, R. R.

Cambril, E.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[CrossRef]

Chang-Hasnain, C. J.

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

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

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, 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, C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett. 92(17), 171108 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, 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, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Chase, C.

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

Debernardi, P.

P. Debernardi, R. Orta, W. Hofmann, “Rigorous, highly-efficient optical tools for HCG-VCSEL design,” Proc. SPIE 8633, 86330A (2013).
[CrossRef]

P. Debernardi, R. Orta, T. Gründl, M.-C. Amann, “3-D vectorial optical model for high-contrast grating vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 49(2), 137–145 (2013).
[CrossRef]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Fiorentino, M.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Friesem, A. A.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

Fu, F.

Giovannini, H.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[CrossRef]

Grasse, C.

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

Gründl, T.

P. Debernardi, R. Orta, T. Gründl, M.-C. Amann, “3-D vectorial optical model for high-contrast grating vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 49(2), 137–145 (2013).
[CrossRef]

Gustavsson, J. S.

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

Haglund, E.

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

Haglund, E. P.

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

Hofmann, W.

P. Debernardi, R. Orta, W. Hofmann, “Rigorous, highly-efficient optical tools for HCG-VCSEL design,” Proc. SPIE 8633, 86330A (2013).
[CrossRef]

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

W. Hofmann, D. Bimberg, “VCSEL-based light sources—Scalability challenges for VCSEL-based multi-100-Gb/s Systems,” IEEE Photon. J. 4(5), 1831–1843 (2012).
[CrossRef]

W. Hofmann, “Evolution of high-speed long-wavelength vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 26(1), 014011 (2011).
[CrossRef]

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, 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, C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett. 92(17), 171108 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, 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, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Ignatowski, M.

A. F. Benner, M. Ignatowski, J. A. Kash, D. M. Kuchta, M. B. Ritter, “Exploitation of optical interconnects in future server architectures,” IBM J. Res. Develop. 49(4.5), 755–775 (2005).
[CrossRef]

Inoue, S.

J. Kashino, S. Inoue, A. Matsutani, H. Ohtsuki, T. Miyashita, F. Koyama, “Transverse mode control of VCSELs using angular dependent high-contrast grating mirror,” IEEE Photonics Conference (IPC), 244–245 (2013).
[CrossRef]

Jiang, B.

Karagodsky, V.

Kash, J. A.

A. F. Benner, M. Ignatowski, J. A. Kash, D. M. Kuchta, M. B. Ritter, “Exploitation of optical interconnects in future server architectures,” IBM J. Res. Develop. 49(4.5), 755–775 (2005).
[CrossRef]

Kashino, J.

J. Kashino, S. Inoue, A. Matsutani, H. Ohtsuki, T. Miyashita, F. Koyama, “Transverse mode control of VCSELs using angular dependent high-contrast grating mirror,” IEEE Photonics Conference (IPC), 244–245 (2013).
[CrossRef]

Kern, J.

Kostuk, R. K.

Koyama, F.

F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24(12), 4502–4513 (2006).
[CrossRef]

J. Kashino, S. Inoue, A. Matsutani, H. Ohtsuki, T. Miyashita, F. Koyama, “Transverse mode control of VCSELs using angular dependent high-contrast grating mirror,” IEEE Photonics Conference (IPC), 244–245 (2013).
[CrossRef]

Kuchta, D. M.

A. F. Benner, M. Ignatowski, J. A. Kash, D. M. Kuchta, M. B. Ritter, “Exploitation of optical interconnects in future server architectures,” IBM J. Res. Develop. 49(4.5), 755–775 (2005).
[CrossRef]

Larisch, G.

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

Larsson, A.

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

A. Larsson, “Advances in VCSELs for communication and sensing,” J. Sel. Top. Quantum Electron. 17(6), 1552–1567 (2011).
[CrossRef]

Leclercq, J.-L.

S. Boutami, B. Benbakir, J.-L. Leclercq, P. Viktorovitch, “Compact and polarization controlled 1.55 μm vertical-cavity surface emitting laser using single-layer photonic crystal mirror,” Appl. Phys. Lett. 91(7), 071105 (2007).
[CrossRef]

Ledentsov, N. N.

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

Lemarchand, F.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[CrossRef]

Letartre, X.

P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. B. Bakir, X. Letartre, “Surface addressable photonic crystal membrane resonators: generic enablers for 3D harnessing of light,” Proc. SPIE 8270, 827003 (2012).
[CrossRef]

Li, H.

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Liu, A.

Lott, J. A.

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

Magnusson, R.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Matsutani, A.

J. Kashino, S. Inoue, A. Matsutani, H. Ohtsuki, T. Miyashita, F. Koyama, “Transverse mode control of VCSELs using angular dependent high-contrast grating mirror,” IEEE Photonics Conference (IPC), 244–245 (2013).
[CrossRef]

Miyashita, T.

J. Kashino, S. Inoue, A. Matsutani, H. Ohtsuki, T. Miyashita, F. Koyama, “Transverse mode control of VCSELs using angular dependent high-contrast grating mirror,” IEEE Photonics Conference (IPC), 244–245 (2013).
[CrossRef]

Moewe, M.

Moser, P.

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

Müller, M.

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

Mutig, A.

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

Ohtsuki, H.

J. Kashino, S. Inoue, A. Matsutani, H. Ohtsuki, T. Miyashita, F. Koyama, “Transverse mode control of VCSELs using angular dependent high-contrast grating mirror,” IEEE Photonics Conference (IPC), 244–245 (2013).
[CrossRef]

Orta, R.

P. Debernardi, R. Orta, T. Gründl, M.-C. Amann, “3-D vectorial optical model for high-contrast grating vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 49(2), 137–145 (2013).
[CrossRef]

P. Debernardi, R. Orta, W. Hofmann, “Rigorous, highly-efficient optical tools for HCG-VCSEL design,” Proc. SPIE 8633, 86330A (2013).
[CrossRef]

Peng, Z.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

Rao, Y.

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

Ritter, M. B.

A. F. Benner, M. Ignatowski, J. A. Kash, D. M. Kuchta, M. B. Ritter, “Exploitation of optical interconnects in future server architectures,” IBM J. Res. Develop. 49(4.5), 755–775 (2005).
[CrossRef]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

Safaisini, R.

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

Savage, N.

N. Savage, “Linking with light,” IEEE Spectr. 39(8), 32–36 (2002).
[CrossRef]

Sciancalepore, C.

P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. B. Bakir, X. Letartre, “Surface addressable photonic crystal membrane resonators: generic enablers for 3D harnessing of light,” Proc. SPIE 8270, 827003 (2012).
[CrossRef]

Sedgwick, F. G.

Sentenac, A.

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[CrossRef]

Sharon, A.

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

Shokooh-Saremi, M.

Sychugov, V. A.

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

Unrau, W.

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

Viktorovitch, P.

P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. B. Bakir, X. Letartre, “Surface addressable photonic crystal membrane resonators: generic enablers for 3D harnessing of light,” Proc. SPIE 8270, 827003 (2012).
[CrossRef]

S. Boutami, B. Benbakir, J.-L. Leclercq, P. Viktorovitch, “Compact and polarization controlled 1.55 μm vertical-cavity surface emitting laser using single-layer photonic crystal mirror,” Appl. Phys. Lett. 91(7), 071105 (2007).
[CrossRef]

Wang, Y.

Westbergh, P.

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

Wolf, P.

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

Zheng, W.

Zhou, Y.

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, 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, C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett. 92(17), 171108 (2008).
[CrossRef]

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

Appl. Opt. (1)

Appl. Phys. Lett. (3)

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “Single mode high-contrast subwavelength grating vertical cavity surface emitting lasers,” Appl. Phys. Lett. 92(17), 171108 (2008).
[CrossRef]

P. Moser, P. Wolf, A. Mutig, G. Larisch, W. Unrau, W. Hofmann, D. Bimberg, “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavitysurface-emitting lasers,” Appl. Phys. Lett. 100(8), 081103 (2012).
[CrossRef]

S. Boutami, B. Benbakir, J.-L. Leclercq, P. Viktorovitch, “Compact and polarization controlled 1.55 μm vertical-cavity surface emitting laser using single-layer photonic crystal mirror,” Appl. Phys. Lett. 91(7), 071105 (2007).
[CrossRef]

Electron. Lett. (2)

P. Westbergh, E. P. Haglund, E. Haglund, R. Safaisini, J. S. Gustavsson, A. Larsson, “High-speed 850 nm VCSELs operating error free up to 57 Gbit/s,” Electron. Lett. 49(16), 1021–1023 (2013).
[CrossRef]

P. Moser, J. A. Lott, P. Wolf, G. Larisch, H. Li, N. N. Ledentsov, D. Bimberg, “56 fJ dissipated energy per bit of oxide-confined 850 nm VCSELs operating at 25 Gbit/s,” Electron. Lett. 48(20), 1292–1294 (2012).
[CrossRef]

IBM J. Res. Develop. (1)

A. F. Benner, M. Ignatowski, J. A. Kash, D. M. Kuchta, M. B. Ritter, “Exploitation of optical interconnects in future server architectures,” IBM J. Res. Develop. 49(4.5), 755–775 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

P. Debernardi, R. Orta, T. Gründl, M.-C. Amann, “3-D vectorial optical model for high-contrast grating vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 49(2), 137–145 (2013).
[CrossRef]

D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[CrossRef]

IEEE Photon. J. (2)

W. Hofmann, D. Bimberg, “VCSEL-based light sources—Scalability challenges for VCSEL-based multi-100-Gb/s Systems,” IEEE Photon. J. 4(5), 1831–1843 (2012).
[CrossRef]

W. Hofmann, C. Chase, M. Müller, Y. Rao, C. Grasse, G. Böhm, M.-C. Amann, C. J. Chang-Hasnain, “Long-wavelength high-contrast grating vertical-cavity surface-emitting laser,” IEEE Photon. J. 2(3), 415–422 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[CrossRef]

IEEE Photonics Journal (1)

D. Bimberg, “Ultrafast VCSELs for datacom,” IEEE Photonics Journal 2(2), 273–275 (2010).
[CrossRef]

IEEE Spectr. (1)

N. Savage, “Linking with light,” IEEE Spectr. 39(8), 32–36 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

I. A. Avrutsky, V. A. Sychugov, “Reflection of a beam of finite size from a corrugated waveguide,” J. Mod. Opt. 36(11), 1527–1539 (1989).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. Lemarchand, A. Sentenac, E. Cambril, H. Giovannini, “Study of the resonant behavior of waveguide gratings: increasing the angular tolerance of guided-mode filters,” J. Opt. A, Pure Appl. Opt. 1(4), 545–551 (1999).
[CrossRef]

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

A. Larsson, “Advances in VCSELs for communication and sensing,” J. Sel. Top. Quantum Electron. 17(6), 1552–1567 (2011).
[CrossRef]

Nat. Photonics (3)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[CrossRef]

M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, 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 (5)

Proc. SPIE (2)

P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. B. Bakir, X. Letartre, “Surface addressable photonic crystal membrane resonators: generic enablers for 3D harnessing of light,” Proc. SPIE 8270, 827003 (2012).
[CrossRef]

P. Debernardi, R. Orta, W. Hofmann, “Rigorous, highly-efficient optical tools for HCG-VCSEL design,” Proc. SPIE 8633, 86330A (2013).
[CrossRef]

Semicond. Sci. Technol. (1)

W. Hofmann, “Evolution of high-speed long-wavelength vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 26(1), 014011 (2011).
[CrossRef]

Other (2)

R. Michalzik, VCSELs - Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, Springer Series in Optical Sciences, 166 (Springer, 2013).

J. Kashino, S. Inoue, A. Matsutani, H. Ohtsuki, T. Miyashita, F. Koyama, “Transverse mode control of VCSELs using angular dependent high-contrast grating mirror,” IEEE Photonics Conference (IPC), 244–245 (2013).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematics of HCG-VCSEL. (b) Calculation model. Λ denotes the period of the HCG, a is the width of the grating bars, t is the thickness of the slab, and φ is the angle of incident light.. (c) Reflectivity spectrum of an infinite TM-HCG.

Fig. 2
Fig. 2

Reflectivity spectra (a) and transmission spectra (b) for different HCG sizes with a fixed-size (4 μm, 1/e width of the Gaussian source) Gaussian source under normal incidence (φ = 0). The slab without grating structure and the infinite HCG are shown for comparisons. Λ = 0.38 μm, t = 0.235 μm, a = 0.25 μm. The horizontal lines indicate 99.5% reflectivity (a) and 0.5% transmission (b).

Fig. 3
Fig. 3

Reflectivity spectra under off-normal incidence (φ≠0) for infinite HCG. Dip at 0.744 μm.

Fig. 4
Fig. 4

(a) Loss spectra for different HCG sizes. (b) Steady-state field intensity of the Hy component at 0.84954 μm. (c) Steady-state field intensity of the Hy component at 0.7447 μm.

Fig. 5
Fig. 5

Reflectivity spectra at different source sizes for a HCG size of 22*Λ. (1/e width of the Gaussian source). The horizontal line indicates 99.5% reflectivity.

Fig. 6
Fig. 6

(a) Far field profiles of the reflected waves (Hy component) under different HCG sizes at a wavelength of 849.54 nm; (b) Far field profiles of the transmitted waves (Hy component) through the finite HCG at a wavelength of 849.54 nm for different HCG sizes; Λ = 0.38 μm; (c) Far field profiles of the transmitted waves (Hy component) through the finite HCG at a wavelength of 849.54 nm for different source sizes (1/e width of the Gaussian source) with the HCG size of 15.2 μm (40*Λ).

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