Abstract

We numerically investigate the properties of a hybrid grating structure acting as a resonator with ultrahigh quality factor. This reveals that the physical mechanism responsible for the resonance is quite different from the conventional guided mode resonance (GMR). The hybrid grating consists of a subwavelength grating layer and an un-patterned high-refractive-index cap layer, being surrounded by low index materials. Since the cap layer may include a gain region, an ultracompact laser can be realized based on the hybrid grating resonator, featuring many advantages over high-contrast-grating resonator lasers. The effect of fabrication errors and finite size of the structure is investigated to understand the feasibility of fabricating the proposed resonator.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Hybrid grating reflector with high reflectivity and broad bandwidth

Alireza Taghizadeh, Gyeong Cheol Park, Jesper Mørk, and Il-Sug Chung
Opt. Express 22(18) 21175-21184 (2014)

Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating

Ye Zhou, Michael Moewe, Johannes Kern, Michael C. Y. Huang, and Connie J. Chang-Hasnain
Opt. Express 16(22) 17282-17287 (2008)

High-contrast gratings for integrated optoelectronics

Connie J. Chang-Hasnain and Weijian Yang
Adv. Opt. Photon. 4(3) 379-440 (2012)

References

  • View by:
  • |
  • |
  • |

  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]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. W. Yang and C. J. Chang-Hasnain, “Physics of high contrast gratings: a band diagram insight,” Proc. SPIE 8633, 863303 (2013).
  13. 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]
  14. R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014).
    [PubMed]
  15. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
    [PubMed]
  16. 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).
  17. T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. of Lightwave Technol. 14(5), 914–927 (1996).
  18. 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).
  19. 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).
  20. 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).
  21. L. Li, “New formulation of the Fourier modal method for crossed surface relief gratings,” J. Opt. Soc. Am. A 14(10), 2758–2767 (1997).
  22. 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).
  23. 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).
  24. V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
    [PubMed]
  25. 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).
  26. 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.
  27. 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).
  28. 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]
  29. 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]
  30. 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]
  31. E. Istrate and E. H. Sargent, “Photonic crystal heterostructures and interfaces,” Rev. Mod. Phys. 78(2), 455–481 (2006).
  32. 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]

2014 (3)

2013 (3)

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).

2012 (2)

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]

2011 (2)

2010 (3)

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]

2008 (2)

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]

2007 (3)

2006 (1)

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

2005 (1)

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]

2003 (1)

2001 (1)

1997 (1)

1996 (4)

1995 (1)

1993 (1)

Bakir, B. B.

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]

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. 46(9), 1245–1253 (2010).
[Crossref]

Cao, Q.

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 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, “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]

Chase, C.

Chelnokov, A.

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]

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.

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.

Commandré, M.

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).

Fan, S.

Fedeli, J.

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]

Forchel, A.

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).

Gaylord, T. K.

Gerard, J.-M.

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).

Gilet, P.

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]

Granet, G.

Grann, E. B.

Gregersen, N.

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).

Guizal, B.

Harduin, J.

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]

Hattori, H. T.

Hofling, S.

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).

Huang, M. C. Y.

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, “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]

Hugonin, J. P.

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. 46(9), 1245–1253 (2010).
[Crossref]

Istrate, E.

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

Iwahashi, S.

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. 46(9), 1245–1253 (2010).
[Crossref]

Karagodsky, V.

Kern, J.

Kistner, C.

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).

Lalanne, P.

Leclercq, J. L.

Letartre, X.

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]

Li, L.

Liang, Y.

Lu, T.-C.

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]

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. 46(9), 1245–1253 (2010).
[Crossref]

Moewe, M.

Moharam, M. G.

Mørk, J.

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]

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 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, 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, 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.

Morris, G. M.

Mrk, J.

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]

Nicolet, A.

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).

Nielsen, T. R.

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).

Noda, S.

Olivier, N.

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]

Park, G. C.

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]

Peng, C.

Pommet, D. A.

Reitzenstein, S.

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).

Rojo-Romeo, P.

Sakai, K.

Sandhu, S.

Sargent, E. H.

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

Schneider, C.

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).

Sciancalepore, C.

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]

Seassal, C.

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]

Semenova, E.

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]

Shokooh-Saremi, M.

Silberstein, E.

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. 46(9), 1245–1253 (2010).
[Crossref]

Strauss, M.

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).

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]

Taghizadeh, A.

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.

Tamir, T.

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

Vial, B.

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).

Viktorovitch, P.

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]

Wang, K. X.

Wang, S. S.

Wang, S.-C.

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]

We, S.-H.

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]

Worschech, L.

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).

Wu, T.-T.

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]

Xue, W.

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]

Yang, W.

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

Yu, Z.

Yvind, K.

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]

Zhang, S.

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

Zhou, Y.

Zolla, F.

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).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

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]

IEEE J. Quantum Electron. (2)

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]

IEEE Photon. Technol. Lett. (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]

IEEE Photonics Technol. Lett. (2)

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]

J. of Lightwave Technol. (1)

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

J. Opt. Soc. Am. A (7)

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)

Opt. Lett. (4)

Phys. Rev. A (1)

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).

Proc. SPIE (1)

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

Rev. Mod. Phys. (1)

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

Other (2)

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]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 (a) Schematic view of the investigated HG structure with parameter definitions. Refractive indices: nh=3.48, nl=1, ni=1, no=1.47, and nc=3.166. (b) Bloch modes in each layer. (c) Reflectivity matrices defined at a specific plane within the structure.
Fig. 2
Fig. 2 Contour maps of the reflectivity (color scale) versus normalized wavelength and grating thickness (a,b) or normalized wavelength and cap thickness (c,d) at f =50% for TM polarized light. (a) tc/Λ=0.4, (b) tc/Λ=0.6, (c) tg/Λ=0.6, (d) tg/Λ=1.35.
Fig. 3
Fig. 3 (a) Resonance wavelength (dashed lines) and Q-factor (solid lines) as a function of grating thickness around a candidate point for resonance at two values of the duty cycle, f=60 % (blue lines) and f=62 % (red lines). The Q-factor depends sensitively on the structure parameters. (b) Reflectivity spectrum for TM-polarized light of an HG structure with ultrahigh Q-factor found by PSO with Λ=853.5 nm, tg=742.3 nm, f =61.6 %, tc=830.5 nm.
Fig. 4
Fig. 4 (a) Normalized magnetic field profile |Hy| for the HG structure of Fig. 1(a), excited by an incident plane wave with the same wavelength as the resonance wavelength found in Fig. 3(b). (b) Amplitudes of the magnetic modal fields in dB scale for 0-th, 1-st and 2-nd spatial harmonic inside all the layers at the resonance wavelength. TM polarized light is incident from the left.
Fig. 5
Fig. 5 Signal flow graph for an HG structure at the resonance wavelength of Fig. 3(b). The black dots represent the propagating modes in the different layer; the red arrows show the interactions between modes at each interface; the circular red arrows bring self-couplings; the green arrows illustrate the propagations in each layer. The numbers given besides the dots are the mode coefficients.
Fig. 6
Fig. 6 Monte Carlo analysis of fabrication tolerance. Distributions of (a) grating thickness, (b) duty cycle, (c) cap layer thickness. and (d) resulting Q-factor distribution.
Fig. 7
Fig. 7 Normalized mode profiles |Hy| in dB of an HG resonance in (a) xy plane in the cap layer, (b) xz plane, and (c) yz plane.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

Q = λ r 2 ( 1 R r ) λ arg ( R r ) .

Metrics