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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 10 — May. 19, 2014
  • pp: 11804–11811

Two dimensional analysis of finite size high-contrast gratings for applications in VCSELs

Anjin Liu, Werner Hofmann, and Dieter Bimberg  »View Author Affiliations

Optics Express, Vol. 22, Issue 10, pp. 11804-11811 (2014)

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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

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(050.6624) Diffraction and gratings : Subwavelength structures
(140.7260) Lasers and laser optics : Vertical cavity surface emitting lasers

ToC Category:
Diffraction and Gratings

Original Manuscript: February 18, 2014
Revised Manuscript: March 24, 2014
Manuscript Accepted: March 24, 2014
Published: May 7, 2014

Anjin Liu, Werner Hofmann, and Dieter Bimberg, "Two dimensional analysis of finite size high-contrast gratings for applications in VCSELs," Opt. Express 22, 11804-11811 (2014)

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  1. N. Savage, “Linking with light,” IEEE Spectr. 39(8), 32–36 (2002). [CrossRef]
  2. D. Bimberg, “Ultrafast VCSELs for datacom,” IEEE Photonics Journal 2(2), 273–275 (2010). [CrossRef]
  3. F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol. 24(12), 4502–4513 (2006). [CrossRef]
  4. 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]
  5. A. Larsson, “Advances in VCSELs for communication and sensing,” J. Sel. Top. Quantum Electron. 17(6), 1552–1567 (2011). [CrossRef]
  6. R. Michalzik, VCSELs - Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, Springer Series in Optical Sciences, 166 (Springer, 2013).
  7. 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]
  8. 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]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. 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]
  14. R. Magnusson, M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008). [CrossRef] [PubMed]
  15. 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]
  16. 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]
  17. 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]
  18. 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]
  19. M. C. Y. Huang, Y. Zhou, C. J. Chang-Hasnain, “A nanoelectromechanical tunable laser,” Nat. Photonics 2(3), 180–184 (2008). [CrossRef]
  20. 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]
  21. W. Hofmann, “Evolution of high-speed long-wavelength vertical-cavity surface-emitting lasers,” Semicond. Sci. Technol. 26(1), 014011 (2011). [CrossRef]
  22. 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]
  23. 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]
  24. R. R. Boye, R. K. Kostuk, “Investigation of the effect of finite grating size on the performance of guided-mode resonance filters,” Appl. Opt. 39(21), 3649–3653 (2000). [CrossRef] [PubMed]
  25. 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]
  26. P. Debernardi, R. Orta, W. Hofmann, “Rigorous, highly-efficient optical tools for HCG-VCSEL design,” Proc. SPIE 8633, 86330A (2013). [CrossRef]
  27. 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]
  28. M. Shokooh-Saremi, R. Magnusson, “Wideband leaky-mode resonance reflectors: Influence of grating profile and sublayers,” Opt. Express 16(22), 18249–18263 (2008). [CrossRef] [PubMed]
  29. D. Rosenblatt, A. Sharon, A. A. Friesem, “Resonant grating waveguide structures,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997). [CrossRef]
  30. 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]
  31. 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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