OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 10 — May. 9, 2011
  • pp: 9475–9491

Analysis of two-dimensional photonic crystal with anisotropic gain

Shinichi Takigawa and Susumu Noda  »View Author Affiliations


Optics Express, Vol. 19, Issue 10, pp. 9475-9491 (2011)
http://dx.doi.org/10.1364/OE.19.009475


View Full Text Article

Enhanced HTML    Acrobat PDF (1658 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Photonic modes in a two-dimensional square-lattice photonic crystal (PC) with anisotropic gain are analyzed for the first time. A plane-wave expansion method is improved to include the gain, which depends on not only the position but also the propagation direction of each plane wave. The anisotropic gain varies the photonic band structure, the near-field distributions, and the gain dispersion curves through variation in PC symmetry. Low-threshold operation of a PC laser with anisotropic-gain material such as nonpolar InGaN requires that the direction of higher gain in the material aligns along the ΓX direction of the PC.

© 2011 OSA

OCIS Codes
(140.3430) Lasers and laser optics : Laser theory
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: April 4, 2011
Manuscript Accepted: April 20, 2011
Published: April 29, 2011

Citation
Shinichi Takigawa and Susumu Noda, "Analysis of two-dimensional photonic crystal with anisotropic gain," Opt. Express 19, 9475-9491 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9475


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Matsubara, S. Yoshimoto, H. Saito, Y. Jianglin, Y. Tanaka, and S. Noda, “GaN photonic-crystal surface-emitting laser at blue-violet wavelengths,” Science 319(5862), 445–447 (2008). [CrossRef]
  2. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B 65(19), 195306 (2002). [CrossRef]
  3. R. Colombelli, K. Srinivasan, M. Troccoli, O. Painter, C. F. Gmachl, D. M. Tennant, A. M. Sergent, D. L. Sivco, A. Y. Cho, and F. Capasso, “Quantum cascade surface-emitting photonic crystal laser,” Science 302(5649), 1374–1377 (2003). [CrossRef] [PubMed]
  4. K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Comm. 23(7), 1335–1340 (2005). [CrossRef]
  5. G. Scalari, L. Sirigu, R. Terazzi, C. Walther, M. I. Amanti, M. Giovannini, N. Hoyler, J. Faist, M. L. Sadowski, H. Beere, D. Ritchie, L. A. Dunbar, and R. Houdre, “Multi-wavelength operation and vertical emission in THz quantum-cascade lasers,” J. Appl. Phys. 101(8), 081726 (2007). [CrossRef]
  6. L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, J. Faist, L. A. Dunbar, and R. Houdré, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Opt. Express 16(8), 5206–5217 (2008). [CrossRef] [PubMed]
  7. O. P. Marshall, V. Apostolopoulos, J. R. Freeman, R. Rungsawang, H. E. Beere, and D. A. Ritchie, “Surface-emitting photonic crystal terahertz quantum cascade lasers,” Appl. Phys. Lett. 93(17), 171112 (2008). [CrossRef]
  8. E. Matioli, B. Fleury, E. Rangel, T. Melo, E. Hu, J. Speck, and C. Weisbuch, “High extraction efficiency GaN-based photonic crystal light-emitting diodes: comparison of extraction lengths between surface and embedded photonic crystals,” Appl. Phys. Express 3(3), 032103 (2010). [CrossRef]
  9. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen, “Photonic crystal Mach-Zehnder interferometer based on self-collimation,” Appl. Phys. Lett. 90(23), 231114 (2007). [CrossRef]
  10. S. Nojima, “Enhancement of optical gain in two-dimensional photonic crystals with active lattice points,” Jpn. J. Appl. Phys. 37(Part 2, No. 5B), L565–L567 (1998). [CrossRef]
  11. S. Nojima, “Optical-gain enhancement in two-dimensional active photonic crystals,” J. Appl. Phys. 90(2), 545–551 (2001). [CrossRef]
  12. M. M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B Condens. Matter 49(16), 11080–11087 (1994). [CrossRef] [PubMed]
  13. V. Yannopapas, A. Modinos, and N. Stefanou, “Optical properties of metallodielectric photonic crystals,” Phys. Rev. B 60(8), 5359–5365 (1999). [CrossRef]
  14. I. El-Kady, M. M. Sigalas, R. Biswas, K. H. Ho, and C. M. Soukoulis, “Metallic photonic crystals at optical wavelengths,” Phys. Rev. B 62(23), 15299–15302 (2000). [CrossRef]
  15. S. Brand, R. A. Abram, and M. A. Kaliteevski, “Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods,” Phys. Rev. B 75(3), 035102 (2007). [CrossRef]
  16. K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron. 46(5), 788–795 (2010). [CrossRef]
  17. K. Sakai, E. Miyai, and S. Noda, “Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization,” Opt. Express 15(7), 3981–3990 (2007). [CrossRef] [PubMed]
  18. K. Okamoto, J. Kashiwagi, T. Tanaka, and M. Kubota, “Nonpolar m-plane InGaN multiple quantum well laser diodes with a lasing wavelength of 499.8nm,” Appl. Phys. Lett. 94(7), 071105 (2009). [CrossRef]
  19. A. Tyagi, Y.-D. Lin, D. A. Cohen, M. Saito, K. Fujito, J. S. Speck, S. P. DenBaars, and S. Nakamura, “Stimulated emission at blue-green (480nm) and green (514nm) wavelengths from nonpolar (m-plane) and semipolar (11-22) InGaN multiple quantum well laser diode structures,” Appl. Phys. Express 1, 091103 (2008). [CrossRef]
  20. Y. Enya, Y. Yoshizumi, T. Kyono, K. Akita, M. Ueno, M. Adachi, T. Sumitomo, S. Tokuyama, T. Ikegami, K. Katayama, and T. Nakamura, “531 nm green lasing of InGaN based laser diodes on semipolar {20-21} free-standing GaN substrates,” Appl. Phys. Express 2, 082101 (2009). [CrossRef]
  21. P. S. Hsu, K. M. Kelchner, A. Tyagi, R. M. Farrell, D. A. Haeger, K. Fujito, H. Ohta, S. P. DenBaars, J. S. Speck, and S. Nakamura, “InGaN/GaN blue laser diode grown on semipolar (30-31) free-standing GaN substrates,” Appl. Phys. Express 3(5), 052702 (2010). [CrossRef]
  22. T. Ohtoshi and T. Kuroda, “Dependence of optical gain on crystal orientation in wurtzite-GaN strained quantum-well lasers,” Appl. Phys. Lett. 82, 1518–1520 (1997).
  23. S.-H. Park, “Crystal orientation effects on many-body optical gain of wurtzite InGaN/GaN quantum well lasers,” Jpn. J. Appl. Phys. 42(Part 2, No. 2B), L170–L172 (2003). [CrossRef]
  24. W. Scheibenzuber, U. Schwarz, R. Veprek, B. Witzigmann, and A. Hangleiter, “Calculation of optical eigenmodes and gain in semipolar and nonpolar InGaN/GaN laser diodes,” Phys. Rev. B 80(11), 115320 (2009). [CrossRef]
  25. K. Okamoto, H. Ohta, S. F. Chichibu, J. Ichihara, and H. Takasu, “Continuous-wave operation of m-plane InGaN multiple quantum well laser diodes,” Jpn. J. Appl. Phys. 46(9), L187–L189 (2007). [CrossRef]
  26. T. Onuma, K. Okamoto, H. Ohta, and S. F. Chichibu, “Anisotropic optical gain in m-plane InxGa1-xN/GaN multiple quantum well laser diode wafers fabricated on the low defect density freestanding GaN substrate,” Appl. Phys. Lett. 93(9), 091112 (2008). [CrossRef]
  27. H. Kitagawa, T. Suto, M. Fujita, Y. Tanaka, T. Asano, and S. Noda, “Green photoluminescence from GaInN photonic crystals,” Appl. Phys. Express 1, 032004 (2008). [CrossRef]
  28. M. Plihal and A. A. Maradudin, “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B Condens. Matter 44(16), 8565–8571 (1991). [CrossRef] [PubMed]
  29. A. Yariv, Introduction to Optical Electronics (Holts, Rinehart and Winston. Inc, 1974).
  30. T. Kawashima, H. Yoshikawa, S. Adachi, S. Fuke, and K. Ohtsuka, “Optical properties of hexagonal GaN,” J. Appl. Phys. 82(7), 3528–3535 (1997). [CrossRef]
  31. M. J. Bergmann and H. C. Casey., “Optical-field calculations for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys. 84(3), 1196–1203 (1998). [CrossRef]
  32. L. Q. Zhang, D. S. Jiang, J. J. Zhu, D. G. Zhao, Z. S. Liu, S. M. Zhang, and H. Yang, “Confinement factor and absorption loss of AlInGaN based laser diodes emitting from ultraviolet to green,” J. Appl. Phys. 105(2), 023104 (2009). [CrossRef]
  33. K. Inoue and K. Ohtaka, Photonic Crystals (Springer-Verlag, 2004).
  34. R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation losses,” IEEE J. Quantum Electron. 21(2), 144–150 (1985). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited