OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 24672–24686

Coupled-wave analysis for photonic-crystal surface-emitting lasers on air holes with arbitrary sidewalls

Chao Peng, Yong Liang, Kyosuke Sakai, Seita Iwahashi, and Susumu Noda  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 24672-24686 (2011)
http://dx.doi.org/10.1364/OE.19.024672


View Full Text Article

Enhanced HTML    Acrobat PDF (1087 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The coupled-wave theory (CWT) is extended to a photonic crystal structure with arbitrary sidewalls, and a simple, fast, and effective model for the quantitatively analysis of the radiative characteristics of two-dimensional (2D) photonic-crystal surface-emitting lasers (PC-SELs) has been developed. For illustrating complicated coupling effects accurately, sufficient numbers of waves are included in the formulation, by considering their vertical field profiles. The radiation of band-edge modes is analyzed for two in-plane air-hole geometries, in the case of two types of sidewalls: i.e. “tapered case” and “tilted case.” The results of CWT analysis agree well with the results of finite-difference time-domain (FDTD) numerical simulation. From the analytical solutions of the CWT, the symmetry properties of the band-edge modes are investigated. In-plane asymmetry of the air holes is crucial for achieving high output power because it causes partial constructive interference. Asymmetric air holes and tilted sidewalls help in inducing in-plane asymmetries. By breaking the symmetries with respect to the two orthogonal symmetric axes of the band-edge modes, the two factors can be tuned independently, so that the radiation power is enhanced while preserving the mode selectivity performance. Finally, top-down reactive ion etching (RIE) approach is suggested for the fabrication of such a structure.

© 2011 OSA

OCIS Codes
(140.3430) Lasers and laser optics : Laser theory
(160.5298) Materials : Photonic crystals

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 12, 2011
Revised Manuscript: September 8, 2011
Manuscript Accepted: September 13, 2011
Published: November 17, 2011

Citation
Chao Peng, Yong Liang, Kyosuke Sakai, Seita Iwahashi, and Susumu Noda, "Coupled-wave analysis for photonic-crystal surface-emitting lasers on air holes with arbitrary sidewalls," Opt. Express 19, 24672-24686 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24672


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sasaki, “Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure,” Appl. Phys. Lett.75, 316–318 (1999). [CrossRef]
  2. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett.74, 7–9 (1999). [CrossRef]
  3. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science293, 1123–1125 (2001). [CrossRef] [PubMed]
  4. M. Imada, A. Chutinan, S. Noda, and M. Mochizuki, “Multidirectionally distributed feedback photonic crystal lasers,” Phys. Rev. B.65, 195306 (2002).
  5. G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Operating characteristics of a semiconducting polymer laser pumped by a microchip laser,” Appl. Phys. Lett.82, 313–315 (2003). [CrossRef]
  6. Vurgaftman and J. R. Meyer, “Design optimization for high-brightness surface-emitting photonic-crystal distributed-feedback lasers,” IEEE J. Quantum Electron.39, 689–700 (2003). [CrossRef]
  7. D. Ohnishi, T. Okano, M. Imada, and S. Noda, “Room temperature continuous wave operation of a surface-emitting two-dimensional photonic crystal diode laser,” Optics Express.12, 1562–1568 (2004). [CrossRef] [PubMed]
  8. E. Miyai, K. Sakai, T. Okano, W. Kunishi, D. Ohnishi, and S. Noda, “Lasers producing tailored beams,” Nature, 441, 946 (2006). [CrossRef] [PubMed]
  9. M. Kim, C. S. Kim, W. W. Bewley, J. R. Lindle, C. L. Canedy, I. Vurgaftman, and J. R. Meyer, “Surface-emitting photonic-crystal distributed-feedback laser for the midinfrared,” Appl. Phys. Lett.88, 191105 (2006).
  10. L. Sirigu, R. Terazzi, M. I. Amanti, M. Giovannini, and J. Faist, “Terahertz quantum cascade lasers based on two-dimensional photonic crystal resonators,” Optics Express.16, 5206–5217 (2008). [CrossRef] [PubMed]
  11. Y. Chassagneux, R. Colombelli, W. Maineult, S. Barbieri, H. E. Beere, D. A. Ritchie, S. P. Khanna, E.H. Linfield, and A. G. Davies, “Electrically pumped photonic-crystal terahertz lasers controlled by boundary conditions,” Nature, 457, 174–178 (2009). [CrossRef] [PubMed]
  12. 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, 445–447 (2008). [CrossRef]
  13. T. C. Lu, S. W. Chen, L. F. Lin, T. T. Kao, C. C. Kao, P. Yu, H. C. Kuo, and S. C. Wang, “GaN-based two-dimensional surface-emitting photonic crystal lasers with AlN/GaN distributed Bragg reflector,” Appl. Phys. Lett.92, 011129 (2008). [CrossRef]
  14. Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nature Photon.4, 447–450 (2010). [CrossRef]
  15. M. Kamp, “Photonic crystal lasers: On-chip beam steering,” Nature Photonics, News and Views, 4, 412–413 (2010).
  16. M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Optics Express.13, 2869–2880 (2005). [CrossRef] [PubMed]
  17. H. Kogelnik and C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys.43, 2327–2335 (1972). [CrossRef]
  18. W. Streifer, D. R. Scifres, and R. D. Burnham, “Coupled wave analysis of DFB and DBR lasers” IEEE J. Quantum Electron.13, 134–141 (1977). [CrossRef]
  19. 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, 144–150 (1985). [CrossRef]
  20. M. Toda, “Proposed cross grating single-mode DFB laser,” IEEE J. Quantum Electron.28, 1653–1662, (1992). [CrossRef]
  21. K. Sakai, E. Miyai, and S. Noda, “Coupled-wave model for square-lattice two-dimensional photonic crystal with transverse-electric-like mode,” Appl. Phys. Lett.89, 021101 (2006). [CrossRef]
  22. K. Sakai, E. Miyai, and S. Noda, “Coupled-wave theory for square-lattice photonic crystal lasers with TE polarization,” IEEE J. Quantum Electron.45, 788–795 (2010). [CrossRef]
  23. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Three-dimensional coupled-wave model for square-lattice photonic-crystal lasers with TE polarization — a general approach,” Phy. Rev. B. (submitted), http://arxiv.org/abs/1107.1772 .
  24. S. Iwahashi, K. Sakai, Y. Kurosaka, and S. Noda, “Air-hole design in a vertical direction for high-power two-dimensional photonic-crystal surface-emitting lasers,” JOSA B. 27, 1204–1207 (2010). [CrossRef]
  25. H. Y. Ryu, M. Notomi, and Y. H. Lee, “Finite-difference time-domain investigation of band-edge resonant modes in finite-size two-dimensional photonic crystal slab,” Phys. Rev. B.68, 045209 (2003). [CrossRef]
  26. M. J. Bergmann and H. C. Casey, “Optical-field cacualtions for lossy multiple-layer AlxGa1-xN/InxGa1-xN laser diodes,” J. Appl. Phys.84, 1196 (1998). [CrossRef]
  27. Y. Ding and R. Magnusson, “Band gaps and leaky-wave effects in resonant photonic-crystal waveguides,” Optics Express15, 680–694 (2007). [CrossRef] [PubMed]
  28. D. Rosenblatt, A. Sharon, and A. A. Friesen, “Resonant grating waveguide structures,” IEEE J. Quantum Electron.33, 2038–2059 (1997). [CrossRef]
  29. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications181, 687C702 (2010) [CrossRef]
  30. Y. Liang, C. Peng, K. Sakai, S. Iwahashi, and S. Noda, “Coupled-wave analysis for square-lattice photonic-crystal lasers with TE polarizaiton — finite-size effects,” Optics Express. (in preparation). [PubMed]
  31. S. Takahashi, K. Suzuki, M. Okano, M. Imada, T. Nakamori, Y. Ota, K. Ishizaki, and S. Noda, “Direct creation of three-dimensional photonic crystals by a top-down approach,” Nature Materials8, 721–725 (2009). [CrossRef] [PubMed]

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