## Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization |

Optics Express, Vol. 21, Issue 1, pp. 565-580 (2013)

http://dx.doi.org/10.1364/OE.21.000565

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### Abstract

Three-dimensional coupled-wave theory is extended to model triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization. A generalized coupled-wave equation is derived to describe the sixfold symmetry of the eigenmodes in a triangular lattice. The extended theory includes the effects of both surface radiation and in-plane losses in a finite-size laser structure. Modal properties of interest including the band structure, radiation constant, threshold gain, field intensity profile, and far-field pattern (FFP) are calculated. The calculated band structure and FFP, as well as the predicted lasing mode, agree well with experimental observations. The effect of air-hole size on mode selection is also studied and confirmed by experiment.

© 2013 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: October 15, 2012

Revised Manuscript: December 7, 2012

Manuscript Accepted: December 19, 2012

Published: January 7, 2013

**Citation**

Yong Liang, Chao Peng, Kenji Ishizaki, Seita Iwahashi, Kyosuke Sakai, Yoshinori Tanaka, Kyoko Kitamura, and Susumu Noda, "Three-dimensional coupled-wave analysis for triangular-lattice photonic-crystal surface-emitting lasers with transverse-electric polarization," Opt. Express **21**, 565-580 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-565

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