## Efficient computation of equifrequency surfaces and density of states in photonic crystals using Dirichlet-to-Neumann maps |

JOSA B, Vol. 28, Issue 8, pp. 1837-1843 (2011)

http://dx.doi.org/10.1364/JOSAB.28.001837

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### Abstract

We present an efficient method for computing the equifrequency surfaces (EFSs) and density of states of a photonic crystal. The method is based on repeatedly solving a small nonlinear eigenvalue problem formulated using the Dirichlet-to-Neumann map of the unit cell. A simple contouring algorithm is presented for sampling EFSs as well as computing group velocity vectors. We compare our method with several published results to demonstrate its efficiency and accuracy.

© 2011 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(000.4430) General : Numerical approximation and analysis

(160.5298) Materials : Photonic crystals

**ToC Category:**

Mathematical Methods in Physics

**History**

Original Manuscript: February 15, 2011

Revised Manuscript: May 14, 2011

Manuscript Accepted: June 1, 2011

Published: July 6, 2011

**Citation**

Victor Liu and Shanhui Fan, "Efficient computation of equifrequency surfaces and density of states in photonic crystals using Dirichlet-to-Neumann maps," J. Opt. Soc. Am. B **28**, 1837-1843 (2011)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-8-1837

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