## Analysis of semi-infinite periodic structures using a domain reduction technique

JOSA A, Vol. 27, Issue 1, pp. 40-49 (2010)

http://dx.doi.org/10.1364/JOSAA.27.000040

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### Abstract

A new boundary condition is introduced to calculate the effective impedance matrix of semi-infinite periodic structures such as photonic crystals and metamaterials, which leads to a reduction of the solution space. The obtained effective impedance matrix allows one to relate a matrix to a PC, which includes all of its properties in terms of reflection from its interface. For one-dimensional photonic crystals or multilayer films, it is shown that a closed-form equation can be found for the effective impedance. For two-dimensional photonic crystals the impedance is obtained using the scattering matrices by solving a unilateral quadratic matrix equation. Several examples are outlined to validate the developed scheme. In the examples, the goal is mainly the computation of the reflection from a semi-infinite periodic structure when a plane wave illuminates its boundary.

© 2009 Optical Society of America

**OCIS Codes**

(050.1755) Diffraction and gratings : Computational electromagnetic methods

(160.3918) Materials : Metamaterials

(050.5298) Diffraction and gratings : Photonic crystals

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: August 27, 2009

Revised Manuscript: October 28, 2009

Manuscript Accepted: November 5, 2009

Published: December 7, 2009

**Citation**

Arya Fallahi and Christian Hafner, "Analysis of semi-infinite periodic structures using a domain reduction technique," J. Opt. Soc. Am. A **27**, 40-49 (2010)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-1-40

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