Fallahi A, Hafner C. Analysis of semi-infinite periodic structures using a domain reduction technique.
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2010;
27:40-49. [PMID:
20035301 DOI:
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.
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