title: Analysis of semi-infinite periodic structures using a domain reduction technique.
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.
authors.affiliation: Laboratory of Electromagnetic Fields and Microwave Electronics, ETH Zürich, Zürich CH-8092, Switzerland. fallahia@ifh.ee.ethz.ch
authors.forename: Arya
authors.initials: A
authors.lastname: Fallahi
authors.forename: Christian
authors.initials: C
authors.lastname: Hafner