12 th International Conference on Mathematical Methods in Electromagnetic Theory June 29 – July 02, 2008, Odesa, Ukraine 978-1-4244-2284-5/08/$25.00 © 2008 IEEE ONE-DIMENSIONAL ANISOTROPIC PHOTONIC CRYSTALS BASED ON ANISOTROPIC POROUS SILICON V.I. Fesenko 1 , I.A. Sukhoivanov 1,2 , S.N. Shulga 3 , He Shi 1 Kharkov National University of Radio Electronics, Lab “Photonics”, Lenin av., 14, 61166, Kharkov, Ukraine 2 Departamento de Electronica, FIMEE, University Guanajuato, Mexico 3 Kharkov National University, Svobody Sq., 4, 61077, Kharkov, Ukraine e-mail: fesenko@kture.kharkov.ua Abstract – The model for description of one-dimensional anisotropic photonic crystals based on anisotropic porous silicon is proposed. The finite difference technique is applied for the scattering matrix parameter computation. Reflectance spectra for two orthogonal polarizations of the incident plane wave are calculated. The dependence of the shift of the spectral position of the photonic band gap edges on the orientation of the optical axis of the structure with respect to the incidence plane of s- or p-polarization incident plane wave is studied. I. INTRODUCTION In recent years, an increasing effort is dedicated to photonic structures that potentially can manipulate the emission, propagation, and detection of light waves. Photonic crystals are periodic structures in which optical properties are depending on the refractive index and the geometry of the elementary pattern [1]. The simplest photonic crystal is one-dimensional and corresponds to a Bragg reflector. Porous silicon is used in silicon-based optoelectronic devices such as, microcavities [2], waveguides, photonic crystals etc [1]. Porous silicon layers (with dimension of the pore about 10-30 nm), have properties of the negative uniaxial crystal with quantity of the birefringence e n n n 0 (here and – the refractive index for “ordinary” and “extraordinary” waves correspondingly) is up to 0.24 [3]. 0 n e n The technique to prepare one-dimensional anisotropic photonic crystals and microcavities based on anisotropic porous silicon exhibiting optical birefringence was developed (see e.g. [4]). Here, we present theoretical model for the 1-D anisotropic photonic crystal based on anisotropic porous silicon. We calculate reflection spectra for two orthogonal polarizations of the incident plane wave taking effect of the birefringence into account. II. FORMULATION OF THE PROBLEM The porous silicon-based structure is shown in Fig. 1. The investigated structure occupies the domain y x z L , , 0 , and consists of layers of anisotropic porous silicon (with different porosity and arbitrary orientation of the optical axes on the layers). Each of layers is characterized by: the thickness ( N j l 1, 2,..., . j N ); permeability 1 j and permittivity ˆ j , in case uniaxial crystal (under consideration): Fig.1. Geometry of the problem. The dark layers are low porosity (high refractive index) and the bright layers are high porosity (low refractive index). 457