Negative Uniaxial Crystal Behavior Of Circular Photonic Crystal

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we introduce an unconventional photonic crystal (PhC) geometry which defines two resonance frequencies. The presented circular PhC structure behaves as a negative uniaxial crystal and admits two preferred propagation directions defined by an extraordinary and an ordinary refractive index representing two field polarizations. The circular grating profile splits the electromagnetic field into a radial (extraordinary field) and a tangential (ordinary field) component, which represent two modes of the periodic structure. The total field in the PhC slab is generated by the superposition effect of the ordinary and extraordinary field produced in the 2-D periodic plane. This field configuration is obtained by the analogy with the dielectric multilayer structure. The presented PhC circular lattice pattern consists of air holes in a GaAs material <formula formulatype="inline"><tex Notation="TeX">$({n}=3.408)$</tex> </formula> along circular concentric lines which have the same distance defined as the PhC <emphasis emphasistype="bold"><emphasis emphasistype="italic">a</emphasis></emphasis> period. We validate the birefringence theory by the comparison between analytical and numerical results and then between the numerical and experimental ones. </para>