Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach

Abstract

We determine resonant scattering states of two-dimensional photonic crystal nanostructures with defects. To do so, we use the boundary-wall method originally introduced to obtain the scattering eigenstates of one electron moving in a medium with arbitrary boundaries. We investigate geometries including beam bending and interferometer-like waveguides, as well as waveguides connected by resonant cavities. We are able to identify the electromagnetic modes that, due to the special resonance condition attained in the vicinity of defects, provide optimal transmission of an incoming plane wave. Based on the generality of the boundary wall technique and its numerical simplicity and efficiency to identify resonant scattering modes, we briefly discuss further possible applications of this method in analysing the performance of general photonic band-gap devices.