A comprehensive Fourier (k-) space design approach for controllable single and multiple photon localization states

Abstract

A Fourier-space based design approach for the systematic control of single and multiple photon localization states in a 1D lattice is presented. Resultant lattices are aperiodic in nature, such that lattice periodicity is not a useful optimization parameter to achieve novel field localization characteristics. Instead, direct control of field localization comes via control of the Parseval strength competition between the different Fourier components characterizing a lattice. This is achieved via an inverse optimization algorithm, tailoring the aperiodic lattice Fourier components to match that of a target Fourier distribution appropriate for the desired photonic localization properties. We present simulation results indicating the performance of a novel aperiodic lattice exhibiting a doubly-resonant high-Q characteristic.