Reflectionless potentials and cavities in waveguide arrays and coupled-resonator structures

Abstract

We present an approach for the realization of reflectionless potentials in linear coupled-resonator optical waveguides or optical waveguide arrays with modulated coupling. We show that soliton solutions of nonlinear Ablowitz–Ladik equations can be used to define analytically reflectionless modulations for linear photonic structures. Such structures fully transmit incident waves and simultaneously support a pair of localized modes. These results suggest new possibilities for pulse and beam shaping, including a realization of cavities that do not reflect incident light.