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

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 refiectionless 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.