Optimization of nonlinear optical properties of semiconductor quantum wells: a supersymmetric approach

A systematic procedure is proposed for the optimal design of quantum well structures that provide maximal nonlinear optical susceptibility of second order under conditions of double resonance. The method is based on supersymmetric quantum mechanics. It starts from the linear harmonic oscillator potential, itself lacking any nonlinear susceptibilities, to generate a family of isospectral asymmetric potentials-its supersymmetric partners-which are then varied to maximize the products of matrix elements relevant for nonlinear susceptibilities. The best values of susceptibilities obtained exceed those reported in the current literature by a factor of a few. Possibilities of practical realization of quantum well structures having optimized potentials are also discussed.