On the optimization of resonant intersubband nonlinear optical susceptibilities in semiconductor quantum wells

A systematic procedure is proposed for the optimal design of quantum-well structures that provides maximal nonlinear optical susceptibility of second-order under conditions of double resonance. The method is based on the supersymmetric quantum mechanics. It starts from the linear harmonic oscillator potential, itself lacking any nonlinear susceptibility, 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 susceptibility. The best value of susceptibility obtained exceeds those reported in the current literature. Possibilities of practical realization of quantum-well structures having optimized potentials are also discussed.