Optimization of intersubband resonant second-order susceptibility using the supersymmetric quantum mechanics

A systematic procedure is proposed for the design of ternary alloys based quantum well structures optimized for double resonance second harmonic generation. The method relies on the supersymmetric quantum mechanics as derived here for the case of position-dependent effective mass. Starting from a symmetric, truncated quasi-parabolic potential, itself lacking any second-order nonlinearity, we generate a family of asymmetric potentials, fully isospectral with the starting potential, and choose the one which maximizes the product of transition matrix elements relevant for the second order nonlinearity. The best value of nonlinear susceptibility obtained exceeds those reported in the literature.