Optimization of intersubband resonant second-order susceptibility in asymmetric graded AlxGa1-xAs quantum wells using 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 quasiparabolic 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. Realization of the optimized potential (in an approximate manner) by grading the ternary alloy AlxGa1-xAs is then described. The best value of nonlinear susceptibility obtained exceeds those reported in the literature.