Optimization of resonant intersubband nonlinear optical susceptibility in semiconductor quantum wells: The coordinate transform approach

A systematic procedure is proposed for the optimal design of quantum-well structures, which provide maximal resonant second-order susceptibility. The method is based on the coordinate transform. Starting from the linear harmonic-oscillator Hamiltonian, itself lacking any nonlinear susceptibility, it generates a family of asymmetric isospectral Hamiltonians in parametrized form. Their parameters are then varied to maximize the product of matrix elements relevant for nonlinear susceptibility. Practical realization of quantum-well structures having such optimized Hamiltonians is also discussed. Values of nonlinear susceptibility obtained by this method are about equal to the best values reported in current literature. {} 1996 The American Physical Society.