Two methods of quantum well profile optimization for maximal nonlinear optical susceptibilities

Two different approaches for the optimization of the quantum well profile are proposed and discussed. One is the multiparameter procedure, based on the inverse spectral theory (IST) and supersymmetric quantum mechanics (SUSYQM), which is an extension of the single-parameter procedure devised earlier for this purpose. Another approach combines the simulated annealing and variational calculus. The two approaches are compared on the example of optimizing the well profile to get maximal resonant second-order susceptibility at 10.6 μm (116 meV). Within the multiparameter IST/SUSYQM procedures, we find that the two-parameter procedure delivers significantly better results than the single-parameter procedure, while introducing more parameters does not result in any further improvement. However, even better results (by about 20%) were obtained with the variational procedure, which, though more time consuming, is free from any unnecessary constraints and may thus lead to global optimization.