Optimization of Intersubband Optical Nonlinearities in Continually Graded AlGaN Quantum Well Structures

Abstract

A method is proposed for finding optimal AlGaN-based quantum well profiles with respect to specified intersubband optical properties, e.g. nonlinear optical susceptibilities at resonance. It is based on applying the isospectral transformations (supersymmetric and coordinate transform) to an initial Hamiltonian in order to generate a family of parameters of controlled potentials, accompanied by position-dependent effective mass. By varying those control parameters, one call change the values of dipole matrix elements relevant for a particular effect, while energy levels, once obtained in the initial potential, remain unchanged. The internal electrostatic field, originating from piezoelectric and spontaneous polarization in the nitride alloy, has been taken into account. The use of the method is illustrated by maximizing second order nonlinear optical susceptibilities at wavelengths in the near infrared spectral range, and optimal smooth structures are eventually discretized to make their fabrication easier.