Determination of nonresonant optical nonlinearities in undisordered and disordered semiconductor superlattices

Summary form only given. One of the emerging technologies for the control of nonlinear optical coefficients is quantum well disordering, opening up the possibility of integrated (with laser pump) semiconductor optical parametric oscillators. A key requirement is a predictive capability for nonlinear optical coefficients in semiconductor heterostructures and their modification under disordering. It has previously been established that induced second-order coefficients are maximised by increasing the intersubband separation, i.e., a recipe for a short period, deep well superlattice. This also has the benefit of maximising the contrast achievable under disordering. Prediction and optimisation of the linear and nonlinear optical properties requires knowledge of (1) the energies of the electronic states of the material and (2) the optical matrix elements between them (obtainable from the electronic wavefunctions). That is a suitable band structure algorithm must lie at the core of any calculation. Here an algorithm is developed for calculating the band structure in semiconductor superlattices based on the k/spl middot/p method. The basis functions for this algorithm are the topmost valence band triplet, the lowest conduction singlet and the higher triplet states and hence the model is anisotropic and non-centrosymmetric (necessary for obtaining a non-zero second-order nonlinearity). A Fourier analysis is employed transforming the Hamiltonian from coupled set of differential equations to an algebraic set. An analytic expression is found for the Fourier coefficients of a disordered alloy profile.