Calculation of third-order optical susceptibilities due to excitonic nonlinearities in rectangular GaAs/AlGaAs quantum well wires with finite Al-graded band offsets included

Exciton and biexciton binding energies, and wave functions are calculated with a three parameter variational model in an effective mass approximation for a rectangular GaAs quantum well wire surrounded by an AlGaAs cladding. Moreover, the Al interdiffusion into the wire and the finite band offsets between the wire and the cladding have been included. The Coulomb interaction terms are treated exactly in their full 3D form throughout the calculation, especially in the case of the biexciton, a more physically realistic procedure then used in previous calculations which employed an effective 1D potential. Our treatment is unique in the use of a 2D Fourier expansion in the Coulomb potential terms. For the range of dimensions studied, the inclusion of the Al interdiffusion had a pronounced affect on the binding energies when compared to those obtained from the infinite barrier model. Using the results of the exciton and biexciton calculation, we calculate the third-order nonlinear optical susceptibility as a function of pump-probe frequencies in a small range about the exciton absorption resonance. We have found, depending upon wire dimensions and the amount of pump detuning, values of the susceptibilities to be on the order of 10-1 esu and a large off-resonance optical gain due to biexciton formation.