Calculation of giant third-order nonlinear susceptibilities due to excitonic processes in rectangular GaAs quantum well wires

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Abstract
Exciton and biexciton biding energies and wave functions are calculated variationally for rectangular GaAs quantum well wires in an effective mass approximation. Coulomb interaction terms are treated exactly in their full three-dimensional form throughout the calculation, a more physically realistic procedure than employed in previous calculations that used effective one-dimensional potentials. Our treatment is unique in the use of a two-dimensional Fourier expansion of the Coulomb potential, that removes the difficulty of dealing with the 1/r singularity and considerably reduces the computational effort. Using the results of exciton and biexciton calculations and following the approach of T. Ishihara [Phys. Status Solidi 159, 371 (1990)] in order to eliminate the dimensional dependence of the third-order nonlinear optical susceptibility χ(3), we estimate its magnitude for near-resonant excitonic absorption. We obtain χ(3)’s on the order of 10−1–1 esu for various wire sizes.