Prediction of giant ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ values from a calculation of excitonic nonlinear optical properties in rectangular GaAs quantum-well wires

Exciton and biexciton binding energies, wave functions, and oscillator strengths are calculated variationally for rectangular GaAs quantum-well wires in an effective-mass approximation. The Coulomb interaction terms are treated exactly in their full three-dimensional form throughout the calculation, especially in the case of the biexciton, which is a more physically realistic procedure than was employed in previous calculations which used effective one-dimensional potentials. Our treatment is unique in the use of a two-dimensional Fourier expansion of the Coulomb potential, which removes the numerical difficulty with the 1/r singularity and considerably reduces the computational effort. As an intermediate step, we calculate the linear absorption coefficients at the exciton resonance as a function of the wire dimensions. The results compare favorably with those of Suemune and Coldren [IEEE J. Quantum Electron. QE-24, 1778 (1988)]. Using the results of the exciton and biexciton calculation, we then estimate the third-order nonlinear optical susceptibility for near-resonant excitonic absorption by using the approach of Ishihara [Phys. Status Solidi 159, 371 (1990)]. We obtain ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$’s on the order of ${10}^{\mathrm{-}1}$–1 esu for various wire dimensions.