Calculation of the second-order optical nonlinear susceptibilities in biased ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells

The second-order optical nonlinear susceptibilities ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ of biased ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells (QW’s) are theoretically estimated. The contributions of Wannier excitonic states and nonexcitonic excited states to ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ are discussed. It is shown that the transitions between a Wannier excitonic state and nonexcitonic excited states contribute dominantly to ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ of biased ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As QW’s. The ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ values are calculated for various QW widths and electric fields. The strong resonance of exciton energy and pumping-light energy, the strong oscillator strength of Wannier exciton states, and the large dipole of Wannier excitons result in large ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ values greater than 5×${10}^{\mathrm{-}10}$ m/V for QW’s with well widths of less than 70 Å. Because QW’s have large ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ values in the wavelength range near 1.55 μm, they are good candidates for nonlinear optical devices for communication systems.