Determination of second-order nonlinear coefficients in semiconductors using pseudospin equations for three-level systems

Abstract

A pseudospin formalism is developed for analyzing the dynamics of a three-level system analogous to the Maxwell-Bloch equations in the two-level case. These are used in the nonresonant regime to obtain the complete and general form of the second-order optical susceptibility. All the nonzero second-order tensor elements for second-harmonic generation are calculated for bulk GaAs and asymmetric ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wells. It is demonstrated that a partial cancellation of terms occurs which limits the values obtained in the asymmetric quantum wells. It is also demonstrated by example that the band structure can also strongly influence the values obtained. While small values are obtained for the examples given here, it is reasoned that large second-order susceptibilities should be obtainable with short-period asymmetric superlattices.