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One-Electron Formalism for Second-Harmonic Generation in Crystalline Semiconductors

Z. Levine
Journal / Anthology

Physical Review B
Year: 1990
Volume: 42
Issue: 6
Page range: 3567-3577

The one-electron, self-consistent-field formalism for harmonic generation is presented. The solution is expanded in a Fourier series, assuming that the time-dependent perturbation is weak. The equations of harmonic response form a set of inhomogeneous Schrödinger equations which, if solved order by order, are coupled only through self-consistent-field effects. Special attention is paid to the case of second-harmonic generation in crystalline semiconductors with a longitudinal field present. The f-sum rule for crystals is exploited to eliminate certain terms which apparently diverge as w superscript -2, in perfect analogy to the linear-response theory. Additionally, terms which are in the form of numerical first-, second- and third-order finite differences of the frequency are combined into numerically superior forms.

*Science > Physics > Quantum Physics
*Science > Physics > Solid State Physics