Theory of electric field-induced optical second harmonic generation in semiconductors

The nonlinear optical coefficientd _ij(kl) (2, 0,, ) for electric field-induced optical second harmonic generation in semiconductors is calculated by means of a perturbation treatment. The result is given directly as a Brillouin zone integral over a resonant energy denominator. A simplified energy band structure model is used to carry out the Brillouin zone integral. The analytic closed-form expression ford _ij(kl) (2, 0,, ) thus obtained permits the calculation of the absolute value of its spectrum from available energy band parameters. The dispersion ofd ₁₁₍₁₁₎ (2, 0,, ) of Ge is numerically calculated, second harmonic photon energies being close to theE ₀ andE ₁ gaps. The results show pronounced resonant behaviours.