Abstract

Second-harmonic generation is investigated for a medium with second-and third-order nonlinear susceptibilities. All possible solutions assuming zero initial value for the second harmonic are obtained. Based on the analysis, the optimal condition for second-harmonic generation is deduced. A theoretical 100% conversion from the fundamental to the second harmonic is expected when the condition for phase optimization is met. Even when the condition is not satisfied, a possible best efficiency can be sought by estimating a figure of merit ΔT = (½|P|)|Δk/R–QR|, where R is the field intensity of input beam, Δk is the phase mismatch, and B and Q are combinations of the second- and third-order nonlinear susceptibilities, which depend on the angles between the optic axis and the input beam. Generally, as ΔT is reduced, a higher efficiency can be obtained. Hence, the concept of phase matching should be modified to that of phase optimization when the term QR is comparable with Δk/R. A higher efficiency will be obtained if the medium has higher B (i.e., the second-order nonlinearity) or if | Δk/R–QR | is minimized.

© 1990 Optical Society of America