Third harmonic generation with high efficiency

For third harmonic generation in cubic-nonlinear media, the influence of intensity-dependent parts of the refractive index must be taken into account because the corresponding susceptibilities for the parametric process and the process of self-action are of the same order. The intensity dependence of the index of refraction may destroy the phase matching and therefore lower the efficiency. It is well known that at low efficiencies (in the parametric approximation) it is easy to compensate the nonlinear mismatch by a proper linear one. The problem is more complicated beyond the parametric approximation. We present numerical results concerning this question. The maximum efficiency and the dependence of the harmonic on the (normalized) length of the nonlinear medium were calculated for different cases. Neglecting the dispersion of the third-order nonlinear susceptibility, the efficiency is determined only by one parameter Δk · l nl /2, where Δk is the usual linear mismatch Δk = K3 − 3k1, and l nl is the nonlinear interaction length (which is inversely proportional to the input intensity of the fundamental wave and the effective third-order nonlinearity). Whereas for Δk = 0 the maximum efficiency (defined here as ratio of the amplitudes) is 0.55, one gets for an optimum mismatch of (Δk)opt = −0.27 (2/lnl) a maximum attainable efficiency of 0.92; i.e., also in the case including pump depletion it is possible nearly to compensate the nonlinear mismatch. However, as we also show, the dispersion of the nonlinear susceptibility can lower the maximum possible efficiency.