The effects of focusing in type-I and type-II difference-frequency generations

Beam aperture functions are derived for type-I and type-II difference-frequency generations using focused TEM,, Gaussian beams. The effects of walk-off, absorption, focusing and beam waist location are included in the analysis performed under the undepleted input wave approximation, using a Green's function approach. General expressions for the focusing h functions are given for arbitrary values of the input seed-wave confocal parameters, together with their optimized h(m)(B,mu) values as a function of the walk-off and degeneracy parameters (B,mu). The criterion of equal confocal parameters (ECP) is found to be optimal only for non-critical phase-matching. For critical phase-matching, unequal confocal parameters (UCP) generally optimize the efficiency. The theory is illustrated with relevant performance comparisons between the various type-I and type-II DFG couplings using KTP and AgGaS2. (C) 1998 Elsevier Science B.V.