The Green's-function analysis of nonlinear interaction of focused (Gaussian) beams, developed in detail by Boyd and Kleinman (1968), is restricted to the case in which pump depletion is ignored. This makes the theory inadequate for many cases of practical interest, such as the prediction of the conversion efficiency of a singly resonant optical parametric oscillator (SRO) or the prediction of the conversion efficiency of second-harmonic generation (SHG) when the conversion efficiency exceeds /spl sim/5%. Using the Green's-function analysis and a perturbation approach, a previous analysis of SRO was recently extended to the pump-depletion regime, and an analytical expression for SRO conversion efficiency was obtained. A similar analysis is presented here for the simpler case of SHG in the presence of pump depletion. This SHG analysis not only provides some new results but also helps simplify the notation to be used later in extending the SRO theory so that easy reduction to the special case of no diffraction is possible in that case as well.
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