Optical inhomogeneity of nonlinear crystals and maximum efficiencies of parametric frequency amplifiers pumped by beams with inhomogeneous transverse intensity distributions

An analytic and numerical study is made of the interaction of three waves in an homogeneous medium without recourse to linearization. A study is made of the efficiency of parametric frequency conversion of pump beams with inhomogeneous transverse intensity distributions. A theoretical solution is given of the problem of the optimization of the length of a nonlinear medium and of the phase mismatch at the input to the medium. The results are then used to find the maximum frequency conversion efficiencies of the parametric amplification processes. It is shown that in the case of inhomogeneous beams it is not possible to attain the maximum theoretical efficiencies predicted for homogeneous beams even when homogeneous nonlinear crystals are used. The dependences of the maximum frequency conversion efficiencies on a parameter b, representing the quality of a crystal, and on the relative intensity of the signal wave at the input are obtained: a reduction in the signal intensity reduces the maximum possible efficiency of parametric amplification.