Efficiency of generation of the sum and difference frequencies in the field of multimode and multifrequency laser radiation

A theoretical analysis is made of the process of generation of the sum or difference frequency in the field of multimode and multifrequency pump radiation. An allowance is made for the aperture effect under rapid energy exchange conditions. It is shown analytically that on increase in the length of a nonlinear crystal in which the generation process takes place the efficiency of conversion reaches saturation monotonically after a weak maximum. The saturation value of the conversion efficiency increases monotonically on increase in the power of multimode low-frequency pump radiation and attains a limit of 50% in respect of the number of photons. At low pump powers the saturation conversion efficiency is proportional to the square root of the pump power.