Effect of pump depletion on the spectrum of twin beams

The effect of pump depletion on the spectrum of twin beams, which appear in the process of collinear parametric down-conversion in a nonlinear crystal with an aperiodic domain structure and have a high degree of simultaneity, has been described. A system of equations describing the interaction of pump with all modes of scattered light simultaneously has been derived. It has been shown that pump depletion results in a noticeable broadening of the spectrum of twin beams for a quadratic-hyperbolic law of variation of the reciprocal lattice vector of the domain structure. The effect of narrowing of the coherent peak in the sum-frequency generation signal from twin beams has been demonstrated. This effect increases as the pump is depleted.