Phase effects during parametric conversion in layer structures

Coupled-wave equations that describe the parametric amplification and generation of a sum frequency in a three-layer structure are studied theoretically in the constant-intensity approximation taking into account the inverse effect of the excited wave on the phase of the pumping wave. For this purpose, the approximation of constant intensity of the fundamental radiation is applied not to the layer structure as a whole but to each separately taken layer. In this case, the complex amplitudes of the interacting waves at the output of each layer are the input values of the corresponding complex amplitudes for the next layer. Analytical expressions obtained in the constant-intensity approximation for the efficiency of conversion to the sum frequency were analyzed numerically for different parameters of the problem. The efficiency of parametric amplification at a high frequency was found to depend on the intensity of the signal wave at a low frequency.