Effects of Momentum Mismatch on Parametric Gain

Abstract

Solutions to the equations describing traveling‐wave parametric amplification are presented. These results extend previous work by including the effects of momentum mismatch and general initial conditions (nonzero pump, signal, and idler fields) on the gain expressions. In contrast to statements found in some earlier published results it is shown that exponential growth is not required to achieve useful parametric gain. This fact is particularly important in the operation of continuously pumped optical parametric oscillators which operate with very small gain coefficients. The equations for the parametric gain are presented in general as well as for a number of limiting cases, and an optimum phase relation between the three waves giving maximum gain is found.