Light squeezing in optical parametric amplification beyond the slowly-varying amplitude approximation

Optical parametric amplification (OPA) described usually by the coupled-wave equations with the first-order derivatives of the signal and idler waves, is solved under the slowly-varying amplitude approximation (SVA). In this article, by keeping the second-order derivatives in the coupled-wave equations, we obtained an analytical solution for the output signal and idler waves up to the first order of (κ/k)¹; the ratio of coupling constant to the wave number. Furthermore, here the signal and the idler waves are distinguished only by their polarizations with the same frequency. Light squeezing is observed in normally ordered variances of the two quadrature operators of the output combined mode when plotted against κL, where κ is the coupling constant and L the interaction length. The variances have different signs for a range of values of κL and their variations are in opposite directions. We also show that this property is strongly dependent on the relative refractive index of the medium (n). It is worth mentioning that the relative index dependency is not an explicit feature in squeezing of OPA under SVA approximation. Furthermore, the squeezing vanishes when n → 1 and κ/k → 0.