EVOLUTION OF QUANTUM-NOISE IN THE TRAVELING-WAVE 2ND-ORDER [CHI((2))]NONLINEAR PROCESS

We analyze the evolution of quantum noise in both the fundamental and the harmonic fields that are undergoing traveling-wave interaction in a second-order [chi((2))] nonlinear medium. Assuming perfect phase mat ching between the fundamental and the harmonic fields and arbitrary in put boundary conditions, the behavior of quantum noise in the propagat ing fields is studied by linearization of the nonlinear-operator equat ions around the mean-field values. We first consider the degenerate ca se that is applicable to type-I phase-matching geometries, obtaining e xpressions for squeezing in both the fundamental and the harmonic fiel ds. We then analyze the polarization-nondegenerate case that applies t o type-II phase-matching geometries. In the special case, when the two orthogonally polarized fundamental inputs are of equal amplitude, we obtain analytical results and show that the type-II phase-matched seco nd-harmonic-generation process can be configured to generate sub-Poiss onian Light in both polarization components of the fundamental field. Finally, we numerically solve the linearized quadrature-operator equat ions along with the nonlinear mean-field equations for the general cas e of type-II phase matching. For both type-I and type-II processes, we find that whenever the fundamental field experiences deamplification it is associated with amplitude squeezing and phase desqueezing. If, i n contrast, the fundamental field experiences amplification, then it i s accompanied by amplitude desqueezing, but with squeezing in the phas e quadrature. The harmonic field is amplitude squeezed if the input bo undary condition leads to harmonic conversion and is phase squeezed if the input boundary condition leads to parametric amplification. (C) 1 995 Optical Society of America