QUANTUM-NOISE REDUCTION IN TRAVELING-WAVE 2ND-HARMONIC GENERATION

We analyze squeezing of both the fundamental and harmonic fields under going traveling-wave, second-harmonic generation (SHG) in second-order (chi(2)) nonlinear media. We take into account depletion of the funda mental field as well as the phase mismatch between the fundamental and harmonic fields. The behavior of the quantum noises on the propagatin g fields is studied by linearizing the nonlinear operator equations ar ound the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressi ons for squeezing in both the fundamental and harmonic fields under th e conditions of perfect phase matching and large phase mismatch. We sh ow that in the case of a large phase mismatch, the intensity-dependent self-phase shift of the fundamental field, arising due to cascading o f the chi(2) nonlinearity, is responsible for the squeezing generation . We also numerically solve the linearized quadrature-operator equatio ns together with the nonlinear mean-field equations. We find that in t he case of a finite phase mismatch the harmonic field can be highly sq ueezed. This is in contrast to the perfectly phase-matched case where the maximum squeezing is limited to 50%. Finally, we analyze the nonde generate case that applies to type-II phase-matching geometries. Here we show that the commonly used type-II phase-matched SHG process with the input harmonic field in the vacuum state is equivalent to a type-I SHG process iu parallel with a degenerate optical-parametric process. The latter causes squeezing in the mode that is polarized orthogonal to the fundamental beam. In the perfect phase-matching case, the squee zing in the orthogonally polarized mode follows the simple expression S = 1 - gamma, where gamma is the harmonic conversion frequency.