We show that processes such as second-harmonic generation and subsequent downconversion, and parametric mixing in general, can lead to large field-dependent phase shifts for the input beams under a variety of conditions.
We analyze squeezing of both the fundamental and harmonic fields undergoing traveling-wave, second-harmonic generation (SHG) in second-order (${\mathrm{\ensuremath{\chi}}}^{(2)}$) nonlinear media. We take into account depletion of the fundamental field as well as the phase mismatch between the fundamental and harmonic fields. The behavior of the quantum noises on the propagating fields is studied by linearizing the nonlinear operator equations around the mean-field values. We first consider the degenerate case that is applicable to type-I phase-matching geometries, obtaining expressions for squeezing in both the fundamental and harmonic fields under the conditions of perfect phase matching and large phase mismatch. We show that in the case of a large phase mismatch, the intensity-dependent self-phase shift of the fundamental field, arising due to cascading of the ${\mathrm{\ensuremath{\chi}}}^{(2)}$ nonlinearity, is responsible for the squeezing generation. We also numerically solve the linearized quadrature-operator equations together with the nonlinear mean-field equations. We find that in the case of a finite phase mismatch the harmonic field can be highly squeezed. This is in contrast to the perfectly phase-matched case where the maximum squeezing is limited to 50%. Finally, we analyze the nondegenerate 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 in 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 squeezing in the orthogonally polarized mode follows the simple expression S=1-\ensuremath{\gamma}, where \ensuremath{\gamma} is the harmonic conversion frequency.
Second-harmonic generation (SHG) and parametric amplification result from the same physical configuration of the /spl chi//sup (2)/ process, but with different input conditions for the interacting fundamental and harmonic waves. In the former, the input harmonic field is usually in the vacuum state whereas, in the latter, the fundamental is in the vacuum state (or a small-amplitude coherent state). A different set of input conditions can lead to a nonlinear phase shift in both the fundamental and the harmonic waves, while not affecting their relative magnitudes. In conjunction with SHG, we show that this configuration can be used to generate a bright (high-intensity) amplitude-squeezed (sub-Poissonian) field at the harmonic frequency. Large amounts of squeezing are possible. An integrated device with the above characteristics can be fabricated by utilizing the recently developed quasi-phase-matching techniques.
A Fabry-Perot resonator filled with second-order nonlinear optical material is investigated. Attention is devoted to making the resonator act as a nonlinear mirror for ultralow-intensity light signals that can be switched by a control beam at the second-harmonic frequency. The interaction process is an input-phase-independent parametric downconversion. The theoretical problem is solved through implementation of a dummy variable method optimized for a parametric process. Efficient amplification and bistability of low-intensity signals have been found.