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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Four-wave mixing with non-degenerate pumps: steady states and squeezing in the presence of phase modulation

Gagik Yu. Kryuchkyan, Karen V. Kheruntsyan

Published Aug 1, 1995• 6 citations
Publisher

Abstract

We present a quantum theory of an optical four-wave mixing oscillator under pumping by two laser fields of different frequencies. Our analysis includes all the physical processes that are relevant in the parametric limit of interaction in a medium with cubic non-linearity: four-wave mixing, self- and cross-phase modulation. Dynamical aspects of stable above-threshold generation of an intracavity signal mode, the bistability and squeezing phenomena are studied.

DOI
10.1088/1355-5111/7/4/010

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We present a quantum theory of an optical four-wave mixing oscillator under pumping by two laser fields of different frequencies. Our analysis includes all the physical processes that are relevant in the parametric limit of interaction in a medium with cubic non-linearity: four-wave mixing, self- and cross-phase modulation. Dynamical aspects of stable above-threshold generation of an intracavity signal mode, the bistability and squeezing phenomena are studied.
A theoretical investigation is made of parametric generation of light by four-wave mixing in an optical cavity with two pump fields of different frequencies. Mixing configurations resulting in the excitation of one and three cavity modes are considered taking into account the effects of phase modulation and of depletion of the pump fields. An analysis is made of stable steady-state oscillation regimes. Calculations are reported of the intensities of the generated radiation modes at the exit from the cavity above the threshold. An analysis is made of the conditions for the appearance of optical bistability at nonzero values of the cavity detuning.
The authors present a quantum analysis of four-wave mixing in a non-resonant nonlinear medium inside a cavity which is driven by two driving fields. In this process a nonlinear medium couples two pump modes with a signal mode of the frequency equal to the half-sum of the two pump field frequencies. Three types of stable steady-state solutions of the deterministic problem, describing three regimes of oscillation, are found: one below threshold and two different above-threshold regimes. The spectra of fluctuations of the quadrature-phase amplitudes for all three modes are calculated. It is found that in the above-threshold regime each of three modes may display a squeezed noise reduction. Below threshold a squeezing is realized for the central mode.
A theoretical investigation is made of parametric generation of light by four-wave mixing in an optical cavity with two pump fields of different frequencies. Mixing configurations resulting in the excitation of one and three cavity modes are are considered taking into account the effects of phase modulation and ef depletion of the pump fields. An analysis is made of stable steady-state oscillation regimes. Calculations are reported or the intensities of the generated radiation modes at the exit from the cavity above the threshold. An analysis is made of the conditions for the appearance of optical bistability at nonzero values of the cavity detuning.
We analyze the classical behavior and the quantum fluctuations for the system of degenerate four-wave mixing inside a doubly resonant optical cavity. Two frequency-degenerate but orthogonally polarized modes are coupled together in a ${\mathrm{\ensuremath{\chi}}}^{(3)}$ medium. We include all significant phase-matched interactions that occur in a third-order polarization (self-phase modulation, cross-phase modulation, and four-wave mixing). Two critical points are predicted to occur in the system. The first occurs for low pumping, associated with the excitation of the single mode. The second critical point occurs for higher pumping, associated with the onset of self-pulsing. Quantum fluctuations are analyzed for the various regions of pumping. At the first critical point, perfect squeezing is possible in both the pump and the signal modes when the damping of the signal mode is greater than the damping of the pump (${\ensuremath{\gamma}}_{\mathit{a}}$>${\ensuremath{\gamma}}_{\mathit{b}}$). In the case where the damping of the signal mode is much greater than that of the pump (${\ensuremath{\gamma}}_{\mathit{a}}$\ensuremath{\gg}${\ensuremath{\gamma}}_{\mathit{b}}$), nearly perfectly squeezed states of the signal mode are possible in the entire region between the two critical points.
The exact theory of degenerate four-wave mixing in a Kerr-like medium in the Bragg scattering regime is used to study the reflectivity of phase-conjugate mirrors pumped by intense laser beams. The analysis takes into account pump depletion, nonlinear phase modulation and the relaxation time of the nonlinearity. The steady-state response exhibits multivalued reflectivity, hysteresis and potential bistability; however, the transient response shows that at most one value of the phase-conjugate reflectivity is stable. Periodic or chaotic pulsations are predicted beyond threshold values of pump intensity. The onset of a natural oscillation in the Kerr-like medium is also predicted in the absence of a continuous probe beam; the resulting field amplitude is stable and weakly sensitive upon the presence of external noise.
We show that an optomechanical cavity pumped by a bichromatic light beam can generate a signal whose frequency lies halfway between the two driving frequencies. This process can be understood as a degenerate four-wave mixing, in which two pump photons (one from each frequency) are combined to yield two identical signal photons. This process takes place between a lower and an upper threshold in terms of the pump intensity, which depend on the pump frequency difference. Close to the signal oscillation threshold a clear noise reduction in one of its quadratures is shown numerically.