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Journal of the Optical Society of America B

Coherent light wave generated from incoherent pump light in nonlinear Kerr medium

Yan Yan, Changxi Yang

Published Oct 12, 2009• 8 citations
Publisher

Abstract

We show theoretically and numerically that in an instantaneous-response Kerr medium, a coherent signal light can be generated spontaneously from an incoherent pump light in the degenerate four-wave mixing process. Our analysis shows that this phenomenon requires the same group velocities of pump wave and idler wave as well as the convection (walk-off) between the signal wave and pump/idler waves.

DOI
10.1364/josab.26.002059

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We show theoretically and numerically that in an instantaneous-response Kerr medium, a coherent signal light can be generated spontaneously from an incoherent pump light in the degenerate four-wave mixing process. Our analysis shows that this phenomenon requires the same group velocities of pump wave and idler wave as well as the convection (walk-off) between the signal wave and pump/idler waves.
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.
Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). The quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which is entangled if the pump is a coherent state produced by a laser. The signal and the idler modes remain populated by photons even if the pump becomes incoherent (dephased by a medium, superposed with a thermal state, or produced by an alternative source such as the superluminescent diode). However, the incoherent pump does effect the entanglement and purity of the signal and the idler modes, which is of vital importance for quantum information applications and interferometry. Here we develop an approach to infer the signal-idler entanglement and purity for a general quantum incoherent pump with the given Glauber-Sudarshan function. We show that the signal-idler entanglement is extremely sensitive to the phase distribution of the pump and illustrate our findings by physically relevant examples of the incoherent pump: the noisy coherent state, slightly dephased and phase-averaged coherent states, the thermal state, and states modulated by the Kerr medium. The effect of an incoherent pump on the combined quadratures is discussed as well.
This paper presents an exact solution to the slowly varying envelope equations for the probe and signal fluxes in degenerate four-wave mixing in Kerr media. The analysis is performed for a noncollinear geometry, and all beams have the same linear polarization in the nonlinear medium. It is assumed that the angle separating the directions of the counterpropagating pumps and probe and signal beams is large enough so that cross-coupled waves do not contribute to the envelope equations describing the spatial evolution of the pump, probe, and signal beams. Multiple values of the transmitted probe are obtained for equal pump fluxes above a threshold determined by the nonlinear phase shift in the medium. Significant pump depletion occurs in this regime, but it can also occur without the appearance of multiple solutions. Since exact optical phase conjugation occurs only in the limit where the pumps are undepleted in Kerr media, this result implies that there are fundamental upper limits on the pump intensity that can be used to increase signal reflectivities in optical phase conjugation.
The nonlinear signal in a degenerate four-wave mixing experiment as a result of diffraction of a spatially distributed third-order nonlinearity is studied theoretically. The approach has been applied for the case of monochromatic and ultrashort pulses. As a consequence, the degenerate four-wave mixing signal is found to be independent of light-coherence parameters and cannot be explained as a product of diffraction on a dynamic grating. In this model only the fast component of the signal (the coherent artifact) is related directly to third-order nonlinear processes. The main features (the origins, temporal shapes, dependencies of pump intensity, and modulation effects) of the coherent artifact and a slow-decay component are discussed theoretically and experimentally.
A parametric amplification of input signal wave in the field of broadband incoherent light is analyzed at group-velocity matching of pump and idler waves. It is shown that such group-velocity matching is possible both in Type-I and Type-II phase-matching nonlinear crystals. The appropriate conditions at which an evolution of the signal wave in the field of the incoherent pump coincides with an evolution in the field of the monochromatic pump wave are demonstrated. The large parametric gain of the signal wave which is not sensitive to pump fluctuations is feasible in Type-II phase-matching nonlinear crystals.
Distributed positive feedback established by a counterpropagating three-wave mixing process in a submicrometer structured second-order nonlinear medium leads to mirrorless parametric oscillation with unusual spectral properties. In this work, we demonstrate experimentally and theoretically that the phase modulation of the pump is coherently transferred to the co-propagating parametric wave, while the counterpropagating wave retains a narrow bandwidth and high coherence. The main mechanisms responsible for these properties are the maximized convective separation between the counterpropagating waves and the associated phase-locking between the pump and the co-propagating parametric wave. This suggests that mirrorless optical parametric oscillators can be pumped with incoherent light and still generate highly coherent backward-propagating radiation.