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Physical Review A

Parametric amplification in the field of incoherent light

V. Pyragaitė, A. Stabinis, A. Piskarskas, V. Smilgevičius

Published Jun 7, 2013• 7 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.87.063809

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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.
We present analytical solutions to nonlinear coupling equations for parametric down-conversion of a broadband pump at large gain. The feasibility of analytical expressions is demonstrated for the case of a collinear type II parametric interaction in beta-barium borate crystal and group-velocity matching of signal and pump waves. The correlation function of amplified signal wave is obtained, and it is revealed that the bandwidth of a noise-seeded optical parametric amplifier increases with a decrease in pump pulse duration, especially for femtosecond pump pulses.
An approximate theory of parametric amplification and stimulated Raman scattering is developed for a pumping field which is incoherent in terms of the transverse coordinates and time. Expressions are obtained for the increments of the average field and the conditions of validity of the obtained expressions are determined. It is shown, in particular, that if the longitudinal length of the correlation between the pump radiation and the signal wave is small in comparison with the length of correlation of this radiation with the idler wave, then the employed approximation describes with sufficient accuracy the transition from the case of δ-correlated pumping (incoherent interaction) to the case when the gain achieved in a distance equal to the correlation length of the pump and idler waves exceeds unity (quasicoherent interaction). The intensity increment is then close to double the increment of the average field or the signal wave. In addition, for the indicated ratio of the correlation lengths, it is relatively easy to calculate the correlation function at a distance from the point of entry into a crystal, which is short but sufficient for an appreciable gain. Analogous conclusions hold also for stimulated Raman scattering in a pumping field with a spectral width exceeding the spontaneous-scattering linewidth.
We study the influence of group-velocity dispersion (or diffraction) on the coherence properties of the parametric three-wave interaction driven from an incoherent pump wave. We show that, under certain conditions, the incoherent pump may efficiently amplify a signal wave with a high degree of coherence, in contrast with the usual kinetic description of the incoherent three-wave interaction. The group-velocity dispersion is shown to be responsible for a spectral filtering process, in which the coherence of the generated signal increases, as the coherence of the pump wave decreases. As a result, the coherence acquired by the signal in the presence of an incoherent pump, is higher than that acquired in the presence of a fully coherent pump. The mechanism underlying this intriguing result is based on the emergence of a mutual coherence between the incoherent pump and the generated idler wave. We calculate explicitly the degree of mutual coherence between the pump and idler waves and show that the two incoherent waves become completely correlated in the full incoherent regime of interaction. The theory is in quantitative agreement with the numerical simulations. To motivate the experimental confirmation of our theory, we characterize the dispersion properties of an actual quadratic nonlinear optical crystal in which the process of signal coherence enhancement induced by pump incoherence may be studied experimentally.