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Journal of the Optical Society of America B

Optical parametric amplification by incoherent pump in the trapping regime

Viktorija Tamulienė, Paulius Stanislovaitis

Published Mar 21, 2016• 0 citations
Publisher

Abstract

Optical parametric amplification of signal and idler waves in the field of the incoherent pump is investigated. The improvement of the coherence of the amplified waves in the trapping regime is demonstrated. Numerical simulations for the experimental situation in the BBO crystal are provided. It is elucidated that the wide range of wavelengths of the interacting waves can be used.

DOI
10.1364/josab.33.000720

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Optical parametric amplification of signal and idler waves in the field of the incoherent pump is investigated. The improvement of the coherence of the amplified waves in the trapping regime is demonstrated. Numerical simulations for the experimental situation in the BBO crystal are provided. It is elucidated that the wide range of wavelengths of the interacting waves can be used.
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.
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.
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.
The consequences of the deviation from ideal coherence of the driving (pump) field in nonlinear processes are examined. A detailed treatment of the processes of parametric amplification and frequency upconversion is presented. The treatment utilizes two different approximation methods to suit the two different physical situations considered. For slow phase variations of the pump field an adiabatic approach is useful, whereas in the treatment of fast phase variations (the nonadiabatic case) an equation describing the time evolution of thePrepresentation is found to be a good starting point. In this latter case, a closed hierarchy of equations for the moments of the photon number distribution in the signal (or idler) mode is found. In particular, we find that the efficiencies of both the amplification and the upconversion processes are reduced as a result of pump incoherence, the reduction becoming more severe in the highly incoherent case. For the frequency converter, the very nature of the process is modified as compared to the ideal case, and this modification is again of particular significance for the highly incoherent pump. Second-order moments are explicitly calculated and some of the statistical properties of the output signals are examined.