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Journal of Experimental and Theoretical Physics Letters

Effect of Pump Depletion on the Spectrum of Twin Beams

Pavel A. Prudkovskii

Published Jun 1, 2018• 1 citation
Publisher

Abstract

The effect of pump depletion on the spectrum of twin beams, which appear in the process of collinear parametric down-conversion in a nonlinear crystal with an aperiodic domain structure and have a high degree of simultaneity, has been described. A system of equations describing the interaction of pump with all modes of scattered light simultaneously has been derived. It has been shown that pump depletion results in a noticeable broadening of the spectrum of twin beams for a quadratic-hyperbolic law of variation of the reciprocal lattice vector of the domain structure. The effect of narrowing of the coherent peak in the sum-frequency generation signal from twin beams has been demonstrated. This effect increases as the pump is depleted.

DOI
10.1134/s0021364018120123

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The effect of pump depletion on the spectrum of twin beams, which appear in the process of collinear parametric down-conversion in a nonlinear crystal with an aperiodic domain structure and have a high degree of simultaneity, has been described. A system of equations describing the interaction of pump with all modes of scattered light simultaneously has been derived. It has been shown that pump depletion results in a noticeable broadening of the spectrum of twin beams for a quadratic-hyperbolic law of variation of the reciprocal lattice vector of the domain structure. The effect of narrowing of the coherent peak in the sum-frequency generation signal from twin beams has been demonstrated. This effect increases as the pump is depleted.
The shape and propagation velocities of pulsed twin beams generated in the process of parametric light down-conversion have been theoretically studied in the case where the delays caused by the dispersion of group velocities exceed the length of a pump pulse. It has been shown that the effective group velocity of the scattered pulse is determined by the arithmetic mean of the group velocities at the scattered radiation and pump frequencies. The scattering matrix elements for the large parametric gain have been numerically found. It has been shown that mixing of the spectral components of scattered radiation can cause a significant narrowing of the twin beam pulses. Finally, for the case of generation of broadband twin beams sequentially in two crystals with an aperiodic domain structure, it has been shown that the visibility of the three-frequency interference decreases as the pump pulse lags behind the scattered radiation pulses.
It is well known that optical twin-beam states (TWB) generated by spontaneous parametric down-conversion (PDC) exhibit spatial and spectral correlations, which can appear in single-shot images obtained by using an imaging spectrometer to resolve emission angles and wavelengths simultaneously. By analyzing series of single-shot images recorded by an EMCCD camera at different powers of the pump beam, we studied the evolution of several quantities characterizing the generated TWB. In particular, we demonstrated that correlation widths in spectrum and space increase monotonically at low pump powers and then start decreasing at higher powers due to the onset of pump depletion. In a complementary way, the Fedorov ratio decreases and then increases again. At the same time, the number of modes evaluated from photon statistics follows a complementary behavior to correlation widths that can be interpreted in terms of the evolution of the number of Schmidt modes in the field.
Abstract Properties of intense twin beams generated in parametric down-conversion in periodically poled LiNbO3 crystals and their chirped variants by intense pump fields are analyzed along the model of intense parametric down-conversion that allows for pump depletion and uses the dual spatio-spectral Schmidt modes. Spectral and spatial intensity auto- and cross-correlation functions are determined as they depend on the pump power. Temporal correlations in intense twin beams at the fs time scale are investigated using the Hong-Ou-Mandel interferometer and the process of sum-frequency generation.
Using the model of parametric interaction based on the spatiospectral Schmidt modes and generalized parametric approximation, we analyze coherence and the mode structure of ultraintense twin beams generated in the regime with pump depletion. We show that the increase of spatial and spectral coherence with the increasing pump power observed for moderate powers is replaced by a decrease for the pump powers at which pump depletion occurs. This behavior of coherence is opposed to that exhibited by a number of spatiospectral modes effectively constituting the twin beam. The conditions for maximal coherence are analyzed by considering pump-beam parameters (spectral width and transverse radius). The existence of additional coherence maxima occurring at even higher pump powers is predicted and explained by the oscillatory evolution of the modes' populations.
We present the experimental investigation of the coherence properties of the light produced by parametric down conversion in the macroscopic regime, also including pump depletion. In particular, we compare the results obtained in very similar geometric conditions by using two nonlinear crystals having different lengths. We observe that the number of generated photons, the size of spatio-spectral coherence areas, and the number of modes in the photon number statistics exhibit a similar behavior in the two crystals as a function of pump mean power, even if we notice that the absolute values are different. The available theory of parametric down conversion cannot account for these differences.
Twin-beam coherence properties are analyzed in both spatial and spectral domains at high gain, including also the regime of pump depletion. We show an increase in the size of the intensity autocorrelation and cross-correlation areas at increasing pump power, replaced by a decrease in the pump depletion regime. This effect is interpreted as a progressive loss in the mode selection occurring at high-gain amplification. The experimental determination of the number of spatiospectral modes from the measurements of the g(2){g}^{(2)}g(2)-intensity autocorrelation coefficient confirms this explanation.