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Scientific Reports

Waves in spatio-spectral and -temporal coherence of evolving ultra-intense twin beams

Jan Peřina

Published Mar 12, 2019• 6 citations
Publisher

Abstract

Waves in the spatio-spectral and -temporal coherence of evolving ultra-intense twin beams are predicted: Twin beams with low intensities attain maximal coherence in the beam center until certain threshold intensity is reached. Then the area of maximal coherence moves with increasing intensity from the beam center towards its edges leaving the beam center with low coherence (the first coherence wave). For even larger intensities, a new coherence maximum is gradually built in the beam center with the increasing intensity and, later, it again moves towards the beam edges forming the second coherence wave. Rotationally-symmetric twin beams are analyzed within a three-dimensional model that couples spectral and spatial degrees of freedom. Relation between the twin-beam coherence and its local density of modes during the nonlinear evolution is discussed.

DOI
10.1038/s41598-019-39482-x

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Scientific Reports•Feb 29, 2016•19 citations
Waves in the spatio-spectral and -temporal coherence of evolving ultra-intense twin beams are predicted: Twin beams with low intensities attain maximal coherence in the beam center until certain threshold intensity is reached. Then the area of maximal coherence moves with increasing intensity from the beam center towards its edges leaving the beam center with low coherence (the first coherence wave). For even larger intensities, a new coherence maximum is gradually built in the beam center with the increasing intensity and, later, it again moves towards the beam edges forming the second coherence wave. Rotationally-symmetric twin beams are analyzed within a three-dimensional model that couples spectral and spatial degrees of freedom. Relation between the twin-beam coherence and its local density of modes during the nonlinear evolution is discussed.
Spatiospectral properties of twin beams at their transition from low to high intensities are analyzed in parametric and paraxial approximations using decomposition into paired spatial and spectral modes. Intensity auto- and cross-correlation functions are determined and compared in the spectral and temporal domains as well as the transverse wave-vector and crystal output planes. Whereas the spectral, temporal, and transverse wave-vector coherence increases with the increasing pump intensity, coherence in the crystal output plane is almost independent of the pump intensity owing to the mode structure in this plane. The corresponding auto- and cross-correlation functions approach each other for larger pump intensities. The entanglement dimensionality of a twin beam is determined with a comparison of several approaches.
Strong correlations between the signal and idler beams imprinted during their generation dominantly determine the properties of twin beams. They are also responsible for the waves in intensity coherence observed in the wave-vector space of a twin beam propagating in a nonlinear crystal in the regime with pump depletion. These waves start to develop at certain twin-beam intensities and move from the signal- and idler-beam centers towards their tails. They manifest themselves via the change of coherence volume monitored in the far field by the measurement of local modified g‾(2){\overline{g}}^{(2)}g​(2) function, which acts as a sensitive and stable tool for investigating field intensity coherence.
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.
Spatial and spectral coherence of high-intensity twin-beam states propagating from the near-field to the far-field configurations is experimentally investigated by measuring intensity auto- and cross-correlation functions. The experimental setup includes a moving crystal and an iCCD camera placed at the output plane of an imaging spectrometer. Evolution from the tight near-field spatial position cross-correlations to the far-field momentum cross-correlations, accompanied by changeless spectral cross-correlations, is observed. Intensity autocorrelation functions and beam profiles are also monitored as they provide the number of degrees of freedom constituting the down-converted beams. The strength of intensity cross-correlations as an alternative quantity for the determination of the number of degrees of freedom is also measured. The relation between the beam coherence and the number of degrees of freedom is discussed.
The dynamics of intense twin beams in pump-depleted parametric down-conversion is studied. A generalized parametric approximation is suggested to solve the quantum model. Its comparison with a semiclassical model valid for larger twin-beam intensities confirms its applicability. The experimentally observed maxima in the spectral and spatial intensity auto- and cross- correlation functions depending on pump power are explained in terms of different speeds of the (back-) flow of energy between the individual down-converted modes and the corresponding pump modes. This effect is also responsible for the gradual replacement of the initial exponential growth of the down-converted fields by the linear one. Furthermore, it forms a minimum in the curve giving the effective number of twin-beam modes. These effects manifest a tight relation between the twin-beam coherence and its internal structure, as clearly visible in the model. Multiple maxima in the intensity correlation functions originating in the oscillations of energy flow between the pump and down-converted modes are theoretically predicted.