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arXiv:1202.6000 · Physical Review A

Nonlinear propagation of an optical speckle field

Stanislav Derevyanko, Eran Small

Published May 14, 2012• 27 citations
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Abstract

We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010)]. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates.

DOI
10.1103/physreva.85.053816

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We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010)]. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates.
The phenomenon of random intensity patterns, for waves propagating in the presence of disorder, is well known in optics and in mesoscopic physics. We study this phenomenon for cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.
We investigate the propagation of Γˆ(x1,x2,ν) the Fourier transform of the mutual coherence function Γ(x1,x2,τ) in nonlinear dielectrics. We assume that the classical phenomenological equations govern the electric field within the dielectric, and we restrict our discussion to the propagation of fields with narrow angular spread. The indeterminate character of the propagation equations is emphasized, and it is shown that a determinate equation results only if the nonlinear term is small. In the quasimonochromatic limit, we investigate for this latter case the dependence of the two-point coherence of the second harmonic on the full fourth-order coherence of the incident beam, a result implied by Ducing and Bloembergen (1964), and Akhmanov et al. (1966). We also show under what circumstances the Hanbury-Brown and Twiss experiment may be performed using a single nonlinear dielectric.
We study the propagation of speckle patterns in a tunable nonlinear medium. Starting from a spatial pattern of photons with a normal distribution (speckle field), we characterize the evolution of the radiation to either subthermal or superthermal distributions and demonstrate the control of this evolution through a single parameter. Our experimental control of the local degree of coherence of the output photons is well described by numerical simulations that consider both dispersive and absorptive nonlinear effects. Particularly, we analyze the role of the nonlinear absorption that either enhances or competes with the dispersive effects in the evolution of speckle fields. In some realizations, an asymptotic power law is observed in the photon spatial distribution.
Significance In recent years, significant progress concerning matter–wave creation and manipulation has been achieved. Fresnel diffraction, atom lasers, and nonlinear matter wave phenomena are just a few examples of recent interesting research topics. There have also been numerous studies related to the propagation of matter waves interacting with disordered potentials, but not as many concerning the disorder existing into the matter wave itself. In the present study, we analyze the disorder imprinted into a Bose–Einstein condensate (BEC) and its characteristic spatial evolution afterward. We performed careful analyses and traced a few analogies that led us to the conclusion that the perturbed BECs evolve very much in a speckle-like manner, in close analogy with a traveling-light (optical) speckle.