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Physical Review A

Exact solutions for non-Rayleigh nondiffracting speckles

José G. M. N. Neto, E. J. S. Fonseca, Alcenísio J. Jesus‐Silva

Published Nov 28, 2022• 6 citations
Publisher

Abstract

We report on a speckle field that is non-Rayleigh, nondiffracting, and an exact solution to the scalar Helmholtz equation. We have shown that these fields can be directly optimized to a continuous range of contrast values corresponding to the sub-Rayleigh or super-Rayleigh statistics maintaining its nondiffracting characteristics. Besides, this work extends the range of non-Rayleigh statistics of nondiffracting fields, which may find many applications in the areas of solid-state physics, cold atoms, and optical imaging.

DOI
10.1103/physreva.106.053519

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We report on a speckle field that is non-Rayleigh, nondiffracting, and an exact solution to the scalar Helmholtz equation. We have shown that these fields can be directly optimized to a continuous range of contrast values corresponding to the sub-Rayleigh or super-Rayleigh statistics maintaining its nondiffracting characteristics. Besides, this work extends the range of non-Rayleigh statistics of nondiffracting fields, which may find many applications in the areas of solid-state physics, cold atoms, and optical imaging.
Abstract Classical correlation of Rayleigh speckle fields E ( x ) can only mimic second-order correlation in quantum imaging. Here, we propose a method to explore the high-order correlation of non-Rayleigh speckle fields E N ( x ) which shows a totally different property from the Rayleigh speckle fields. As a specific example, we illustrate and analyze in detail the third-order speckle scanning imaging which overcomes the diffraction barrier by a factor of 3 . The influences of diffractions in the illumination path and the detection path are also discussed. This investigation may pave the way for applications in super-resolution imaging.
The irradiation of a dilute cloud of cold atoms with a coherent light field produces a random intensity distribution known as laser speckle. Its statistical fluctuations contain information about the mesoscopic scattering processes at work inside the disordered medium. Following up on earlier work by Assaf and Akkermans [Phys. Rev. Lett. 98, 083601 (2007)], we analyze how static speckle-intensity correlations are affected by an internal Zeeman degeneracy of the scattering atoms. It is proven on general grounds that the speckle correlations cannot exceed the standard Rayleigh law. On the contrary, because which-path information is stored in the internal atomic states, the intensity correlations suffer from strong decoherence and become exponentially small in the diffusive regime applicable to an optically thick cloud.
We consider estimating the length of an incoherently radiating quasimonochromatic extended object of length much smaller than the traditional diffraction limit, the Rayleigh length. This is the simplest abstraction of the problems of estimating the diameter of a star in astronomical imaging or the dimensions of a cellular feature in biological imaging. We find, as expected by the Rayleigh criterion, that the Fisher information (FI) of the object's length, per integrated photon, vanishes in the limit of small sub-Rayleigh length for an ideal image-plane direct-detection receiver. With an image-plane Hermite-Gaussian (HG) mode sorter followed by direct detection, we show that this normalized FI does not diminish with decreasing object length. The FI per photon of both detection strategies gradually decreases as the object length greatly exceeds the Rayleigh limit, due to the relative inefficiency of information provided by photons emanating from near the center of the object about its length. We evaluate the quantum Fisher information per unit integrated photon and find that the HG mode sorter exactly achieves this limit at all values of the object length. Further, a simple binary mode sorter maintains the advantage of the full mode sorter at highly sub-Rayleigh lengths. In addition to this FI analysis, we quantify improvement in terms of the actual mean-square error of the length estimate using predetection mode sorting. We consider the effect of imperfect mode sorting and show that the performance improvement over direct detection is robust over a range of sub-Rayleigh lengths.