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arXiv:1911.08694 · Physical Review A

Photon statistics of quantum light on scattering from rotating ground glass

Sheng-Wen Li, Fu Li, Tao Peng, G. S. Agarwal

Published Jun 2, 2020• 13 citations
arXivHTMLPDF

Abstract

When a laser beam passes through a rotating ground glass (RGG), the scattered light exhibits thermal statistics. This is extensively used in speckle imaging. This scattering process has not been addressed in the photon picture and is especially relevant if nonclassical light is scattered by the RGG. We develop the photon picture for the scattering process using the Bose statistics for distributing $N$ photons in $M$ pixels. We obtain an analytical form for the $P$ distribution of the output field in terms of the $P$ distribution of the input field. In particular, we obtain a general relation for the $n\mathrm{th}$-order correlation function of the scattered light, i.e., ${g}_{\text{out}}^{(n)}\ensuremath{\simeq}n!\phantom{\rule{0.16em}{0ex}}{g}_{\text{in}}^{(n)}$, which holds for any order $n$ and for arbitrary input states. This result immediately recovers the classical transformation of coherent light to pseudothermal light by RGG.

DOI
10.1103/physreva.101.063806

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When a laser beam passes through a rotating ground glass (RGG), the scattered light exhibits thermal statistics. This is extensively used in speckle imaging. This scattering process has not been addressed in the photon picture and is especially relevant if nonclassical light is scattered by the RGG. We develop the photon picture for the scattering process using the Bose statistics for distributing NNN photons in MMM pixels. We obtain an analytical form for the PPP distribution of the output field in terms of the PPP distribution of the input field. In particular, we obtain a general relation for the nthn\mathrm{th}nth-order correlation function of the scattered light, i.e., gout(n)\ensuremath≃n!gin(n){g}_{\text{out}}^{(n)}\ensuremath{\simeq}n!\phantom{\rule{0.16em}{0ex}}{g}_{\text{in}}^{(n)}gout(n)​\ensuremath≃n!gin(n)​, which holds for any order nnn and for arbitrary input states. This result immediately recovers the classical transformation of coherent light to pseudothermal light by RGG.
Superbunching pseudothermal light has important applications in studying the second- and higher-order interference of light in quantum optics. Unlike the photon statistics of thermal or pseudothermal light is well understood, the photon statistics of superbunching pseudothermal light has not been studied yet. In this paper, we will employ single-photon detectors to measure the photon statistics of superbunching pseudothermal light and calculate the degree of second-order coherence. It is found that the larger the value of the degree of second-order coherence of superbunching pseudothermal light is, the more the measured photon distribution deviates from the one of thermal or pseudothermal light in the tail part. The results are helpful to understand the physics of two-photon superbunching with classical light. It is suggested that superbunching pseudothermal light can be employed to generate non-Rayleigh temporal speckles.
We report some experimental results concerning the statistical properties of a light beam scattered by a rotating ground glass with average-size inhomogeneities of approximately 1 μm. Photocount statistics measured at different scattering angles and for different angular velocities of the ground glass have confirmed the known result that the scattered-light amplitude is a stochastic gaussian variable. The Bose–Einstein nature of the photocount statistics has been verified with an accuracy of a few parts per thousand. Self-beating measurements on the scattered light of a He–Ne laser in a TEM00 configuration have shown that the power spectrum is a gaussian function of the frequency. The dependence of its half-width on the angular velocity of the ground glass and on the focal length of the lens that focuses the beam on the scattering surface has been measured. The experimental results agree very closely with our theoretical predictions.
Several imaging techniques, such as ghost imaging, are based on the use of classical and quantum correlated light states. This fact has encouraged the search for new strategies to produce light states more correlated than the thermal states that are typically used. In this work, we produce and characterize classical states of light with “more than thermal” statistics. Such states are obtained by means of a sequence of two rotating ground-glass disks and by appropriately selecting the speckle field produced at the output of each disk. The experimental results are in excellent agreement with the developed theoretical model, suggesting the potential of this kind of light for imaging applications.
Pseudothermal light exhibits photon bunching, like thermal light, but it does not originate from randomly phased emission. As photon bunching is common in both pseudothermal and thermal light, the analysis of photon bunching is insufficient to differentiate pseudothermal light and thermal light. However, thermal light obeys the Siegert relation, which connects the interferometric visibility ∥g(1)(τ )∥ and second-order photon correlation g(2)(τ ). In this work, we present a direct test test for Siegert relation by a single-shot measurement. Using our technique, we demonstrate that laser light scattered off a rotating ground glass, violates the Siegert relation, which provides further evidence that it is a pseudothermal light source.
Microscopic scattering processes are discussed for two structures of light incident on thermal particles. One is composed of two collinear light beams originating from different oscillating modes of a laser, and another is composed of two counter propagating beams originating from the same oscillating mode. A comparison of the cumulant expansions for the above two cases has allowed discerning which terms in the scattering structures led to the same statistical properties of the scattered photons. It is shown that, for the scattering of multimode-laser light, the statistical properties of scattered photons are not affected by the noncorrelating random phases of the incident laser fields but are the same as those in the case of single-mode laser light under practical scattering experiments. The factorial moments ${F}_{k}[=〈n(n\ensuremath{-}1)\ensuremath{\cdots}(n\ensuremath{-}k+1)〉]$ up to sixth order of the scattered photons were measured for various scattering situations including the above two cases, and they were found to support the theoretical results.
The theoretical dependence of optical birefringence phenomena on the statistical nature of the light is investigated. Photon S-matrix calculations lead to expressions relating the change induced in the statistical nature of the beam to the molecular properties of the target sample. A hypothetical generalized optical birefringence experiment is analysed: in the experiment the coincidences of photons arriving at spatially separated detectors sensitive to different polarizations are observed with and without the sample in the beam, and the difference in the photon correlations depend on the initial statistical composition and polarization of the beam and the molecular properties of the sample. When the beam is generated by a thermal source the difference of the signals (with and without the sample) depends on the product of the polarizability and optical rotation tensors. When the light is generated by a single-mode coherent source the statistical properties of the light are such as to eliminate the second-order interaction terms, and so the experiment yields the hyperpolarizability and hyper-rotation tensors automatically and with the explicit exclusion of the polarization and rotation tensor contributions.