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Physical Review A

Photon statistics of multimode-laser light scattered by thermal particles

Tadashi Aoki, Katsumi Sakurai

Published Aug 1, 1980• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.22.684

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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 Fk[=〈n(n\ensuremath−1)\ensuremath⋯(n\ensuremath−k+1)〉]{F}_{k}[=〈n(n\ensuremath{-}1)\ensuremath{\cdots}(n\ensuremath{-}k+1)〉]Fk​[=〈n(n\ensuremath−1)\ensuremath⋯(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.
Statistical properties of partially polarized Gaussian light were studied experimentally for degrees of polarization PPP from 0.03 to 1 by a standard technique of photon counting. The Gaussian light with an arbitrary degree of polarization was obtained from Rayleigh scattering of orthogonally polarized laser beams. The factorial moments up to sixth order of the photoelectron distribution were measured with an arbitrary temporal and spatial coherence. After corrections were taken for the experimental conditions, the theoretical values of these factorial moments were compared with the experimental results. It is shown that the theoretical predictions were quantitatively well verified by the present measurements. The microscopic process is discussed from the standpoint of the light scattering system used in the present measurements, and it is shown that the orthogonally polarized components of the scattered light observed are statistically independent.
The structure of a liquid can be investigated through the photostatistics of scattered light. A theoretical approach is given in which the deviation from the Poisson distribution, followed by the photons of a single-mode laser beam, is connected with the two- and four-particle distribution functions of the scattering medium. In particular, the presence of the Mandelstam-Brillouin doublet is put into evidence through the time behavior of a non-Poissonian statistical term, by using an explicit form of the two-particle correlation function.
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.
The fluctuation and correlation properties of light scattered by a fluid are studied, without neglect of the spectral linewidth of the incident field. When the source is a single-mode laser, it is shown that, although the instantaneous amplitude of the scattered field obeys a Gaussian probability density, the scattered field is not a Gaussian field. The linewidth of the laser beam is reflected in the amplitude correlations of the scattered light, but not in the intensity correlations. On the other hand, when the laser is oscillating in more than one mode simultaneously, the spectral profile of the laser beam makes a contribution to the spectral density of the scattered intensity fluctuations, and cannot be neglected.
Results were recently reported on statistical properties of phase-modulated laser light. A detailed analysis is presented here of random-phase modulation. In particular it is shown that there are two kinds of such modulation: modulation by phase fluctuations, in which the instantaneous phase is a stationary stochastic process, and modulation by phase diffusion in which the phase is a diffusion process with an always increasing variance. In the case of a Gaussian modulation we show that the optical fields in the two preceding cases are very different, and we calculate their coherence functions. This difference can be detected by an interference experiment, but more easily by photon coincidence or intensity-correlation experiments on a beat between a reference beam and the modulated beams. We present a theoretical analysis of such experiments in the two cases of modulation.
The paper contains a quantum theoretical analysis of laser beam fluctuations and of the light beat experiments with two lasers. With the help of experimental results on photon counting fluctuations in a single-mode laser field, some correlation properties of the field are derived. It is shown that the correlation equations are satisfied by states of the field which are much more general than "coherent" states. The equations lead directly to the spectral density of the intensity operator in the light beat experiments, which can be obtained from photoelectric measurements. The resulting expression is practically identical to that found by Forrester for light having thermal statistical properties. The reasons for this are discussed by a comparison of the corresponding probability distributions of photon counts and of the classical wave amplitude.