Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Photoelectron statistics and autocorrelation of Rayleigh scattering

T. Aoki, Yutaka Okabe, Kenji Sakurai

Published Jul 1, 1974• 8 citations
Publisher

Abstract

The statistics and autocorrelation function of the light scattered from polystyrene latex have been studied with a light-detecting system on-line with a small digital computer. The distributions of photoelectric counts have been measured during count intervals from 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ to 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ sec. The results were well accounted for by the approximate theory of Mandel. The factorial moments have been measured to sixth order and the results were in excellent agreement with theoretical calculations. For the first time, we have directly measured the autocorrelation function without using a clipping or scaling method. With this direct method, the comparison between the results of the composite measurements and the theoretical predictions can be quantitatively discussed.

DOI
10.1103/physreva.10.259

Related papers

Photoelectron statistics and autocorrelation of a mixture of chaotic and coherent light of same and different frequencies

T. Aoki, Y. Endo, Hiromitsu Takayanagi +1 more

The statistics and autocorrelation function of Rayleigh-scattered light mixed with coherent light were experimentally studied. The factorial moments were measured for the cases of both heterofrequencies and homofrequencies. In the case of heterofrequencies, the mean frequency of the scattered light was shifted from that of the coherent light by using a flowing scatterer. The second- and third-order factorial moments obtained were compared with the theory of Jaiswal and Mehta and were found to be experimental proof for the theory. The autocorrelation function was also measured in the case of a heterofrequency, and the result was explained well by the theoretical expression deduced here.

Physical Review A•Feb 1, 1976•4 citations

Photon statistics of partially polarized Gaussian light

Tadashi Aoki, Katsumi Sakurai

Statistical properties of partially polarized Gaussian light were studied experimentally for degrees of polarization $P$ 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.

Physical Review A•Oct 1, 1979•5 citations

Third-Order Temporal Correlation of Rayleigh Scattering

Yutaka Okabe, Tadashi Aoki, Katsumi Sakurai

The third-order correlation properties of the integrated intensity of a Rayleigh scattering are discussed. The third-order temporal cumulant of the Rayleigh scattered light from polystyrene latex has been measured with a computer-controlled data acquisition system. The results of the experiment are in good agreement with the theoretical predictions.

Journal of the Physical Society of Japan•Mar 15, 1976•3 citations

ON THE DETERMINATION OF THE STATISTICAL PROPERTIES OF LIGHT FROM PHOTOELECTRIC MEASUREMENTS

J. PEf Ina

A relation is derived between the probability distribution of the integrated intensity of light incident on a photoelectric detector and that of the emission of n photoelectrons in a time interval (t, t + T) from the properties of a quantized electromagnetic field. Both the direct and the inverse relations are derived, thereby enabling the statistical properties of light to be determined from photoelectric measurements. An explicit expression is given for the coefficients for calculating the moments ( W k) by means of the moments (n J) (] = 1, 2 ..... k). The correctness of the operations in which generalized functions occur is confirmed by some direct calculations. The significance of photoelectric detectors has been increasing of late. Since their response is proportional to the intensity of incident light (to the square of the amplitude of light) (more exactly, to the local mean time value of the intensity), one speaks of quadratic detectors. These detectors are of basic importance in the theory of the coherence of the electromagnetic field, since if we place N such detectors into N different points in space and if we lead the outputs of these detectors to the correlator we can measure the correlation (coherence) effects of the 2N-th order in the given field [1]. Such correlation measurements provide information on the energy distribution in the radiation spectrum [2], the angular dimensions of stars [3], and the state of polarization [4] and also enable the phase of physically important functions (e.g. the scattering amplitudes) [5] to be determined. Although in such experiments the properties of photoelectrons are studied rather than of photons, they reflect the basic properties of photons. Let the probability distribution Of the emission of n photoelectrons in a time interval (t, t + T) be p(n, T, t) - p(n) and let the probability distribution of the quantity W(T, t) = W = J'tt+r I(t') dr', where I(t) is the intensity of linearly polarized light incident on the photodetector (for simplicity we assume that the sensitivity of the photocathode is a = 1), be P(W). The quantity W can be regarded as a classical characteristic of the field, the quantity n represents the quantum characteristic of the field. Then, on the basis of such a semi-classical description, in which the field is described classically, but its interaction is described quantum-wise, one can derive the following relation [6]

•Jan 1, 1967•1 citation

Photoelectron Counting Statistics of Laser Light Scattered by Very Dilute Solution

Manabu Yoshikawa, Norihito Suzuki, Tatsuro Suzuki

The photon counting statistics of light is studied, in which the various types of photon counting distribution can be represented by Nakagami'sm-distribution. To investigate this theoretical utility we have measured the photon counting distribution of laser light scattered by a very dilute solution in which non-Gaussian statistics appear. The comparison is also made by the factrial moment between the experimental value and theoretical one. The experimental distribution is in agreement with the theoretical distribution.

Japanese Journal of Applied Physics•Mar 1, 1981•3 citations

Photoelectron Counting Statistics of Light Transmitted through Multimode Optical Fiber

Manabu Yoshikawa, Norihito Suzuki, Tatsuro Suzuki

The photon counting statistics of light transmitted through multimode optical fiber are studied. We have measured the intensity correlation function of light scattered by polystyrene particles suspended in water using transmitted He–Ne laser light. The coherence characteristics are degraded for long fiber and also fluctuations in the intensity occur. The experimental distribution is represented well by the theoretical distribution. The intensity fluctuation is reduced when an incoherent light source is used.

Japanese Journal of Applied Physics•Mar 1, 1982•4 citations
The statistics and autocorrelation function of the light scattered from polystyrene latex have been studied with a light-detecting system on-line with a small digital computer. The distributions of photoelectric counts have been measured during count intervals from 5 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−5{10}^{\ensuremath{-}5}10\ensuremath−5 to 5 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−3{10}^{\ensuremath{-}3}10\ensuremath−3 sec. The results were well accounted for by the approximate theory of Mandel. The factorial moments have been measured to sixth order and the results were in excellent agreement with theoretical calculations. For the first time, we have directly measured the autocorrelation function without using a clipping or scaling method. With this direct method, the comparison between the results of the composite measurements and the theoretical predictions can be quantitatively discussed.
The statistics and autocorrelation function of Rayleigh-scattered light mixed with coherent light were experimentally studied. The factorial moments were measured for the cases of both heterofrequencies and homofrequencies. In the case of heterofrequencies, the mean frequency of the scattered light was shifted from that of the coherent light by using a flowing scatterer. The second- and third-order factorial moments obtained were compared with the theory of Jaiswal and Mehta and were found to be experimental proof for the theory. The autocorrelation function was also measured in the case of a heterofrequency, and the result was explained well by the theoretical expression deduced here.
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.
A relation is derived between the probability distribution of the integrated intensity of light incident on a photoelectric detector and that of the emission of n photoelectrons in a time interval (t, t + T) from the properties of a quantized electromagnetic field. Both the direct and the inverse relations are derived, thereby enabling the statistical properties of light to be determined from photoelectric measurements. An explicit expression is given for the coefficients for calculating the moments ( W k) by means of the moments (n J) (] = 1, 2 ..... k). The correctness of the operations in which generalized functions occur is confirmed by some direct calculations. The significance of photoelectric detectors has been increasing of late. Since their response is proportional to the intensity of incident light (to the square of the amplitude of light) (more exactly, to the local mean time value of the intensity), one speaks of quadratic detectors. These detectors are of basic importance in the theory of the coherence of the electromagnetic field, since if we place N such detectors into N different points in space and if we lead the outputs of these detectors to the correlator we can measure the correlation (coherence) effects of the 2N-th order in the given field [1]. Such correlation measurements provide information on the energy distribution in the radiation spectrum [2], the angular dimensions of stars [3], and the state of polarization [4] and also enable the phase of physically important functions (e.g. the scattering amplitudes) [5] to be determined. Although in such experiments the properties of photoelectrons are studied rather than of photons, they reflect the basic properties of photons. Let the probability distribution Of the emission of n photoelectrons in a time interval (t, t + T) be p(n, T, t) - p(n) and let the probability distribution of the quantity W(T, t) = W = J'tt+r I(t') dr', where I(t) is the intensity of linearly polarized light incident on the photodetector (for simplicity we assume that the sensitivity of the photocathode is a = 1), be P(W). The quantity W can be regarded as a classical characteristic of the field, the quantity n represents the quantum characteristic of the field. Then, on the basis of such a semi-classical description, in which the field is described classically, but its interaction is described quantum-wise, one can derive the following relation [6]
The photon counting statistics of light is studied, in which the various types of photon counting distribution can be represented by Nakagami'sm-distribution. To investigate this theoretical utility we have measured the photon counting distribution of laser light scattered by a very dilute solution in which non-Gaussian statistics appear. The comparison is also made by the factrial moment between the experimental value and theoretical one. The experimental distribution is in agreement with the theoretical distribution.
The photon counting statistics of light transmitted through multimode optical fiber are studied. We have measured the intensity correlation function of light scattered by polystyrene particles suspended in water using transmitted He–Ne laser light. The coherence characteristics are degraded for long fiber and also fluctuations in the intensity occur. The experimental distribution is represented well by the theoretical distribution. The intensity fluctuation is reduced when an incoherent light source is used.