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Journal of physics. A, Proceedings of the Physical Society. General

Statistics of heterodyction of Gaussian light

Eric Jakeman, Edward R. Pike

Published Jan 1, 1968• 59 citations
Publisher

Abstract

Discusses the statistical properties of the intensity fluctuations of light fields consisting of an incoherent Gaussian component heterodyned with a single-frequency coherent beam. The second moment of the intensity- fluctuation distribution is obtained in an analytic form for a Lorentzian incoherent spectrum for arbitrary values of the bandwidth and frequency displacement from the coherent mode. The analysis includes as special cases many of the exact results obtained in statistical optics over the last decade.

DOI
10.1088/0305-4470/2/1/016

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A QUANTUM STATISTICAL ANALYSIS OF A FREQUENCY MODULATED LASER COMMUNICATION SYSTEM.

Neil F. Ruggieri

In this analysis the quantum statistics of the received signal of a frequency modulated laser communication system are derived. In particular the detection statistics for heterodyne and electric field detection of the frequency modulated laser beam are determined. These detection statistics are used to define a measure of the communication system performance in terms of a signal to noise ratio. The development of the quantum electromagnetic field in terms of the photon annihilation eigenstates is the basis for determining these statistics. The derivation used accounts for fluctuations in the carrier, fluctuations due to background radiation introduced after modulation, fluctuations due to the local laser oscillator, and zero point field fluctuations. The results of this analysis indicate the probability distribution for the optical heterodyne detection is not a familiar one of classical communication theory, but it is of the form of probability distribution that satisfies experimentally measured photocount statistics of unmodulated laser radiation. The probability distribution for the electric field intensity detection of the frequency modulated laser beam is the familiar Gaussian distribution. (Author)

•Apr 30, 1967•1 citation
Discusses the statistical properties of the intensity fluctuations of light fields consisting of an incoherent Gaussian component heterodyned with a single-frequency coherent beam. The second moment of the intensity- fluctuation distribution is obtained in an analytic form for a Lorentzian incoherent spectrum for arbitrary values of the bandwidth and frequency displacement from the coherent mode. The analysis includes as special cases many of the exact results obtained in statistical optics over the last decade.
Recently derived formulae for the integrated intensity distribution, the photon-counting distribution and its factorial moments in the statistics of the superposition of coherent and chaotic multimode fields are proposed as approximate formulae for light of arbitrary spectrum. It is shown by explicit calculations of the third factorial moment for the superposition of a one-mode coherent field with a Gaussian-Lorentzian field that the proposed formulae hold with good accuracy over a wide range of conditions. An application to the determination of spectral parameters of light is given.
Intensity fluctuations arising from a random walk in 2α dimensions are governed by the gamma-distribution of parameter α. When 2α is fractional, conventional methods of calculating statistical properties of the integrated intensity, based on a gaussian noise theory approach, can no longer be used. In this paper the single interval statistics of an integrated gamma-distributed variable with lorentzian spectrum are derived directly from a rate equation for the process. The results include, as a special case, the integrated photon statistics predicted by a model for single-mode thermal radiation in a cavity.
We calculate the intensity fluctuations of the light transmitted by a Fabry-P\'erot interferometer when a broadband laser is incident upon it. The laser field is assumed to have a Lorentzian spectrum and to be broadened by random amplitude fluctuations (real or complex) or random frequency fluctuations. In each case we obtain closed-form expressions for the intensity autocorrelation function, from which we can obtain the magnitude of the intensity fluctuations, as well as the power spectrum. These results indicate a strong dependence of the transmitted intensity fluctuations on the higher-order statistical properties of the incident field. Agreement with similar results concerning atomic fluorescence fluctuations is very good.
We study the photocounting statistics and the integrated intensity distribution of partially polarized Gaussian light. Expressions for the characteristic functions of the two distributions are obtained in terms of the eigenvalues of an associated integral equation. Closed-form expressions for these characteristic functions are derived for the special case when the spectral profile of the light is Lorentzian. Results from a numerical evaluation of the factorial moments of the number of photoelectrons in a given time interval and of the integrated intensity distribution are also presented.
In this analysis the quantum statistics of the received signal of a frequency modulated laser communication system are derived. In particular the detection statistics for heterodyne and electric field detection of the frequency modulated laser beam are determined. These detection statistics are used to define a measure of the communication system performance in terms of a signal to noise ratio. The development of the quantum electromagnetic field in terms of the photon annihilation eigenstates is the basis for determining these statistics. The derivation used accounts for fluctuations in the carrier, fluctuations due to background radiation introduced after modulation, fluctuations due to the local laser oscillator, and zero point field fluctuations. The results of this analysis indicate the probability distribution for the optical heterodyne detection is not a familiar one of classical communication theory, but it is of the form of probability distribution that satisfies experimentally measured photocount statistics of unmodulated laser radiation. The probability distribution for the electric field intensity detection of the frequency modulated laser beam is the familiar Gaussian distribution. (Author)