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Japanese Journal of Applied Physics

Factorial Moment of Two Poissonian Lights Superposed on Gaussian-Lorentzian Light

Hideaki Satō, Norihito Suzuki

Published Jun 1, 1981• 0 citations
Publisher

Abstract

A photon counting method is adapted to spectroscopy in very low intensity, as it is useful for data acquisition. There are two Poissonian lights which cannot be discriminated by this method. One is coherent light, and the other is Gaussian-Lorentzian light with infinite spectral linewidth. In this experiment, Gaussian-Lorentzian light with finite spectral linewidth was superposed on each Poissonian light, and the difference of the two radiation mechanisms was determined by profiles of the second-order factorial moment of the photon counting distribution.

DOI
10.1143/jjap.20.1055

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A photon counting method is adapted to spectroscopy in very low intensity, as it is useful for data acquisition. There are two Poissonian lights which cannot be discriminated by this method. One is coherent light, and the other is Gaussian-Lorentzian light with infinite spectral linewidth. In this experiment, Gaussian-Lorentzian light with finite spectral linewidth was superposed on each Poissonian light, and the difference of the two radiation mechanisms was determined by profiles of the second-order factorial moment of the photon counting distribution.
In this paper we study the possibility of analyzing a low intensity light beam whose spectrum has two lines with Lorentzian or Gaussian profiles by measuring n(2)(T) (the normalized second-order factorial moment). To do this the spectrum is scanned periodically by a spectrometer, and the normalized second-order factorial moment of the beam intensity at the exit aperture of the spectrometer is measured. The errors involved in the determination of the width, relative height, and separation between the two lines are calculated and discussed.
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.
It is well known that the photocount distribution associated with the photoelectric detection of fluctuating light beams carries information about the probability density of the light intensity. In this paper, we present an exact solution to a problem of particular interest which arises in connection with the photoelectric detection of narrow-band Gaussian (thermal or pseudothermal) light, namely, the problem of determining the photocount distribution when the counting-time interval is not necessarily short compared to the coherence time of the light. The method developed in this paper is applied to the case where the spectral profile of the light is Lorentzian; it leads to an exact expression for the photocount generating function and it provides simple recurrence relations for the photocount distribution and for its factorial moments.
Analytic aspects of the photon-counting distributions in quantum optics are investigated for the case where the underlying field includes a mixture of harmonic signal and thermal noise. A Lorentzian spectral profile for the thermal light is used to find simple iterative relations for the factorial cumulant moments. Explicit analytic expressions for the moments are then given to eighth order. Approximate interpolation formulas, which display proper limiting behavior at small and large correlation length, are also investigated.