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

Annalen der Physik

Photon Counting Statistics of Thermal Light Consisting of Two Spectral Lines

N. Tornau, B. Echtermeyer

Published Jan 1, 1973• 1 citation
Publisher

Abstract

Abstract The generating function for the photon counting distribution is calculated for polarized thermal light in the case that the spectral profile of the light is a superposition of two LORENTZian lines with the same central frequency but different halfwidth at half height. Further we present results for the moments of the counting distribution in this case and also for a frequency separation of both line‐centers.

DOI
10.1002/andp.19734840402

Related papers

Photon Counting Statistics of Thermal Light Consisting of Two Spectral Lines

N. Tornau, B. Echtermeyer

The generating function for the photon counting distribution is calculated for polarized thermal light in the case that the spectral profile of the light is a superposition of two LORENTZian lines with the same central frequency but different halfwidth at half height. Further we present results for the moments of the counting distribution in this case and also for a frequency separation of both line-centers.

Annalen der Physik•Jan 1, 1973•5 citations

Counting statistics of partial coherent light with Lorentzian spectrum

Chia Chang Shih

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.

Physical Review A•Aug 1, 1989•3 citations

Photon counting statistics with thermal light having a multiple-peak spectrum

C. L. Mehta, Sushma Gupta

We consider the photon-counting statistics with polarized thermal light having arbitrary rational spectral profile. The method is illustrated for a light beam having a two-peak symmetric Lorentzian spectrum. The associated integral equation is converted into a differential equation and the eigenvalues are determined. Using the standard techniques of contour integration, an explicit expression is obtained for the generating function valid for an arbitrary value of the counting interval.

Physical Review A•May 1, 1975•4 citations

Photon Counting and Intensity Fluctuations of Partially Polarized Gaussian Light

A. K. Jaiswal, C. L. Mehta

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.

Physical Review•Oct 25, 1969•18 citations

Onefold photoelectron-counting statistics of mixtures of thermal and coherent radiation

Richard G. Barakat

We consider onefold photoelectron-counting statistics, for arbitrary counting times, when the wave field on the detector is a mixture of thermal light of a specified spectral profile (incoherent component) and a harmonic signal (coherent component). The probability density function of the time-integrated intensity W(Ω) is obtained from the inverse Laplace transform of the moment-generating function by the Dubner–Abate algorithm. The corresponding probability distribution of the detected photoelectrons, P(m), is then evaluated directly by numerical integration of W(Ω). Numerical results for W(Ω) and P(m) have been obtained when the thermal line shape is Lorentzian for both the homodyne situation (coherent line coincides with the mean frequency of the thermal spectral profile) and the heterodyne situation (coherent line is now off center with respect to the mean frequency of the thermal spectral profile).

Journal of the Optical Society of America A•Apr 1, 1985•3 citations

Photon Counting Statistics of Gaussian Light

Gabriel Bédard

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.

Physical Review•Nov 25, 1966•97 citations
Abstract The generating function for the photon counting distribution is calculated for polarized thermal light in the case that the spectral profile of the light is a superposition of two LORENTZian lines with the same central frequency but different halfwidth at half height. Further we present results for the moments of the counting distribution in this case and also for a frequency separation of both line‐centers.
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.
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.
We consider onefold photoelectron-counting statistics, for arbitrary counting times, when the wave field on the detector is a mixture of thermal light of a specified spectral profile (incoherent component) and a harmonic signal (coherent component). The probability density function of the time-integrated intensity W(Ω) is obtained from the inverse Laplace transform of the moment-generating function by the Dubner–Abate algorithm. The corresponding probability distribution of the detected photoelectrons, P(m), is then evaluated directly by numerical integration of W(Ω). Numerical results for W(Ω) and P(m) have been obtained when the thermal line shape is Lorentzian for both the homodyne situation (coherent line coincides with the mean frequency of the thermal spectral profile) and the heterodyne situation (coherent line is now off center with respect to the mean frequency of the thermal spectral profile).
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.