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

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

Approximate formulae for the superposition of coherent and chaotic fields

R. Horák, Ladislav Mišta, Jan Peřina

Published Mar 1, 1971• 14 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/4/2/008

Related papers

N-photon factorial moments for superposition of coherent and chaotic fields

Ladislav Mišta

The first and the second N-photon factorial moments for the superposition of coherent and chaotic fields and the third N-photon factorial moment for the chaotic field are given for arbitrary spectrum and counting time intervals.

Journal of physics. A, Proceedings of the Physical Society. General•Jul 1, 1971•2 citations

On the quantum statistics of the superposition of coherent and chaotic fields

Jan Peřina, R. Horák

The generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators in quantum optics. An alternative description is also given based on a recent analysis of the superposition of coherent and chaotic fields in terms of the correlation functions which makes it possible to derive a number of results valid for arbitrary mean occupation numbers per mode from which the model considered follows as a special case. Many earlier results obtained for coherent and chaotic fields and their superposition are included as special cases. The present results generally describe a superposition experiment for an N-mode coherent field (e.g. generated by an N-mode laser operating far above threshold) and an M-mode chaotic field (M>or=N) as well as a field generated by an M-mode laser operating above threshold.

Journal of physics. A, Proceedings of the Physical Society. General•Nov 1, 1969•34 citations

Approximate Formulas for Photoelectric Counting Distributions

Gabriel Bédard, Jane C. Chang, L. Mandeļ

The validity of a simple approximate formula for the photoelectric counting probability in a thermal optical field, which was proposed by one of us (L.M.) in 1959, is investigated. The formula is based on a generalization of the Bose-Einstein distribution and should hold for light of arbitrary spectral density. It is shown by explicit calculation for three different spectral distributions that the formula holds with good accuracy over a very wide range of conditions. It should therefore prove useful when the spectral distribution of the light being studied is not known.

Physical Review•Aug 25, 1967•71 citations

N -Fold Photoelectric Counting Statistics of Mixed Chaotic and Coherent Light

Cyrus D. Cantrell

General formulas for the factorial cumulants of the photocounting distribution and the cumulants of the integrated intensity are obtained for chaotic light superposed with coherent light, for experiments involving $N$ different counting intervals. The chaotic light may be partially polarized, need not be time stationary or single mode, may differ in frequency from the coherent light, and may have any spectral distribution.

Physical Review A•Feb 1, 1971•10 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

Approximate Formulae for Mixed Modulated Coherent and Partially Polarized Chaotic Light

Jan Peřina, Vlasta Peřinová, Ladislav Mišta

Exact and approximate formulae are obtained for the counting statistics of mixed cosine-modulated coherent and partially polarized chaotic light, particularly with Lorentzian spectrum, for one-photon as well as multiphoton absorption. They are numerically analysed and the accuracy of the approximate formulae is discussed. As a special case chaotic light is investigated. A closer relation to recent papers is outlined.

Optica Acta International Journal of Optics•Jul 1, 1972•13 citations
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.
The generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators in quantum optics. An alternative description is also given based on a recent analysis of the superposition of coherent and chaotic fields in terms of the correlation functions which makes it possible to derive a number of results valid for arbitrary mean occupation numbers per mode from which the model considered follows as a special case. Many earlier results obtained for coherent and chaotic fields and their superposition are included as special cases. The present results generally describe a superposition experiment for an N-mode coherent field (e.g. generated by an N-mode laser operating far above threshold) and an M-mode chaotic field (M>or=N) as well as a field generated by an M-mode laser operating above threshold.
The validity of a simple approximate formula for the photoelectric counting probability in a thermal optical field, which was proposed by one of us (L.M.) in 1959, is investigated. The formula is based on a generalization of the Bose-Einstein distribution and should hold for light of arbitrary spectral density. It is shown by explicit calculation for three different spectral distributions that the formula holds with good accuracy over a very wide range of conditions. It should therefore prove useful when the spectral distribution of the light being studied is not known.
General formulas for the factorial cumulants of the photocounting distribution and the cumulants of the integrated intensity are obtained for chaotic light superposed with coherent light, for experiments involving NNN different counting intervals. The chaotic light may be partially polarized, need not be time stationary or single mode, may differ in frequency from the coherent light, and may have any spectral distribution.
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.