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Higher-order Photon Counting Statistics of Gaussian-lorentzian Light

Manmohan Singh

A method of arriving at the closed-form expression for an Nth-order generating function for gaussian-lorentzian light is described. Various aspects of the third-order photon counting statistics are derived explicitly for counting times of arbitrary duration.

Optica Acta International Journal of OpticsNov 1, 19849 citations

Statistics of photoelectric pulses for Gaussian-Lorentzian light

Hideyuki Sonoda, Atsushi Kikkawa, Norihito Suzuki

The practical treatment of statistics for Gaussian-Lorentzian light is studied theoretically and experimentally by using the time interval distribution of photoelectric pulses, which is derived in two approaches that are based on Markovian processes and the generating function of photon counting statistics, taking the experimental conditions into account. The limits of the validity of the Markovian assumption are made clear. In arbitrary light intensity it is valid experimentally to employ the practical generating function of photon counting distribution expressed as the product of an ideal generating function and a Poissonian one.The practical treatment of statistics for Gaussian-Lorentzian light is studied theoretically and experimentally by using the time interval distribution of photoelectric pulses, which is derived in two approaches that are based on Markovian processes and the generating function of photon counting statistics, taking the experimental conditions into account. The limits of the validity of the Markovian assumption are made clear. In arbitrary light intensity it is valid experimentally to employ the practical generating function of photon counting distribution expressed as the product of an ideal generating function and a Poissonian one.

Applied OpticsApr 1, 19788 citations

Many-time photocount distributions

S. K. Srinivasan, S Sukavanam, E. C. G. Sudarshan

The generating function is obtained for N photocounts for a gaussian optical field with a lorentzian profile without any restriction to the intervals during which the photodetectors are open. The method may be generalized to arbitrary spectral profiles using the method of Srinivasan and Sukavanam (1971 and 1972).

Journal of Physics A Mathematical Nuclear and GeneralDec 1, 19739 citations

Photoelectric pulse interval distribution of gaussian-lorentzian light

Atsushi Kikkawa, Kunihiko Ohkubo, Hideaki Satō +1 more

Optics CommunicationsNov 1, 197419 citations

Time interval statistics of the Brillouin spectrum

Singh, Manmohan

Based on the unique analytic form of the one-fold generating-function very recently given by the present author in [3], we provide in this paper a complete and an exact anaysis of the time-interval-statistics of the Brillouin spectrum with its central Rayleigh line. We also distinguish the time-interval-distributions for the present Brillouin triplet from the time-interval-distributions for the pure Brillouin spectrum (a doublet) given in Ref. [4]. As in Ref. [4], we establish here too the invalidity of the earlier numerical-results due to Blake and Barakat [5] for the present Brillouin triplet, as they violate even the well known equation (32) for the time-interval-distribution for the conditional photocountBased on the unique analytic form of the one-fold generating-function very recently given by the present author in [3], we provide in this paper a complete and an exact anaysis of the time-interval-statistics of the Brillouin spectrum with its central Rayleigh line. We also distinguish the time-interval-distributions for the present Brillouin triplet from the time-interval-distributions for the pure Brillouin spectrum (a doublet) given in Ref. [4]. As in Ref. [4], we establish here too the invalidity of the earlier numerical-results due to Blake and Barakat [5] for the present Brillouin triplet, as they violate even the well known equation (32) for the time-interval-distribution for the conditional photocount

Jun 15, 19900 citations

Approximate joint photocount statistics for Gaussian light with arbitrary spectral shape

Bahaa E. A. Saleh

An approximate formula is found for the joint moment generating function of integrated intensity fluctuations of Gaussian light in two time intervals. Some lower−order joint moments generated by this approximate formula are compared to their exact values known in case of Lorentzian light and good accuracy is obtained.

Journal of Applied PhysicsFeb 1, 19755 citations

Rigorous Analysis of the Time-interval Probabilities for Gaussian-Lorentzian Light

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Rigorous Analysis of the Time-interval Probabilities for Gaussian-Lorentzian Light

Abstract

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