Statistical Characterization of Optical Fields

C. Bendjaballah, B. Picinbono

Gabriel Popescu

N. A. Silva, A. J. Almeida, Armando N. Pinto

We report on the theoretical statistical characterization of a single-photon source based on the stimulated four-wave mixing process inside an optical fiber. We quantify the photon statistics by means of the expectation number of photons generated on the signal and idler waves, 〈Ňs〉 and 〈Ňi〉 respectively, and Mandel's Qsand Qiparameters. The obtained solutions take into account the spontaneous and stimulated Raman contributions for the generation of the idler wave. Results show that the idler wave generated inside the fiber follows a super-Poissonian statistics. Findings also show that the signal wave change their own statistics from a Poissonian to a super-Poissonian, due to the interaction with the pump field and the optical fiber.

Sergei A. Akhmanov, A. S. Chirkin

V. P. Vykov, G V Shepelev

G. S. Agarwal, E. Wolf

In the general theory of optical coherence, the following problem discussed in the present paper, arises: to determine the statistical properties of a field represented by an analytic signal from the knowledge of the statistical properties of the corresponding real field. It is shown by the use of the characteristic functionals that in order to determine the joint probability distributions of the complex field at N space-time points, the knowledge of the complete statistical description of the real field is required; on the other hand, the moments of the complex field up to that order can be determined from the knowledge of the moments of the real field up to the same order. The results are illustrated by explicit calculations relating to the Gaussian random process, which, as is well known, characterizes the fluctuations of thermal light. A converse of a well-known theorem of Kac and Siegert relating to a Gaussian random process is derived as an immediate consequence of our analysis.