STATISTICS OF PHOTOCOUNTS OF A FIELD FORMED BY SUPERPOSITION
Nick Laskin, Александр Сергеевич Мазманишвили
We consider the photocount statistics of a field formed by superposition of a coherent signal of an arbitrary form, and the Brownian noise (Ornstein--Uhlenbeck process). We obtain an analytical expression for the generating function of photocounts. In the case of a harmonic coherent signal, we analyze the count statistics of the superposed field as a function of the shift of the carrier frequency of the harmonic signal relative to the maximum of the Lorentz spectral contour, as a function of the partial intensity components of the superposed radiation, and also as a function of the product of the duration of photodetection and the spectral line width of the noise. I. The aim of the present work is to derive and study a formula for the probability of counts under the assumption that the photodetector registers an optical field formed by the superposition of a coherent signal and Brownian noise. This problem is of interest in the study of the count distribution in a detector which absorbs a mixture of coherent and incoherent radiation [i]. In the derivation of the formula for the probability density of the number of counts, one encounters specific mathematical difficulties associated with the fact that the photodetection process is extended in time. The probability P(m, T) that, during a time interval T, m photoelectrons are detected when the superposition of a coherent signal B(t) and noise ~(t) falls on the detector, is given by the Mandel formula [2]
•Jan 1, 1985•0 citations