Statistical properties of a wave with random frequency modulation in a dispersive medium

The probability distributions of frequency, intensity, and other parameters of a wave with random frequency modulation propagating in a dispersive medium are determined and studied. In particular, the probability distributions for photon density are found for the limiting cases of linear and quadratic medium dispersion characteristics. It is demonstrated that in the latter case the photon density probability distribution has a singularity produced by the absence of time focusing of the wave in the vicinity of dispersion curve inflection points. The statistics of wave frequency in a multifrequency regime are considered in detail.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 12, pp. 1797–1802, December, 1978.The authors thank A. N. Malakhov for his interest in the study.