EVOLUTION OF THE STATISTICAL PROPERTIES OF PHOTONS PASSED THROUGH A TRAVELING-WAVE LASER-AMPLIFIER

We determine the evolution of the photon statistics of a light beam as it passes through a traveling-wave laser amplifier, modeled as a birth-death-immigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but possibly varying) birth, death, and immigration rates for arbitrary input statistics is obtained. The case of constant birth, death, and immigration rates is considered in particular detail. The photon statistics at the output of a general BDI traveling-wave amplifier are always broader than those at the input, and they can take many forms. Our most general solution can be applied when the input distribution to the amplifier takes the form of a negative-binomial transform. The results are expected to be useful in calculating the performance characteristics of lightwave systems using optical amplifiers in which the object is to detect light with a broad range of statistical properties, including scattered light, spontaneous-emission light, and light emitted from a laser. In the latter case the input is Poisson, and the output distribution assumes the form of a noncentral-negative-binomial (Laguerre) distribution which is usually associated with a multimode (phase-preserving) superposition of coherent and chaotic fields.