Optical Communications, 2nd Edition

3.3 COUNTING STATISTICS

The relationship of the received electromagnetic field and the number of released electrons is governed by the interaction between the radiation field and electrons of the photosensitive material. There are two accepted ways to treat this relaltionship. In the purely quantum treatment, the field is quantized into photons, and each field photon gives rise to an electron with some probability. The electrons released are, therefore, a statistical measurement of the photon occupancy in the field, and electron counting is often called photon or photoelectron counting. The alternate treatment (and the one we use) is the semiclassical approach, which is actually a consequence of the quantum treatment. This model treats the field classically (i.e., as a wave) and prescribes a probabilistic relation to account for its interaction with the atomic structure of the detector surface. Although a complete description of the emission and absorption of light by an atom is well beyond our interest here, an outline of the approach is as follows [1]. The semiclassical procedure begins with a charged particle in an electromagnetic field. It is then assumed that the combined system of atom plus field begins in some initial state, and a set of coupling equations is derived for the state transition probabilities. From these, one determines the probability rate of finding the combined system in a particular state. Summing over all final states, and making some simplifying assumptions, ...