Quantum Theory of Optical Coherence

The concept of coherence which has conventionally been used in optics is found to be inadequate to the needs of recently opened areas of experiment. To provide a fuller discussion of coherence, a succession of correlation functions for the complex 6eld strengths is de6ned. The nth order function expresses the correlation of values of the fields at 2n different points of space and time. Certain values of these functions are measurable by means of n-fold delayed coincidence detection of photons. A fully coherent field is defined as one whose correlation functions satisfy an in6nite succession of stated conditions. Various orders of incomplete coherence are distinguished, according to the number of coherence conditions actually satis6ed. It is noted that the 6elds historically described as coherent in optics have only first-order coherence. On the other hand, the existence, in principle, of 6elds coherent to all orders is shown both in quantum theory and classical theory. The methods used in these discussions apply to fields of arbitrary time dependence. It is shown, as a result, that coherence does not require monochromaticity. Coherent fields can be generated with arbitrary spectra.