Degree of Higher-Order Optical Coherence

Abstract

In this paper we define the normalized coherence function of arbitrary order (m, n), in a manner which seems to be a natural generalization of that defined for the second-order coherence function. Both classical and quantized optical fields are considered and the results are compared. It is shown that for classical fields and also for quantized optical fields having nonnegative definite diagonal coherent state representations of the density operator, the modulus of these normalized coherence functions is bounded by the values 0 and 1. This definition differs from the one recently given by Glauber for quantized optical fields, where the normalized coherence functions may take arbitrarily large values even for fields having nonnegative definite diagonal representations of the density operator. Conditions for ``complete coherence,'' i.e., those under which the modulus of the normalized coherence function attains the limiting value 1, are discussed. Some consequences of stationarity and quasi-monochromaticity are also discussed.