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Physical Review A

Quantum theory of optical coherence of nonstationary light in the space-frequency domain

Mayukh Lahiri, E. Wolf

Published Oct 26, 2010• 11 citations
Publisher

Abstract

Classical theories of coherence for statistically stationary, as well as, nonstationary optical fields are frequently discussed both in the space-time and in the space-frequency domains. However, the quantum treatment of coherence theory is generally carried out in the space-time domain. In this paper, we present a quantum-mechanical theory of first-order coherence for statistically nonstationary light in the space-frequency domain.

DOI
10.1103/physreva.82.043837

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Classical theories of coherence for statistically stationary, as well as, nonstationary optical fields are frequently discussed both in the space-time and in the space-frequency domains. However, the quantum treatment of coherence theory is generally carried out in the space-time domain. In this paper, we present a quantum-mechanical theory of first-order coherence for statistically nonstationary light in the space-frequency domain.
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This article presents a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum. Analyses based on both the classical and quantum theories are described. After a brief historical introduction, the elementary concepts which are frequently employed in the discussion of interference phenomena are summarized. The measure of second-order coherence is then introduced in connection with the analysis of a simple interference experiment and some of the more important second-order coherence effects are studied. Their uses in stellar interferometry and interference spectroscopy are described. Analysis of partial polarization from the standpoint of correlation theory is also outlined. The general statistical description of the field is discussed in some detail. The recently discovered universal "diagonal" representation of the density operator for free fields is also considered and it is shown how, with the help of the associated generalized phase-space distribution function, the quantum-mechanical correlation functions may be expressed in the same form as the classical ones. The sections which follow deal with the statistical properties of thermal and nonthermal light, and with the temporal and spatial coherence of blackbody radiation. Later sections, dealing with fourth- and higher-order coherence effects include a discussion of the photoelectric detection process. Among the fourth-order effects described in detail are bunching phenomena, the Hanbury Brown-Twiss effect and its application to astronomy. The article concludes with a discussion of various transient superposition effects, such as light beats and interference fringes produced by independent light beams.