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Journal of the Optical Society of America A

Coherence waves

Adolf W. Lohmann, David Mendlovic B, Gal Shabtay

Published Feb 1, 1999• 7 citations
Publisher

Abstract

In 1955 Wolf noticed that the mutual coherence function Γ obeys two wave equations [Proc. R. Soc. London230, 246 (1955)]. The physical optics of this finding is thoroughly presented in Mandel and Wolf’s recent monograph [Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK1995)]. We discuss those coherence waves in the spirit of optical signal processing. The term coherence waves is justified if one accepts the following paradigm: A wave is whatever obeys the wave equation.

DOI
10.1364/josaa.16.000359

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In 1955 Wolf noticed that the mutual coherence function Γ obeys two wave equations [Proc. R. Soc. London230, 246 (1955)]. The physical optics of this finding is thoroughly presented in Mandel and Wolf’s recent monograph [Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK1995)]. We discuss those coherence waves in the spirit of optical signal processing. The term coherence waves is justified if one accepts the following paradigm: A wave is whatever obeys the wave equation.
Abstract Coherence phenomena play an important role in any kind of interferometry (Gabor 1956; Glauber 1963; Mandel and Wolf 1965, 1995; Born and Wolf 1975; Walls and Milburn 1994; Mandel and Wolf 1995). In this chapter we summarize some known results, add some new ones obtained with neutrons, and analyse them in terms of general quantum optics, which can be applied to photon and matter waves as well. Indeed, neutrons have many well-known particle properties, but in interference experiments they behave like wave fields, which provides the connection to the quantum optical terminology. Coherence appears as a system property (neutron + apparatus) which persists as long as it does not become destroyed by statistical or dissipative effects.
Coherence is theorized as the normalized correlation between two superposed optical signals, usually replicated by a two-beam interferometer or by a double-slit system. Prevailing coherence theory is presented as field–field correlation, as it does not go into the technical details of how the measurable transformations are physically generated and registered. Teaching coherence theory using a semiclassical model has been very successful as is evidenced in literature from the extensive reference to the text by M. Born and E. Wolf. This has been further strengthened by the work of Sudarshan, who demonstrated the optical equivalence between Wolf’s classical theory and Glauber’s quantum coherence theories. The discussion about the classical concept of coherence remains incomplete without presenting the van Cittert–Zernike theorem on spatial coherence, because the concept of coherence evolved with historic attempts to understand spatial coherence.
Many years ago, a paper by Emil Wolf inspired one of us (MAF) to look more closely at the analytic properties of propagating and scattered optical fields. In 1962, Wolf discussed how Michelson’s interferometer could provide information about the energy distribution in the spectrum of a light beam from measurements of the visibility of interference fringes. A simple relationship exists between the visibility function V(τ) and the modulus of the complex degree of coherence, γ(τ). The methods of Hanbury Brown, and Twiss showed that |γ(τ)| could be determined in various ways, and the important question arose as to how one might recover spectral information, g(ν) from |γ(τ)|. Since V(τ) is proportional to the Fourier transform of g(ν), one might think that only the autocorrelation function of g(ν) might be found, without explicitly knowing the phase of γ(τ). How does one determine the missing phase? The deep insight used to address this question was to take into account the analytic properties from which a complete recovery of g(ν) became possible. It is the underlying analytic properties of the functions that we so routinely employ in modeling optical processes that can provide a deeper understanding of relationships between field parameters and information; this is what we address here.