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Physical Review A

Generalized Hanbury Brown–Twiss effect in partially coherent electromagnetic beams

Gaofeng Wu, David Kuebel, Taco D. Visser

Published Mar 25, 2019• 29 citations
Publisher

Abstract

The recently introduced concept of Stokes fluctuations generalizes both the Hanbury Brown--Twiss effect and the notion of scintillation. Here we apply this new framework to the specific example of a Gaussian Schell-model (GSM) beam. We derive formulas for Stokes scintillations and Stokes fluctuation correlations, which explicitly express the dependence of these quantities on the GSM source parameters. It is found that the normalized Stokes scintillations vary significantly with position. Also, they can be either positively or negatively correlated.

DOI
10.1103/physreva.99.033846

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The recently introduced concept of Stokes fluctuations generalizes both the Hanbury Brown--Twiss effect and the notion of scintillation. Here we apply this new framework to the specific example of a Gaussian Schell-model (GSM) beam. We derive formulas for Stokes scintillations and Stokes fluctuation correlations, which explicitly express the dependence of these quantities on the GSM source parameters. It is found that the normalized Stokes scintillations vary significantly with position. Also, they can be either positively or negatively correlated.
Hanbury Brown and Twiss (HBT) effect has broad applications in optics and other branches of physics, and traditionally this effect is considered in pure spatial or temporal domain. Here we investigate the spatiotemporal HBT effect, extending this phenomenon from spatial or temporal to spatiotemporal domain. By assuming the Gaussian statistics of partially coherent spatiotemporal pulsed sources, we find the generalized analytical results for spatiotemporal HBT effect in the compact form, with the help of the matrix-optics method, which can consider the HBT effect in spatial and temporal domain simultaneously. Furthermore, for Gaussian Schell-model pulsed beams (GSMPBs) used as a spatiotemporal correlated source, we have obtained the generalized expression to calculate spatiotemporal HBT effect, which is useful for up to three-dimensional cases in any second-order linear dispersive medium. By taking a simple two-dimensional case and using air as an example of a linear dispersive medium, we numerically illustrate the properties of the spatiotemporal HBT effect by adjusting the spatial and temporal parameters of the GSMPB source, and reveal the influence of both the spatial and temporal parameters on the spatiotemporal HBT effect. This work paves the path towards the detailed study of HBT effect for a source containing spatiotemporal information with Gaussian statistics.
By treating light fluctuations as a random process (stationary and Gaussian to second order), an expression is derived for the correlation in the output fluctuations of two square-law detectors which are illuminated by a plane light wave of any state of coherence and polarization. The expression takes a particularly simple form when, as is usually the case, the light is spectrally pure in the sense of a definition introduced elsewhere. The solution yields, as a special case, the basic formula relating to the Hanbury Brown-Twiss effect. The generalization discussed here is of particular interest for correlation experiments performed with light beams from optical maser sources. Moreover, the present analysis appears to be simpler than other treatments previously given in connection with more restricted cases.