Goos–Hänchen and Imbert–Fedorov shifts: relation with the irradiance moments of a beam

Abstract

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We present closed and simple expressions of the spatial and angular Goos–Hänchen and Imbert–Fedorov shifts in terms of the second-order irradiance moments of a beam. Our results are applicable to a general totally polarized partially coherent beam. One of the main advantages of this formalism is that it can be applied directly from the knowledge of the cross-spectral density function and the polarization state without using any modal beam expansion. The obtained expressions allow understanding of the relationship between the global spatial characteristics of the incident beam and the experimented shifts in the reflected beam. Cosine-Gaussian Schell-model beams with rectangular symmetry are used to exemplify results.