Bessel-Gauss beams

Some published computational work has suggested that partially coherent beams may be less susceptible to distortions caused by propagation through random media than fully coherent beams. In this paper this suggestion is studied quantitatively by examining the mean squared width of partially coherent beams in such media as a function of the propagation distance. The analysis indicates under what conditions, and to what extent, partially coherent beams are less affected by the medium.

Spreading of partially coherent beams in random media

We introduce a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables. This phase twists the beam about its axis during propagation and is shown to be bounded in strength because of the positive semidefiniteness of the cross-spectral density. Propagation characteristics and invariants for such beams are derived and interpreted, and two different geometric representations are developed. Direct effects of the twist phase on free propagation as well as on parabolic index fibers are demonstrated. Production of such twisted GSM beams, starting with Li-Wolf anisotropic GSM beams, is described.

Twisted Gaussian Schell-model beams

Recent researches have revealed that there exists an intimate connection between radiometry and the theory of partial coherence. In this paper a review is presented of some of these developments. After a brief discussion of various models for energy transport in optical fields and of some of the basic concepts of the classical theory of optical coherence, the following topics are discussed: the foundations of radiometry, the coherence properties of Lambertian sources, and the relationship between the state of coherence of a source and the directionality of the light that the source generates. Some very recent work is also described which reveals that certain sources that are spatially highly incoherent in a global sense will generate light that is just as directional as a laser beam.

Coherence and radiometry

Gaussian kernels representing operators on the Hilbert space scrH=L2(openRn) are studied. Necessary and sufficient conditions on such a kernel in order that the corresponding operator be positive semidefinite, corresponding to a density matrix (cross-spectral density) in quantum mechanics (optics), are derived. The Wigner distribution method is shown to be a convenient framework for characterizing Gaussian kernels and their unitary evolution under Sp(2n,openR) action. The nontrivial role played by a phase term in the kernel is brought out. The entire analysis is presented in a form which is directly applicable to n-dimensional oscillator systems in quantum mechanics and to Gaussian Schell-model partially coherent fields in optics.

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M.S. Zubairy

Papers

The directionality of gaussian Schell-model beams☆

Exact equations for radiative transfer of energy and momentum in free electromagnetic fields