Bessel-Gauss beams

It is shown by use of a simple model that in general the state of polarization of a light beam generated by a partially coherent source changes as the beam propagates in free space.

Change of polarization of light beams on propagation in free space

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

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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E. Collett

Papers

Partially coherent sources which produce the same far-field intensity distribution as a laser

Beams generated by Gaussian quasi-homogeneous sources

Determination of the Mueller-Stokes matrix using fourier analysis