We consider a class of beams that are both partially polarized and partially coherent from the spatial standpoint. They are characterized by a correlation matrix whose elements have the same form as the mutual intensity of a Gaussian Schell-model beam. We focus our attention on those beams that would appear identical to ordinary Gaussian Schell-model beams in a scalar treatment. After establishing some inequalities that limit the choice of the matrix parameters, we study the main effects of propagation. Starting from the source plane, in which the beam is assumed to be uniformly polarized, we find that in the course of propagation the degree of polarization generally becomes non-uniform across a typical section of the beam. Furthermore, we find that the intensity distribution at the output of an arbitrarily oriented linear polarizer is Gaussian shaped at the source plane whereas it can be quite different at other planes.

/pdf/partially-polarized-gaussian-schell-model-beams-1tn1rk5u1q.pdf

Partially polarized Gaussian Schell-model beams

It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.

/pdf/coherent-mode-decomposition-of-partially-polarized-partially-1nbcyoxz0o.pdf

Coherent-mode decomposition of partially polarized, partially coherent sources.

Attention is called to a polarization basis formed by four Jones vectors that is reducible to two basic structures. In these states the field is linearly polarized at any point, but the polarization direction changes with the angular coordinate. Very simple equations hold for the field lines of these basis vectors. The adoption of this basis is of interest for beams possessing a single vortex of any order, say, m, as well as for beams with two vortices of opposite charges, m and -m. As an example, the application to vectorial Bessel–Gauss beams is briefly discussed.

Polarization basis for vortex beams.

We examine a family of Bessel–Gauss beam solutions to the vector wave equation that allow a combination of azimuthal and radial polarization in the transverse electric field. Recently reported linear and azimuthal Bessel–Gauss beams may be identified as members of this set. Several free parameters determine the form and behavior of each beam; varying these parameters can produce distinctly different intensity patterns and beam behavior. We find a general diffraction integral for circularly symmetric disturbances and investigate two special cases, a thin lens and a circular aperture.

Properties and diffraction of vector Bessel–Gauss beams

A simple correspondence between the paraxial propagation formulas along the optical axis of a uniaxial crystal and inside an isotropic medium is found in the case of beams with linearly polarized circularly symmetric boundary distributions. The electric fields of the ordinary and the extraordinary beams are related to the corresponding expressions in a medium with refractive index no and ne2/no, where no and ne are the ordinary and the extraordinary refractive indexes, respectively. Closed-form expressions for Laguerre–Gauss and Bessel–Gauss beams propagating through an anisotropic crystal are given.

Laguerre-gauss and bessel-gauss beams in uniaxial crystals

We report the emission properties of concentric-circle-grating, surface-emitting (CCGSE), distributed-feedback semiconductor lasers oscillating in single high-order azimuthal spatial modes. The evolution of the spatial profile of the beam emitted by such lasers with increasing excitation depends upon the spatial gain distribution and the depth of the circular waveguide grating. The polarization of the high-order spatial modes is predominantly radial.

Craig Olson

Papers

High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers