F. Gori

Bessel-Gauss beams

Abstract A new type of solution of the paraxial wave equation is presented. It encompasses as limiting cases both the diffraction-free beam and the gaussian beam. The propagation features of this solution are discussed.

Flattened gaussian beams

Abstract New light beams of various orders are introduced. Their field distribution across the waist plane is similar to that produced by an ordinary gaussian beam except that the central region is flattened. The flat zone occupies a larger fraction of the cross section as the order of the beam increases. A simple propagation law is found.

Partially polarized Gaussian Schell-model beams

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.

Measuring Stokes parameters by means of a polarization grating

Ordinary gratings act on the amplitude and (or) the phase of a wave front. Polarization gratings produce instead a periodic modulation of the state of polarization. A simple grating of the latter type is constituted by a linear polarizer whose orientation varies periodically along a line. It is shown that, for a generic polarization state of the incident field, such a grating gives rise to first-order diffracted beams with counterrotating circular polarizations. It is also shown that such a grating can be used for measuring the Stokes parameters of a light beam in an achromatic manner. Several extensions are briefly discussed.

Matrix treatment for partially polarized, partially coherent beams.

A matrix method is outlined for dealing with quasi-monochromatic, partially polarized light when spatial coherence is not necessarily complete and propagation occurs along beams. Both spatial coherence and polarization properties are described by a single 2x2 matrix whose elements have the structure of mutual intensity functions. Through a simple example it is shown that this matrix can account for differences that would not be revealed by a scalar treatment or by a locally defined polarization matrix.

Devising genuine spatial correlation functions

The choice of the mathematical form of spatial correlation functions for optical fields is restricted by the constraint of nonnegative definiteness. We discuss a sufficient condition for ensuring the satisfaction of such a constraint.

An example of a Collett-Wolf source

Abstract It is shown that a Collett-Wolf source can be produced starting from a spatially incoherent source and using a collimating lens and an amplitude filter. The results of an experiment testing this prediction are reported.

Propagation of axially symmetric flattened Gaussian beams

Flattened Gaussian beams are characterized by a waist profile that passes in a continuous way from a nearly flat illuminated region to darkness. The steepness of the transition region is controlled by an integer parameter N representing the order of the beam. Being expressible as a sum of N Laguerre–Gauss modes, a flattened Gaussian beam turns out to be very simple to study as far as propagation is concerned. We investigate the main features of the field distribution pertaining to a flattened Gaussian beam throughout the space and present experimental results relating to the laboratory production of this type of beam.

Modal expansion for J0-correlated Schell-model sources

Abstract We evaluate the modes for a Schell-model planar source whose degree of spectral coherence is a Bessel function of zero order and whose optical intensity distribution is an arbitrary circularly symmetric function. These modes are shown to be connected with certain fields recently described as diffraction-free beams.

Realizability condition for electromagnetic Schell-model sources.

The set of functions that appear in the correlation matrix of an electromagnetic source must satisfy the constraint of nonnegative definiteness. Here we derive a necessary and sufficient condition for nonnegativeness for the class of electromagnetic Schell-model sources. This result also suggests a possible synthesis procedure for this type of source. As an illustration, two specific examples of electromagnetic Schell-model sources are discussed.