Massimo Santarsiero

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.

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.

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.

Beam coherence-polarization matrix

We present an approach for describing the properties of a quasi-monochromatic, beam-like field that is both partially polarized and partially coherent from the spatial standpoint. It is based on the use of a single matrix, called the beam coherence-polarization matrix, whose elements have the form of mutual intensities. This approach, which can be viewed as an approximate form of Wolfs general tensorial theory of coherence, appears to be very simple, yet it is able to cover significant aspects of the beam behaviour that would not be accounted for by a scalar theory or by a local polarization matrix approach. A peculiar interference law applying to mutual intensities is derived. We show through simple examples how this approach leads to distinguish fields that would appear identical in a scalar treatment or in a local polarization matrix description. Hints for extensions are given.

Generalized Bessel-Gauss beams

In this paper we describe a superposition model for Bessel-Gauss beams, in which higher orders are included. An analogous model leads to a different class of beams, namely the modified Bessel-Gauss beams. Then a generalized set of beams, containing the previous beams as particular cases, is introduced. The behaviour of these beams upon propagation is investigated, both analytically and numerically.

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.

Coherent-mode decomposition of partially polarized, partially coherent sources

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.

On genuine cross-spectral density matrices

For an electromagnetic stochastic beam, the choice of the mathematical structure of the cross-spectral density matrix is limited by the constraint of non-negative definiteness. We present a sufficient condition for building these matrices in such a way that this constraint is automatically satisfied. This allows us to put into evidence that electromagnetic beams can exhibit very peculiar correlation properties, some of which would not be encountered in scalar treatments. These results are illustrated by means of a number of examples.

Plane-wave scattering by a perfectly conducting circular cylinder near a plane surface: cylindrical-wave approach

A new method for the analysis of the diffraction of a plane wave impinging on a perfectly conducting circular cylinder in front of a generally reflecting surface is presented. The surface is characterized by its complex reflection coefficient, enabling us to treat a wide class of reflecting surfaces. The presence of the surface is taken into account by means of a suitable expansion of the reflected field in terms of cylindrical functions. The method gives the solution of the scattering problem in both the near and the far field regardless of the polarization state of the incident field. Numerical examples for dielectric interfaces are presented, and comparisons are made with results presented in the literature.

Twisted Gaussian Schell-model Beams: A Superposition Model

Abstract We present a simple model in which a twisted Gaussian Schell-model beam is produced by an incoherent superposition of ordinary Gaussian beams. The meaning and some direct consequences of the model are given.