Riccardo Borghi

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.

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.

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.

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.

Synthesis of partially polarized Gaussian Schell-model sources

An experimental procedure for the synthesis of a class of partially polarized Gaussian Schell-model sources is proposed. The experimental set-up is based on Mach-Zenhder interferometer. This kind of sources give rise to not only a coherence degree and intensity profile that are both Gaussian but also a Gaussian local degree of polarization in each plane upon free propagation. Measurements of the local degree of polarization and the intensities in the far field are presented. It is shown that from these measurements some characteristic parameters of the source can be obtained.

Spreading properties of beams radiated by partially coherent Schell-model sources

We derive a general law for the M2 factor of any beam generated by a partially coherent Schell-model source. The fourth power of M differs from its minimum value, attained in the coherent limit, by a term proportional to the second derivative of the modulus of the spectral degree of coherence evaluated for zero argument. Examples are given for cases of practical interest.

Use of the van Cittert–Zernike theorem for partially polarized sources

We introduce an extension of the van Cittert-Zernike theorem to spatially incoherent sources with partial polarization. We show through a simple example that fields generated by such sources can possess correlation matrices with interesting properties. In particular, we show that by suitable modulation of the polarization state across the incoherent source, the correlation between the orthogonal components of the field as well as the degree of polarization may drastically change on propagation.

M 2 factor of Bessel-Gauss beams

We derive the analytical expression of the M(2) factor of a Bessel-Gauss beam of any order and discuss its behavior for high and low values of the width of the Gaussian profile. The case of unapertured Bessel beams can be treated as a limiting case of our analysis.

Focal shift of focused flat-topped beams

The phenomenon of focal shift is studied for the case of focused coherent beams showing a flat-topped transverse profile. The model describing such beams is that of flattened Gaussian beams, which, due to their peculiar analytical expression, are particularly fit for the study of paraxial propagation of flattened beams. Focal shifts for the fundamental Gaussian mode and for the field produced by diffraction of a converging spherical wave by a circular aperture are shown to be obtainable by this model as particular cases.