S. Vicalvi

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.

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.

Partially coherent sources with helicoidal modes

Abstract On the basis of the modal theory of coherence, we study partially coherent sources whose modes belong to the class of Laguerre-Gauss functions for which the Laguerre polynomial has zero order. These modes present a phase profile with a helicoidal structure, which is responsible for notable phenomena, such as the propagation of optical vortices, beam twisting, and the presence of dislocations in interference patterns. By suitably choosing the eigenvalues associated with such modes, different partially coherent sources are obtained: sources with a flattened Gaussian profile, twisted Gaussian Schell-model sources with a saturated twist, and a new class of sources having an annular profile. Owing to the shape-invariance property of the underlying modes, the fields radiated by these sources do not change their transverse profile through propagation, except for scale and phase factors. We also prove that, if any such source is covered by a circularly symmetric filter, the new modal structure can be fou...

Focusing of axially symmetric flattened Gaussian beams

We study the three-dimensional field distribution of a focused axially symmetric flattened Gaussian beam. In particular, exact closed-form expressions for the intensity along the optical axis and at the focal plane are provided, together with a comparison between our results and those pertinent to the case of a converging spherical wave diffracted by a hard-edge circular aperture. Some hints for future investigations are also given.

Analytical derivation of the optimum triplicator

Abstract The analytical derivation of the phase profile of a diffractive optical element that produces three equi-intense replicas of an input beam with the maximum efficiency is presented. Such derivation, based on a functional minimization procedure, leads to a closed form for the phase profile and to an efficiency value slightly lower than the predicted theoretical upper bound.

SHAPE-INVARIANCE RANGE OF A LIGHT BEAM

A typical axially symmetric light beam on paraxial free propagation maintains the same transverse shape as at the waist plane for a certain range along its axis. We discuss a general procedure for estimating this range.

High-precision digital automated measurement of degree of coherence in the Thompson and Wolf experiment

We propose a high-precision digital automated quantitative determination of the modulus of the complex degree of coherence. The Thompson and Wolf experiment is repeated, using a CCD and a measurement method based on the fast Fourier transform. The experimental results agree very well with the predictions of the theory.

Shape-invariance error for axially symmetric light beams

A significant aspect of the propagation of coherent light beams is that the shape of the transverse field distribution changes. In this paper, the concepts of shape-invariance error and shape-invariance range are used to characterize such effects in a quantitative way. Applications of the theoretical analysis to some simple but significant cases are presented.

Experimental determination of the size of a source from spectral measurements

We show how spectral changes measurements in a Young interferometer can be used to determine the dimension of an incoherent source. The experimental results confirm the theoretical predictions.

Shape invariance characterization of coherent axially symmetric beams

A typical axially symmetric beam on paraxial free propagation maintains the same transverse shape as at its waist plane for a certain range along its axis. We introduce a general procedure for estimating this range.