Gemma Piquero

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.

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 the propagation of the kurtosis parameter of general beams

Abstract The behaviour of the kurtosis parameter of a partially coherent beam that freely propagates is investigated. A general classification scheme of light beams is given in terms of the number of extremals of the kurtosis in free space. Propagation through ABCD optical systems is also considered and a number of general properties of the kurtosis parameter are provided concerning the relationship between the extremals of the kurtosis and the position of the beam waist.

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.

Parametric characterization of the spatial structure of non-uniformly polarized laser beams

We present an approach for describing the spatial structure of partially polarized light fields. Unlike the treatments usually encountered in the literature, in which the polarization state is represented by position-dependent functions, the formalism shown here characterizes the polarization by means of a family of measurable overall parameters averaged over the transverse spatial region where the beam intensity reaches significant values. Generalized degrees of polarization are introduced to evaluate the uniformity of the spatial distribution of the polarization state of the beam-like field. The possibility of improvement and optimization of the quality of a polarized laser beam (understood as the general usefulness of such field for collimation and focussing) is analyzed by employing first-order optical systems. Finally, attention is briefly devoted to non-paraxial electromagnetic vector beams, whose parametric description of their polarization properties constitutes, at present, a challenge for theoreticians.

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.

Sharpness changes of gaussian beams induced by spherically aberrated lenses

Sharpness changes of the spatial profile of a gaussian beam induced by spherically aberrated lenses are investigated in terms of the so-called kurtosis parameter. It is shown both theoretically and experimentally that, after a single aberrated lens, it is possible to get flatter and sharper beam intensity distributions than the input gaussian beam depending on the plane where the field is observed. Agreement between analytical and experimental results is discussed.Abstract Sharpness changes of the spatial profile of a gaussian beam induced by spherically aberrated lenses are investigated in terms of the so-called kurtosis parameter. It is shown both theoretically and experimentally that, after a single aberrated lens, it is possible to get flatter and sharper beam intensity distributions than the input gaussian beam depending on the plane where the field is observed. Agreement between analytical and experimental results is discussed.

Parametric characterization of non-uniformly polarized beams

A new overall parameter is defined, namely, the generalized degree of polarization, which involves the spatial distribution of the polarization of a light beam. This parameter is introduced on the basis of a general treatment recently proposed [Optics Lett. 22 (1997) 206] to characterize partially polarized fields, which extends the Stokes-Mueller formalism to describe the intensity moments of a quasimonochromatic beam. The main properties and the physical meaning of this parameter with regard to the spatial inhomogeneities of the polarization state are analysed, and a general measurement procedure is proposed.

Characterization of partially polarized light fields

Representations of the Polarization of Beamlike Fields.- Second-Order Overall Characterization of Non-uniformly Polarized Light Beams.- Polarization and Coherence of Random Electromagnetic Fields.- Non-Paraxial Electromagnetic Beams.

Difference of cross-spectral densities

Generally speaking, the difference between two cross-spectral densities (CSDs) does not represent a correlation function. We will furnish a sufficient condition so that such difference be a valid CSD. Using such a condition, we will show through some examples how new classes of CSDs can be generated.