Synthesis and characterization of non-uniformly totally polarized light beams: tutorial.

Polarization of a light beam is traditionally studied under the hypothesis that the state of polarization is uniform across the transverse section of the beam. In such a case, if the paraxial approximation is also assumed, the propagation of the beam reduces to a scalar problem. Over the last few decades, light beams with spatially variant states of polarization have attracted great attention, due mainly to their potential use in applications such as optical trapping, laser machining, nanoscale imaging, polarimetry, etc. In this tutorial, an introductory treatment of non-uniformly totally polarized beams is given. Besides a brief review of some useful parameters for characterizing the polarization distribution of such beams across transverse planes, from both local and global points of view, several methods for generating them are described. It is expected that this tutorial will serve newcomers as a starting point for further studies on the subject.

Spatial superbunching of light. Model sources.

Sources that exhibit superbunching in the spatial domain are discussed. A few model sources are presented with the pertaining probabilistic treatment. Schemes for the experimental realization of similar sources are suggested, and the results of simulated tests are given.

Pseudo-Schell model sources.

Partially coherent pseudo-Schell model sources are introduced and analyzed. They present radial symmetry and coherence characteristics depending on the difference between the radial distances of two points from the source center. As a consequence, all points belonging to circles centered on the symmetry center of the source are perfectly correlated. We show that such sources radiate fields with peculiar behaviors in paraxial propagation. In particular, when compared to beams produced by Gaussian Schell-model sources with comparable coherence parameters, their irradiance can present sharper profiles and higher peak valuesmono and a better beam quality parameter. Furthermore, when a pseudo-Schell model source presents a vortex, the propagated beam preserves a null of the intensity along its axis.

Maximizing Young fringe visibility with a universal SU2 polarization gadget: erratum.

In this erratum, the experimental value of the maximum attainable visibility reported in Opt. Lett.43, 2844 (2018)OPLEDP0146-959210.1364/OL.43.002844 has been corrected.

Twisted Schell-model beams with axial symmetry.

The problem of when a twist can be impressed on a partially coherent beam is solved for Schell-model fields endowed with axial symmetry. A modal analysis can be performed for any such beam, thus permitting evaluation of whether it will withstand the twisting process. Beyond exemplifying some twistable beams, it is shown that, for certain correlation functions, the beam cannot be twisted, no matter how the numerical parameters are chosen.

Difference of two Gaussian Schell-model cross-spectral densities.

We present a number of results relating to the difference of two Gaussian Schell-model cross-spectral densities (CSDs). They allow us to specify conditions under which such a difference represents itself in a valid CSD. In particular, a sufficient condition is derived for the non-negative definiteness of the resulting CSD, for any admissible choice of the involved parameters, while a necessary and sufficient condition is obtained for the case of CSDs endowed with the property of being shape-invariant upon propagation.

Longitudinal polarization periodicity of unpolarized light passing through a double wedge depolarizer.

The polarization characteristics of unpolarized light passing through a double wedge depolarizer are studied. It is found that the degree of polarization of the radiation propagating after the depolarizer is uniform across transverse planes after the depolarizer, but it changes from one plane to another in a periodic way giving, at different distances, unpolarized, partially polarized, or even perfectly polarized light. An experiment is performed to confirm this result. Measured values of the Stokes parameters and of the degree of polarization are in complete agreement with the theoretical predictions.

Decoding divergent series in nonparaxial optics.

A theoretical analysis aimed at investigating the divergent character of perturbative series involved in the study of free-space nonparaxial propagation of vectorial optical beams is proposed. Our analysis predicts a factorial divergence for such series and provides a theoretical framework within which the results of recently published numerical experiments concerning nonparaxial propagation of vectorial Gaussian beams find a meaningful interpretation in terms of the decoding operated on such series by the Weniger transformation.

Partially correlated thin annular sources: the scalar case.

Thin annular sources, either coherent or completely incoherent from the spatial standpoint, have played a significant role in the synthesis of diffraction-free and J(0)-correlated fields, respectively. Here, we consider thin annular sources with partial correlation. A scalar description is developed under the assumption that the correlation function between two points depends on their angular distance only. We show that for any such source the modal expansion can easily be found. Further, we examine how the correlation properties of the radiated fields change on free propagation. We also give a number of examples and present possible synthesis schemes.

Polarization invariance in a Young interferometer.

Conditions ensuring that the polarization properties at the output plane of a Young interferometer fed by an electromagnetic partially coherent beam are the same as those at the pinholes are derived. Such a behavior is interpreted in terms of the vector modes of the electromagnetic source corresponding to the field emerging from the Young pinholes.

Maximizing Young's fringe visibility through reversible optical transformations.

When a Young's interferometer is fed by an electromagnetic beam, fringes of low, or even zero, visibility do not necessarily indicate lack of correlation between two typical field components at the pinholes. The passage of light that emerges from one of the pinholes through a nonabsorbing anisotropic optical element may enhance the visibility. We inquire about the maximum visibility that can be attained through such a reversible transformation (polarizers being excluded). We find that such a quantity can be evaluated in closed form. Its value is directly related to the Ky Fan 1-norm of the correlation matrix of the illuminating beam.

Phase and amplitude retrieval in ghost diffraction from field-correlation measurements.

We report the results of experiments about the inversion of ghost diffraction with pseudothermal light. A complete retrieval of the complex transmission function of planar transparencies, illuminated by spatially incoherent, quasimonochromatic light, is achieved. This is obtained by measuring the field (instead of the intensity) correlation function. In particular, the determination of the phase of the correlation function is made particularly easy and robust by the use of a suitably modified Young interferometer. The presented results refer to the cases of a clear slit and a phase step.

Measuring spatial coherence by using a reversed-wavefront Young interferometer.

A very simple optical setup for the measurement of the modulus and the phase of the two-point correlation function of a partially coherent light field is presented. The system consists of a slightly modified version of a Young interferometer and requires a single Young mask in order to determine the correlation function at any pairs of points. Experimental results are presented for the case of a synthesized partially coherent secondary source.

Vector mode analysis of a young interferometer.

It is proved that, when the vector modal theory of coherence is applied to a pair of fixed points, exact results are obtained for the mode structure. In particular, it is shown that the field radiated by the pinholes of a Young interferometer can always be represented by the incoherent superposition of no more than four perfectly correlated and polarized modes. The role of such modes is illustrated through a simple example.

Joint spatial-directional localization features of wave fields focused at a complex point.

A systematic study of the joint spatial-directional localization features of monochromatic wave fields focused at a complex point is presented, on the basis of recently introduced measures of spatial and directional spread for wide-angle wave fields. Such features are compared with those of a class of fields defined to achieve the theoretical minimum product of these spread measures. It is found that the two classes of fields are remarkably similar.

Nonparaxial fields with maximum joint spatial-directional localization. I. Scalar case.

In paraxial optics, the spatial and angular localization of a beam are usually characterized through second moments in intensity. For these measures, Gaussian beams have the property of achieving a minimum angular spread for a given spatial spread (or beam waist). For wide-angle fields, however, the standard measures of spatial and angular localization become inappropriate, and new definitions must be used. Previously proposed definitions [J. Opt. Soc. Am. A 17, 2391 (2000)] are adopted, and the scalar monochromatic wave fields that achieve a minimum angular spread for a given spatial spread are found.

Nonparaxial fields with maximum joint spatial-directional localization. II. Vectorial case.

The monochromatic nonparaxial vector fields that achieve a minimum spatial spread for a given directional spread are found. The derivation of these fields is analogous to the one presented in part I of this series for the case of scalar fields. This derivation is based on a variational treatment and multipolar expansion. The resulting lower bounds for the spreads of vector fields turn out to be considerably more restrictive than for scalar fields.

Effects of coherence on the degree of polarization in a young interference pattern.

Recent predictions concerning the relationship between the degree of polarization at a typical point of a Young interference pattern and the degree of coherence of the electromagnetic field at the pinholes are tested by a simple experiment. In particular, it is shown that light that is completely unpolarized at the pinholes can become partially polarized across the fringe pattern.

New basis for rotationally symmetric nonparaxial fields in terms of spherical waves with complex foci.

A scheme for computing rotationally-symmetric nonparaxial monochromatic scalar fields is proposed, based on a new orthonormal basis of solutions of the Helmholtz equation given by combinations of spherical waves focused at imaginary points. These basis fields are found through a mapping of the angular spectra of the multipolar basis over the sphere of directions. The convergence of the basis can be optimized by an appropriate choice of the location of the imaginary focus. The new scheme is tested for the case of converging spherical waves of different numerical apertures, with and without aberrations.

Highly focused spirally polarized beams.

The features of spirally polarized light beams focused by high-numerical-aperture systems are investigated in the nonparaxial regime by means of Debye theory with a multipole expansion technique. General expressions of the expanding coefficients are given, as well as the electric field distributions across the focal plane. Numerical examples are presented for the case of spirally polarized beams of the donut type. Comparisons with recent experimental results are also shown.