Engineering a better light sheet in an axicon-based system using a flattened Gaussian beam of low order.

Lasers are fundamental tools in research and development. The shape of an incident laser beam directly affects the results, when it propagates through complex structured meso-aspheric optical elements. In conic-based systems utilizing elements such as axicons, the impact of secondary lobes is mostly overlooked, although the intensity distributions at the central spot and the side-lobes directly affect the beam properties. We investigate the interaction of two axicons (160° and 170°) with incident beams approximated by Gaussian, high-order Flattened-Gaussian, and low-order Flattened-Gaussian functions. We demonstrate that replacing an incident Gaussian beam with a low-order Flattened-Gaussian beam reduces the secondary lobes and significantly improves the uniformity of the intensity profile. We practically applied this effect in engineering a conic-aspheric-based static light-sheet microscope producing markedly improved results.

Reproducing Kernel Hilbert spaces for wave optics: tutorial.

An introduction to the Hilbert spaces that are endowed with a reproducing kernel is presented on using the mathematical tools of Fourier optics and coherence theory. After giving the basic definition of such spaces, some examples are worked out to show how the inner product can take different forms depending on the particular function space one works with. The basic rule to build a reproducing kernel Hilbert space (RKHS) is then presented together with the basic properties of those spaces. Eigenfunctions and eigenvalues of the reproducing kernel are then illustrated and lead to the important integral representation of the reproducing kernel. The latter is used to present pseudomodal expansions and generalized forms of sampling. The concluding section offers some thoughts on the applications of RKHSs in wave optics. An appendix presents an introduction to treatments using more advanced concepts of functional analysis.

Christoffel-Darboux sources.

A new, to the best of our knowledge, class of partially coherent sources is introduced on the basis of the Christoffel-Darboux (CD) formula read as the expression of a possible cross-spectral density. It will be seen that such an interpretation is possible because the CD formula gives the reproducing kernel of a suitable Hilbert space. After discussing general properties of CD kernels, a specific example is worked out using Hermite polynomials. A connection with the density matrix will be highlighted.

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.

Doubly positive functions in coherent and partially coherent optics.

A function is said to be doubly positive if it is everywhere non-negative and the same holds true for its Fourier transform. After discussing applications to coherent and partially coherent fields, we present examples and properties of such functions together with procedures to devise classes of them.

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.

Policy, procedures, and goals at JOSA A: editorial.

Editorial policy and procedures are described for the benefit of potential authors and reviewers. These policies are described in the context of our goals for the journal.

Introducing JOSA A tutorials: editorial.

We describe the new tutorial article type in detail and give some background on the reasons for its introduction.

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.

Journal of the Optical Society of America a 30th Anniversary: editorial.

Journal of the Optical Society of America A Editor-in-Chief, Franco Gori, announces the 30th Anniversary of the journal.

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.

On a class of electromagnetic diffraction-free beams.

We present a general theory of electromagnetic diffraction-free beams composed of uncorrelated Bessel modes. Our approach is based on the direct application of the nonnegativity constraint to the cross-spectral density tensor describing the electromagnetic field distribution. The field correlation properties are most conveniently derived in the spatial frequency domain, where the angular spectrum takes on the form of an infinitely thin ring. We also present several examples, including a vector generalization of the recently introduced dark and antidark diffraction-free beams.

Correlation matrices of completely unpolarized beams.

The simplest form for the correlation matrix of a completely unpolarized electromagnetic beam is the product of a scalar correlation function times a unit matrix. We show, however, that classes of unpolarized beams exist for which the diagonal elements of the correlation matrix are not equal to each other and the off-diagonal elements do not vanish identically. This gives rise to a distinction between pure and impure unpolarized beams. The two types of beams can be distinguished at the experimental level by their behavior in a Young's interferometer.

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.

Partially correlated sources with complete polarization.

We show that the correlation matrix of any electromagnetic planar source endowed with complete polarization must be of a universal form, no matter how the field components are correlated across the source plane. Such form entails that both the realizability conditions and the search of vector modes of the source reduce to scalar problems. We shall also briefly dwell on how propagation affects the polarization properties of the field and, in particular, we discuss cases in which propagated light remains completely polarized.

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.