Exploring the dynamics of finite-energy Airy beams: a trajectory analysis perspective.

In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In order to investigate the effects generated by the truncation and hence the propagation properties displayed by the designed beams, here we resort to a new perspective based on a trajectory methodology, complementary to the density plots more commonly used to study the intensity distribution propagation.

Affine diffractive beam dividers.

Diffractive optical elements that divide an input beam into a set of replicas are used in many optical applications ranging from image processing to communications. Their design requires time-consuming optimization processes, which, for a given number of generated beams, are to be separately treated for one-dimensional and two-dimensional cases because the corresponding optimal efficiencies may be different. After generalizing their Fourier treatment, we prove that, once a particular divider has been designed, its transmission function can be used to generate numberless other dividers through affine transforms that preserve the efficiency of the original element without requiring any further optimization.

Three-dimensional polarization of fields radiated by partially coherent electromagnetic cylindrical sources.

Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outward are introduced. Their 3 × 3 cross-spectral density matrix is given through expansions of the field components in terms of basis functions related to the Hankel functions. The spectral density and the three-dimensional degree of polarization of such sources and the fields they radiate are examined.

Partially coherent spherical sources with spherical harmonic modes.

A class of partially coherent spherical sources is introduced whose cross-spectral density across the surface has a modal expansion made up of spherical harmonics. For such sources, the solution of the propagation problem in all the outer spaces can be written through a series of the propagated modes, which maintains the spherical harmonic structure. The main features of this class of cross-spectral densities are derived illustrating their coherence properties with examples.

Cylindrical partially coherent scalar sources.

Partially coherent scalar sources with cylindrical symmetry radiating outwards are introduced. Homogeneous cross-spectral densities are shown to possess angularly modulated Hankel modes, whose amplitudes are subject to a filtering process during propagation. Simple criteria for treating such sources are given.

Lattice Resonances Excited by Finite-Width Light Beams.

Periodic arrays of metallic nanostructures support collective lattice resonances, which give rise to optical responses that are, at the same time, stronger and more spectrally narrow than those of the localized plasmons of the individual nanostructures. Despite the extensive research effort devoted to investigating the optical properties of lattice resonances, the majority of theoretical studies have analyzed them under plane-wave excitation conditions. Such analysis not only constitutes an approximation to realistic experimental conditions, which require the use of finite-width light beams, but also misses a rich variety of interesting behaviors.

On-axis polarization of beams radiated by electromagnetic circularly coherent sources.

On-axis spectral density and degree of polarization of beams radiated by electromagnetic (EM) sources with circular correlations are shown to be finely controlled by changing the source parameters. We reveal, in particular, that in this beam class, unlike for all previously known stationary beams, it is possible to control independently the dynamics of the on-axis spectral density and the degree of polarization. This was enabled by the obtained analytical expression for the on-axis polarization matrix, derived for general EM sources with circular coherence and Gaussian spectral density across the source plane.

Tailoring on-axis spectral density with circularly coherent light beams.

The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circular coherence state and a Gaussian spectral density is obtained in the closed form. It is revealed that the on-axis CSD is expressed via the Laplace transform of the source's degree of coherence or the Hilbert transform of the corresponding pseudo-mode weighting function. Such relations enable efficient tailoring of the on-axis spectral density, as we show with a slew of numerical examples.

On z-coherence of beams radiated by Schell-model sources with Gaussian profile.

The degree of coherence and the intensity distribution on the axis of the beam radiated by a planar partially coherent source of the Schell-model type are investigated. We present an expression for the on-axis cross-spectral density which is valid for a very general Schell-model source, with the only constraint that the intensity distribution across the source is Gaussian. Furthermore, we show that such an expression takes very simple analytical forms for several commonly used degrees of coherence of the source.

On z-coherence in self-focusing.

Both the intensity distribution and the degree of coherence between pairs of points along the propagation axis (z-coherence) are derived in closed form for a phenomenon of self-focusing produced by circularly coherent light. The first confirms results previously obtained numerically, while the second exhibits new complex features. The physical interpretation is obtained by a suitable pseudo-modal expansion that suggests an analogy with a simple two-mode structure.

Efficient calculation of highly focused electromagnetic Schell-model beams.

The calculation of the propagation of partially coherent and partially polarized optical beams involves using 4D Fourier Transforms. This poses a major drawback, taking into account memory and computational capabilities of nowadays computers. In this paper we propose an efficient calculation procedure for retrieving the irradiance of electromagnetic Schell-model highly focused beams.

Experimental estimation of the longitudinal component of a highly focused electromagnetic field.

The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way.

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.

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.

Uncertainty principle for axial power content of highly focused fields.

In the analysis of the on-axis intensity for a highly focused optical field, it is highly desirable to deal with effective relations aimed at characterizing the field behavior in a rather simple fashion. Here, a novel and adequate measure for the size of the region where the axial power content mainly concentrates is proposed on the basis of an uncertainty principle. Accordingly, a meaningful relationship is provided for both the spread of the incident beam at the entrance of the highly focused optical system and the size of the region where the on-axis power mainly concentrates.

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.

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.

Effect of linear polarizers on the behavior of partially coherent and partially polarized highly focused fields.

In this Letter, we describe the behavior of partially coherent, partially polarized focused vector beams after passing a linear polarizer placed at the focal plane of a high numerical aperture microscope lens. In particular, we develop a mathematical framework for such beams that helps the understanding of the performance of polarizers when interact with non-paraxial beams. The features of the focused field after the polarizer are numerically evaluated for some illustrative examples.

Partially coherent sources with radial coherence.

Partially coherent sources with radial coherence are proposed. They present a circularly symmetric intensity profile and a degree of coherence whose absolute value only depends on the angular difference between the two considered points. In particular, the source is completely coherent at pairs of points belonging to the same radius.

Synthesis of light needles with tunable length and nearly constant irradiance.

We introduce a new method for producing optical needles with tunable length and almost constant irradiance based on the evaluation of the on-axis power content of the light distribution at the focal area. According to theoretical considerations, we propose an adaptive modulating continuous function that presents a large derivative and a zero value jump at the entrance pupil of the focusing system. This distribution is displayed on liquid crystal devices using holographic techniques.

Goos-Hänchen and Imbert-Fedorov shifts: relation with the irradiance moments of a beam.

We present closed and simple expressions of the spatial and angular Goos-Hänchen and Imbert-Fedorov shifts in terms of the second-order irradiance moments of a beam. Our results are applicable to a general totally polarized partially coherent beam. One of the main advantages of this formalism is that it can be applied directly from the knowledge of the cross-spectral density function and the polarization state without using any modal beam expansion.

Flat top surface plasmon polariton beams.

Surface plasmon polaritons (SPPs) have emerged as powerful tools for guiding and manipulating light below the diffraction limit. In this context, the availability of flat top SPP beams displaying a constant transversal profile can allow for uniform excitation and coupling scenarios, thus opening the door to developing novel applications that cannot be achieved using conventional Gaussian SPP beams. Here, we present a rigorous theoretical description of flat top SPP beams propagating along flat metal-dielectric interfaces.

Synthesis of circularly coherent sources.

An experiment is presented in which a partially coherent source endowed with circular coherence is generated. The source is synthesized through a time averaging procedure, so that the mutual intensity is used as the basic correlation function. The correlation between points at different radial distances from the source center is tested by means of a Young interferometer.

Partially coherent sources with circular coherence.

A new class of partially coherent light sources is introduced. At the source plane, they exhibit perfect coherence along any annulus that is concentric to the source center. Between two points at different distances from the center, coherence can be partial or even vanishing.

Polarisers in the focal domain: Theoretical model and experimental validation.

Polarisers are one of the most widely used devices in optical set-ups. They are commonly used with paraxial beams that propagate in the normal direction of the polariser plane. Nevertheless, the conventional projection character of these devices may change when the beam impinges a polariser with a certain angle of incidence.