Circular polarizers and their effect on partial coherence.

We examine the action of a circular polarizer on an incident beam that is spatially partially coherent and partially polarized. It is found that the beam's coherence area can be significantly increased or decreased by the polarizer. Furthermore, an expression for the transmission efficiency is derived.

Scattering of partially coherent electromagnetic beams by a sphere.

We examine the scattering of a partially coherent, partially polarized electromagnetic beam by a homogeneous sphere (Mie scattering). The degree of polarization and the Stokes parameters in the far zone are found to be strongly dependent on the state of coherence and polarization of the incident beam. In particular, we demonstrate the emergence of polarization singularities and show that partial spatial coherence gives rise to significant depolarization effects. In addition we explore the symmetry properties of the scattered field.

Lissajous singularities in Young's interference experiment.

We explore the interference of two bichromatic vector beams in Young's interference experiment. Our analysis focuses on determining the conditions under which the superposition of such beams, emerging from the pinholes, can give rise to Lissajous-type polarization singularities on the observation screen. Two independent sufficiency conditions are derived. This analysis aids in comprehending the inherent characteristics of Lissajous singularities. To the best of our knowledge, this is the first demonstration of the singular behavior of polarization in a two-frequency field in Young's interference experiment.

Polarization-resolved scintillations in Young's experiment.

The conventional scintillation, or intensity fluctuation, that occurs in random electromagnetic beams is just one member of a broader class of four interconnected, polarization-resolved scintillations. We examine these generalized scintillations, called Stokes scintillations, that occur when two stochastic electromagnetic beams are made to interfere in Young's experiment. We find that the magnitude of the conventional scintillation can be decreased, within certain limits, at the expense of an increase of one or more of the other Stokes scintillations. For certain applications however, it may be beneficial to suppress the latter.

Generalization of Malus' law and spatial coherence relations for linear polarizers and non-uniform polarizers.

We study the transmission of partially polarized, partially coherent beams through linear polarizers and polarization elements that are non-uniform. An expression for the transmitted intensity, which reproduces Malus' law for special cases, is derived, as are formulas for the transformation of spatial coherence properties.

Spectral polarization of Gaussian Schell-model beams.

We present a class of broadband electromagnetic Gaussian Schell-model sources whose state of polarization is both uniform and identical for all frequencies, but whose far-zone polarization properties strongly depend on wavelength. Also, these sources can produce beams whose polarized portion is always linearly polarized but with a polarization angle that evolves on propagation. Our results offer new insights into the behavior of broadband partially coherent sources.

Spectral invariance of Gaussian Schell-model beams.

It is well known that in general the spectrum of a beam that is generated by a partially coherent source will change on propagation. Here we derive necessary and sufficient conditions under which the often-used Gaussian Schell-model sources can produce beams whose normalized spectrum is invariant everywhere, or is invariant just along the beam axis. These sources are not necessarily quasi-homogeneous or obeying the scaling law.

Reconstruction of an electromagnetic Gaussian Schell-model source from far-zone intensity measurements.

An electromagnetic Gaussian Schell-model source that produces a random beam may be characterized by eight independent quantities. We show how far-zone measurements of the Stokes parameters, together with the Hanbury Brown-Twiss coefficient, allow one to determine all the source parameters. This method provides, to the best of our knowledge, a new tool to identify distant sources.

Coherence modification and phase singularities on scattering by a sphere: Mie formulation.

When light that is spatially partially coherent, such as sunlight, is incident on a sphere, the scattered field exhibits surprising coherence properties. The observed oscillatory behavior with deep minima means that the field in certain pairs of directions is highly correlated, whereas in others, it is essentially uncorrelated, and can even have correlation singularities. Because any subsequent scattering event is strongly affected by the state of coherence, these results are particularly important for multiple scattering in discrete disordered media.

Fraunhofer diffraction and the state of polarization of partially coherent electromagnetic beams.

We generalize the concept of Fraunhofer diffraction to partially coherent electromagnetic beams and show how the state of polarization is affected by a circular aperture. It is illustrated that the far-zone properties of a random beam can be tuned by varying the aperture radius. We find that even an incident beam that is completely unpolarized can sometimes produce a field that is highly polarized.

Generalized Hanbury Brown-Twiss effect for Stokes parameters.

The classic experiments by Hanbury Brown and Twiss (HBT) were concerned with the correlation of intensity fluctuations at two different positions in a wave field. We generalize the HBT effect that occurs in random electromagnetic beams by examining its polarization-resolved version. This leads naturally to the concept of correlations of fluctuations of the four Stokes parameters. We calculate the correlations of such "Stokes fluctuations" for the case of Gaussian statistics. When the two points of observation coincide, these correlations reduce to "Stokes scintillations." Our work reveals a new layer of complexity in random beams by showing that the HBT effect and the scintillation coefficient are just two of many correlations that are present. We illustrate that, in general, the fluctuations of the various Stokes parameters are all correlated by studying beams and sources with different polarization states.

Active Two-Dimensional Steering of Radiation from a Nanoaperture.

We experimentally demonstrate control over the direction of radiation of a beam that passes through a square nanoaperture in a metal film. The ratio of the aperture size and the wavelength is such that only three guided modes, each with different spatial symmetries, can be excited. Using a spatial light modulator, the superposition of the three modes can be altered, thus allowing for a controlled variation of the radiation pattern that emanates from the nanoaperture. Robust and stable steering of 9.5° in two orthogonal directions was achieved.

Degree of polarization in the focal region of a lens.

We examine the 3D distribution of the degree of polarization (DOP) in the focal region of a thin paraxial lens. Analytic expressions for the case of a focused Gaussian-Schell model beam are derived. These show that the DOP satisfies certain spatial symmetry relations. Furthermore, its value varies strongly in the vicinity of the geometrical focus, and its maximum, which need not occur at the focus, can be significantly higher than that of the incident beam.

Controlling the degree of polarization of partially coherent electromagnetic beams with lenses.

We show theoretically that the degree of polarization of a partially coherent electromagnetic beam changes dramatically as the beam is being focused. A low numerical aperture lens can considerably enhance the degree of polarization at its geometrical focus. When two identical lenses are employed in a 4f configuration, the degree of polarization of a beam can be tailored by using amplitude masks in the Fourier plane located in the middle of the two lenses. Our findings open up the possibility to control this fundamental property of random beams in a simple manner.

Comparison of different theories for focusing through a plane interface: reply.

The correction pointed out by Kim et al. [J. Opt. Soc. Am. A35, 591 (2018)JOAOD60740-323210.1364/JOSAA.35.000591] to our paper [J. Opt. Soc. Am. A14, 1482 (1997)JOAOD60740-323210.1364/JOSAA.14.001482] is welcome. A few additional remarks are included in this reply.

Fourier processing with partially coherent fields.

We describe how Fourier signal processing techniques can be generalized to partially coherent fields. Using standard coherence theory, we first show that focusing of a partially coherent beam by a lens modifies its coherence properties. We then consider a 4f imaging system composed of two lenses and discuss how spatial filtering in the Fourier plane allows one to tune the coherence properties of the beam. This, in turn, provides control over the beam's directionality, spectrum, and degree of polarization.

Electromagnetic diffraction theory of refractive axicon lenses.

We study the field that is produced by a paraxial refractive axicon lens. The results from geometrical optics, scalar wave optics, and electromagnetic diffraction theory are compared. In particular, the axial intensity, the on-axis effective wavelength, the transverse intensity, and the far-zone field are examined. A rigorous electromagnetic diffraction analysis shows that the state of polarization of the incident beam strongly affects the transverse intensity distribution, but not the intensity distribution in the far zone.

Surface Plasmons Carry the Pancharatnam-Berry Geometric Phase.

Surface plasmon polaritons (SPPs) are electromagnetic surface waves that travel along the boundary of a metal and a dielectric medium. They can be generated when freely propagating light is scattered by structural metallic features such as gratings or slits. In plasmonics, SPPs are manipulated, amplified, or routed before being converted back into light by a second scattering event. In this process, the light acquires a dynamic phase and perhaps an additional geometric phase associated with polarization changes. We examine the possibility that SPPs mediate the Pancharatnam-Berry phase, which follows from a closed path of successive in-phase polarization-state transformations on the Poincaré sphere and demonstrate that this is indeed the case. The geometric phase is shown to survive the light→SPP→light process and, moreover, its magnitude agrees with Pancharatnam's rule. Our findings are fundamental in nature and highly relevant for photonics applications.

Modulation of optical spatial coherence by surface plasmon polaritons.

The interference pattern observed in Young's double-slit experiment is intimately related to the statistical correlations of the waves emitted by the slits. As the waves in the slits become more correlated, the visibility of the interference pattern increases. Here, we experimentally modulate the statistical correlations between the optical fields emitted by a pair of slits in a metal film. The interaction between the slits is mediated by surface plasmon polaritons and can be tuned by the slit separation, which allows us to either increase or decrease the spatial coherence of the emerging fields relative to that of the incoming fields.

Strong suppression of forward or backward Mie scattering by using spatial coherence.

We derive analytic expressions relating Mie scattering with partially coherent fields to scattering with fully coherent fields. These equations are then used to demonstrate how the intensity of the forward- or backward-scattered field can be suppressed several orders of magnitude by tuning the spatial coherence properties of the incident field. This method allows the creation of cone-like scattered fields, with the angle of maximum intensity given by a simple formula.