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.

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.

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.

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.

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.

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.

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.

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.

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.

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

The correction pointed out by Kim et al. [J. Opt.

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.

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.

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.

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.

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.

Cycle of phase, coherence and polarization singularities in Young's three-pinhole experiment.

It is now well-established that a variety of singularities can be characterized and observed in optical wavefields. It is also known that these phase singularities, polarization singularities and coherence singularities are physically related, but the exact nature of their relationship is still somewhat unclear. We show how a Young-type three-pinhole interference experiment can be used to create a continuous cycle of transformations between classes of singularities, often accompanied by topological reactions in which different singularities are created and annihilated.

Tunable, anomalous Mie scattering using spatial coherence.

We demonstrate that a J0-Bessel-correlated beam that is incident on a homogeneous sphere produces a highly unusual distribution of the scattered field, with the maximum no longer occurring in the forward direction. Such a beam can be easily generated using a spatially incoherent, annular source. Moreover, the direction of maximal scattering can be shifted by changing the spatial coherence length.

Dynamic control of optical transmission through a nano-slit using surface plasmons.

We demonstrate how the optical transmission by a directly illuminated, sub-wavelength slit in a metal film can be dynamically controlled by varying the incident beam's phase relative to that of a stream of surface plasmon polaritions which are generated at a nearby grating. The transmission can be smoothly altered from its maximum value to practically zero. The results from a simple model and from rigorous numerical simulations are in excellent agreement with our experimental results.

Correlation of intensity fluctuations in beams generated by quasi-homogeneous sources.

We derive expressions for the far-zone correlation of intensity fluctuations (the Hanbury Brown-Twiss effect) that occurs in electromagnetic beams that are generated by quasi-homogeneous sources. Such sources often have a radiant intensity pattern that is rotationally symmetric, irrespective of the source shape. We demonstrate how from the far-zone correlation of intensity fluctuations the spectral density distribution across the source plane may be reconstructed.

Hanbury Brown-Twiss effect with partially coherent electromagnetic beams.

We derive expressions that allow us to examine the influence of different source parameters on the correlation of intensity fluctuations (the Hanbury Brown-Twiss effect) at two points in the same cross section of a random electromagnetic beam. It is found that these higher-order correlations behave quite differently than the lower-order amplitude-phase correlations that are described by the spectral degree of coherence.