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.

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.

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.

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.

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.

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. In this process, the total power that is scattered remains constant. This new tool to control scattering directionality may be used to steer the scattered field away from the forward direction and selectively address detectors situated at different angles.

Topological reactions of correlation functions in partially coherent electromagnetic beams.

It was recently shown that so-called coherence vortices, singularities of the two-point correlation function, generally occur in partially coherent electromagnetic beams. We study the three-dimensional structure of these singularities and show that in successive cross sections of a beam a rich variety of topological reactions takes place. These reactions involve, apart from vortices, the creation or annihilation of dipoles, saddles, maxima and minima of the phase of the correlation function. Since these reactions happen generically, i.e., under quite general conditions, these observations have implications for interference experiments with partially coherent, electromagnetic beams.

Correlation singularities in partially coherent electromagnetic beams.

We demonstrate that coherence vortices, singularities of the correlation function, generally occur in partially coherent electromagnetic beams. In successive cross sections of Gaussian Schell-model beams, their locus is found to be a closed string. These coherence singularities have implications for both interference experiments and correlation of intensity fluctuation measurements performed with such beams.

Geometric interpretation of the Pancharatnam connection and non-cyclic polarization changes.

If the state of polarization of a monochromatic light beam is changed in a cyclical manner, the beam acquires-in addition to the usual dynamic phase-a geometric phase. This geometric or Pancharatnam-Berry phase equals half the solid angle of the contour traced out on the Poincaré sphere. We show that such a geometric interpretation also exists for the Pancharatnam connection, the criterion according to which two beams with different polarization states are said to be in phase. This interpretation offers what is to our knowledge a new and intuitive method to calculate the geometric phase that accompanies non-cyclic polarization changes.

The Pancharatnam-Berry phase for non-cyclic polarization changes.

We present a novel setup that allows the observation of the geometric phase that accompanies polarization changes in monochromatic light beams for which the initial and final states are different (so-called non-cyclic changes). This Pancharatnam-Berry phase can depend in a linear or in a nonlinear fashion on the orientation of the optical elements, and sometimes the dependence is singular. Experimental results that confirm these three types of behavior are presented. The observed singular behavior may be applied in the design of optical switches.

Connection between phase singularities and the radiation pattern of a slit in a metal plate.

We report a new fundamental relation between the minima of the far-zone radiation pattern of a narrow slit in a metal plate and the location of phase singularities in the intermediate field. If a system parameter such as the wavelength is changed, a previously unappreciated singular optics phenomenon occurs: namely, the transition of a near-zone phase singularity into a singularity of the radiation pattern. Our results have significance for the design of novel nanoscale light sources and antennas.

New effects in Young's interference experiment with partially coherent light.

We analyze the coherence properties of a partially coherent optical field emerging from two pinholes in a plane opaque screen. We show that at certain pairs of points in the region of superposition the light is fully coherent, regardless of the state of coherence of the light at the pinholes. In particular, this result also holds if each pinhole is illuminated by a different laser.

Phase singularities of the coherence functions in Young's interference pattern.

We analyze the coherence properties of a partially coherent field emerging from two pinholes in an opaque screen and show that the spectral degree of coherence possesses phase singularities on certain surfaces in the region of superposition. To our knowledge, this is the first illustration of the singular behavior of the spectral degree of coherence, and the results extend the field of singular optics to the study of phase singularities of correlation functions.

Light transmission through a subwavelength slit: waveguiding and optical vortices.

The anomalous (i.e., more than 100%) light transmission through a subwavelength slit in a thin metal plate is accompanied by a combination of waveguiding and phase singularities of the field of power flow near the slit. The crucial role of these phase singularities (such as optical vortices and saddle points) in exciting the waveguide modes is systematically studied. We predict transmission efficiencies as high as 300% for certain configurations.