arXiv subjects

Mark R. Dennis

Publications and source records attributed to Mark R. Dennis.

26 records · Page 2Linked to original sources

arXiv2012

Topological aberration of optical vortex beams and singularimetry of dielectric interfaces

The splitting of a high-order optical vortex into a constellation of unit vortices, upon total reflection, is described and analyzed. The vortex constellation generalizes, in a local sense, the familiar longitudinal Goos-Hänchen and transverse Imbert-Federov shifts of the centroid of a reflected optical beam. The centroid shift is related to the centre of the constellation, whose geometry otherwise depends on higher-order terms in an expansion of the reflection matrix. We present an approximation of the field around the constellation of increasing order as an Appell sequence of complex polynomials whose roots are the vortices, and explain the results by an analogy with the theory of optical aberration.

physics.optics↗

arXiv2011

Relativistic Electron Vortex Beams: Angular Momentum and Spin-Orbit Interaction

Motivated by the recent discovery of electron vortex beams carrying orbital angular momentum (AM), we construct exact Bessel-beam solutions of the Dirac equation. They describe relativistic and nonparaxial corrections to the scalar electron beams. We describe the spin and orbital AM of the electron with Berry-phase corrections and predict the intrinsic spin-orbit coupling in free space. This can be observed as a spin-dependent probability distribution of the focused electron vortex beams. Moreover, the magnetic moment is calculated, which shows different $g$-factors for spin and orbital AM and also contains the Berry-phase correction.

quant-ph↗

arXiv2011

Fermionic out-of-plane structure of polarization singularities

A new classification of circular polarization C points in three-dimensional polarization ellipse fields is proposed. The classification type depends on the out-of-plane variation of the polarization ellipse axis, in particular, whether the ellipse axes are in the plane of circular polarization one or three times. A minimal set of parameters for this classification are derived, and discussed in the context of the familiar in-plane C point classification into lemon, star, and monstar types. This new geometric classification is related to the Möbius index of polarization singularities recently introduced by Freund.

physics.optics↗

arXiv2009

On the Burgers vector of a wave dislocation

Following Nye and Berry's analogy with crystal dislocations, an approach to the Burgers vector of a wave dislocation (phase singularity, optical vortex) is proposed. It is defined to be a regularized phase gradient evaluated at the phase singularity, and is computed explicitly. The screw component of this vector is naturally related to the helicoidal twisting of wavefronts along a vortex line, and is related to the helicity of the phase gradient. The edge component is related to the nearby current flow (defined by the phase gradient) perpendicular to the vortex, and the distribution of this component is found numerically for random two-dimensional monochromatic waves.

physics.optics↗

arXiv2008

Superoscillation in speckle patterns

Waves are superoscillatory where their local phase gradient exceeds the maximum wavenumber in their Fourier spectrum. We consider the superoscillatory area fraction of random optical speckle patterns. This follows from the joint probability density function of intensity and phase gradient for isotropic gaussian random wave superpositions. Strikingly, this fraction is 1/3 when all the waves in the two-dimensional superposition have the same wavenumber. The fraction is 1/5 for a disk spectrum. Although these superoscillations are weak compared with optical fields with designed superoscillations, they are more stable on paraxial propagation.

physics.optics↗

arXiv2008

Polarization singularity anisotropy: determining monstardom

C points, that is isolated points of circular polarization in transverse fields of varying polarization, are classified morphologically into three distinct types, known as lemons, stars and monstars. These morphologies are interpreted here according to two natural parameters associated with the singularity, namely the anisotropy of the C point, and the polarization azimuth on the anisotropy axis. In addition to providing insight into singularity morphology, this observation applies to the densities of the various morphologies in isotropic random polarization speckle fields.

physics.optics↗

arXiv2007

Probability Density of the Multipole Vectors for a Gaussian Cosmic Microwave Background

We review Maxwell's multipole vectors, and elucidate some of their mathematical properties, with emphasis on the application of this tool to the cosmic microwave background (CMB). In particular, for a completely random function on the sphere (corresponding to the statistically isotropic Gaussian model of the CMB), we derive the full probability density function of the multipole vectors. This function is used to analyze the internal configurations of the third-year Wilkinson Microwave Anisotropy Probe quadrupole and octopole, and we show the observations are consistent with the Gaussian prediction. A particular aspect is the planarity of the octopole, which we find not to be anomalous.

astro-ph↗

arXiv2007

The plasmon Talbot effect

The plasmon analog of the self-imaging Talbot effect is described and theoretically analyzed. Rich plasmon carpets containing hot spots are shown to be produced by a row of periodically-spaced surface features. A row of holes drilled in a metal film and illuminated from the back side is discussed as a realizable implementation of this concept. Self-images of the row are produced, separated from the original one by distances up to several hundreds of wavelengths in the examples under consideration. The size of the image focal spots is close to half a wavelength and the spot positions can be controlled by changing the incidence direction of external illumination, suggesting the possibility of using this effect (and its extension to non-periodic surface features) for far-field patterning and for long-distance plasmon-based interconnects in plasmonic circuits, energy transfer, and related phenomena.

cond-mat.other↗