Related papers: Polarization singularity anisotropy: determining m…
M\"{o}bius strips with one, two, three, and four, half-twists are shown to be generic features of three-dimensional (nonparaxial) elliptically polarized light. The geometry and topology of these unusual singularities is described and the…
We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.
The fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle $\theta$…
Geometrical and statistical properties of polarization of CMB are analyzed. Singular points of the vector field which describes CMB polarization are found and classified. Statistical distribution of the singularities is studied. A possible…
A cold gas of particles with anisotropic interactions of general form, due to a polarizing field, is studied. Special cases are atoms or molecules with dipole-dipole or quadrupole-quadrupole interactions. It is shown that the angular…
We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analyzing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the…
We explicitly describe the tropicalization of a cluster variety of finite type C, realizing it as the space of axially symmetric phylogenetic trees. We also find all occurring sign patterns of coordinates, for both the cluster variety and…
Departing from a Moufang set related to a polarity in an exceptional Moufang quadrangle of type F_4, we construct a rank three geometry. The main property of this new geometry is that its automorphism group is identical to the one of the…
We present a general, systematic theory of electromagnetism and chirality in crystalline solids. Symmetry is its basic guiding principle, enabling us to consider macroscopic multipole densities without reference to any specific microscopic…
We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric…
We examine the polarization signal of the cosmic microwave background radiation associated with distant clusters. The polarization is induced by the Thomson scattering of microwave photons with ionized gas of clusters and contains…
We investigate the properties of the normal modes in a strongly magnetized hydrogen gas for conditions expected in atmospheres of isolated neutron stars. We derive and compute the polarizations and absorption coefficients of the normal…
For $\pi^0\eta$-photoproduction on the nucleon formal expressions are developed for the five-fold differential cross section and the recoil polarization including beam and target polarizations. The polarization observables are described by…
The polarization of light is a critically under-utilized, rich source of information in astronomy. For stars in particular, surface magnetism polarization that can be detected and measured with spectro-polarimetry. Many questions about…
Mapping CMB polarization is an essential ingredient of current cosmological research. Particularly challenging is the measurement of an extremely weak B-mode polarization that can potentially yield unique insight on inflation. Achieving…
This paper addresses a very classical topic that goes back at least to Pl\"ucker: how to understand a plane curve singularity using its polar curves. Here, we explicitly construct the singular points of a plane curve singularity directly…
A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for…
Many types of point singularity have a topological index, or 'charge', associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple…
The interaction of polarized light with photonic crystals exhibit unique features due to its sub-wavelength nature on the surface and the periodic variation of refractive index in the depth of the crystals. Here, we present a detailed study…
Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outwards are introduced. Their $3\times3$ cross-spectral density matrix is given through expansions of the field components in terms of basis…