Related papers: Optical M\"{o}bius Singularities
The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence,…
The polarization properties of monochromatic light beams are studied. In contrast to the idealization of an electromagnetic plane wave, finite beams which are everywhere linearly polarized in the same direction do not exist. Neither do…
Singular optics aims to understand and manipulate light's topological defects, pioneered by the discovery that phase vortex lines, strands of destructive interference, naturally occur in scalar wave fields. Monochromatic electromagnetic…
We consider the enumeration of tropical curves in M\"obius strips for two different lattice structures and relate them to the enumeration of curves in two rational ruled surfaces over a complex elliptic curve. Using this correspondence, we…
Polarization singularities and topological polarization structures are generic features of inhomogeneous vector wave fields of any nature. However, their experimental studies mostly remain restricted to optical waves. Here we report…
The polarization of the cosmic microwave background radiation will have a distribution of singularities and anti-singularities, points where the polarization vanishes for topological reasons. The statistics of polarization singularities…
Singular Mueller matrices play an important role in polarization algebra and have peculiar properties that stem from the fact that either the medium exhibits maximum diattenuation and/or polarizance, or because its associated canonical…
We study three-dimensional microlensing where two lenses are located at different distances along the line of sight. We formulate the lens equation in complex notations and recover several previous results. There are in total either 4 or 6…
We introduce M\"obius strip diagram algebras (and their monoid and categorical versions) as subalgebras of a partition-style diagram calculus in which strands may carry handles and M\"obius strip features. We identify the resulting diagram…
Let f : X -> S be any elliptic fibration. If X has dimension 3 and is not uniruled, then X has a minimal model (with terminal singularities) [Mori]. In earlier work we have shown that there exists a birationally equivalent elliptic…
We determine and list all possible configurations of singular fibres on rational elliptic surfaces in characteristic three. In total, we find that 267 distinct configurations exist. This result complements Miranda and Persson's…
In recent years, there has been a mounting interest in better methods of measuring nanoscale objects, especially in fields such as nanotechnology, biomedicine, cleantech, and microelectronics. Conventional methods have proved insufficient,…
A new category of optical microring resonator, which is analogous to the M\"obius strip, is proposed. The "M\"obius" microring resonator allows the conversion between modes with different polarizations in the ring and light must circulate…
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…
In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence…
We present a systematic study of threefolds fibred by K3 surfaces that are mirror to sextic double planes. There are many parallels between this theory and the theory of elliptic surfaces. We show that the geometry of such threefolds is…
Optical polarization singularities (PSs) in real space carry rich topological properties and can enable highly precise manipulations of light fields. Conventional studies focus on the PSs in the open space of optical systems. The properties…
Planetary nebulae (PNe) have diverse morphological shapes, including point-symmetric and multipolar structures. Many PNe also have complicated internal structures such as torus, lobes, knots, and ansae. A complete accounting of all the…
We study the free-propagation features of an optical field endowed with a non-uniform polarization pattern with elliptical symmetry. The fields derived in this way are called Elliptically Symmetric Polarized Beams (ESPB for short). Some…
Symmetries and conservation laws of energy, linear momentum and angular momentum play a central role in physics, in particular in nonlinear optics. Recently, light fields with non trivial topology, such as polarization M\"obius strips or…