Related papers: Optical M\"{o}bius Singularities
Surface plasmons dominate the optical response of metal surfaces, and their nature is controlled by surface geometry. Here we study metasurfaces containing singularities in the form of sharp edges and characterized by three quantum numbers…
Vortices are topologically stable singularities at the center of a swirl of energy. Optical vortices are conventionally formed using diffractive optics or by bespoke optical elements. We report room temperature integrated lasers directly…
Three-dimensional gravitational cloaking is known to require exotic matter and energy sources, which makes it arguably physically unrealizable. On the other hand, typical astronomical observations are performed using one-dimensional…
Polarization maintaining (PM) fibers are meant to maintain linear polarization along a preferred axis. A PM fiber can be seen as the fiber version of a very high order waveplate, designed with different refractive indices along two…
Non-orientable manifolds, such as the M\"obius strip and the Klein bottle, defy conventional geometric intuition through their twisted boundary conditions. As a result, topological defects on non-orientable manifolds give rise to novel…
Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After…
A complete list of irreducible triangulations is identified on the M\"obius band.
We provide a theoretical investigation of optical Poincar\'e beams that exhibit interwinding chiral polarized domains upon propagation. We employ both analytical and numerical methods in order to investigate this phenomenon. Specifically,…
Heterotic orbifold models are promising candidates for models with MSSM like spectra. But orbifolds only correspond to a special place in moduli space, the bigger picture is described by the moduli space of Calabi-Yau spaces. In this talk…
We scrutinize the geometrical properties of light propagation inside a nonlinear medium modeled by a fully covariant electromagnetic theory in $2+1$-dimensions. After setting the nonlinear constitutive relations, the phase velocity and the…
The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids…
In F-theory, if a fiber type of an elliptic fibration involves a condition that requires an exceptional curve to split into two irreducible components, it is called ``split'' or ``non-split'' type depending on whether it is globally…
We report that conventional saturable periodic structures, in sharp contrast to the conventional systems with different nonlinearities which exhibit the typical S- shaped optical bi- and multi-stable states, reveal some unusual and unique…
Polarization singularities including bound states in the continuum (BICs) and circularly polarized states have provided promising opportunities in the manipulation of light waves. Previous studies show that BICs in photonic crystal slabs…
We study singularities of surfaces which are given by Kenmotsu-type formula with prescribed unbounded mean curvature.
An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit strength vortices is described. This…
We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a…
The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are…
The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…
We disclose the existence of a type of optical skyrmion, Gauss-Stokes (GS) skyrmions, that is naturally present in an optical vortex around its phase singularity. Contrary to previous research with optical skyrmions, we neither shape vector…