Related papers: SU(2) polarization evolution on higher-order Poinc…
The classical Pancharatnam-Berry phase, a variant of the geometric phase, arises purely from the modulation of the polarization state of a light beam. Due to its dependence on polarization changes, it cannot be effectively utilized for…
We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge $q$ at its center ($q$-plate). The polarization topological structures for different $q$-plates…
In this paper we achieve the quantization of a particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using group-theoretical methods. For this purpose, a fundamental role is played by contact,…
Spin-orbit coupled (SOC) light fields with spatially inhomogeneous polarization have attracted increasing research interest within the optical community. In particular, owing to their spin-dependent phase and spatial structures, many…
In this paper we generalize the concept of $q$-plate, allowing arbitrary functions of both the radial and the azimuthal variables, and study their effect on uniformly polarized beams in the near and far-field regime. This gives a tool for…
We show that there are number of ways to transform an arbitrary polarization state to another with just two quarter wave plates (QWP). We have verified this geometrically using the trajectories of the initial and final polarization states…
We introduce a tomography approach to describe the optical response of a cavity quantum electrodynamics device, beyond the semiclassical image of polarization rotation, by analyzing the polarization density matrix of the reflected photons…
Inspired by recent use of polarimetry to study the Cosmic Microwave Background and extragalatic supernovae, a foray into the statistical properties of Stokes parameters expressed in spherical coordinates is began, allowing circular…
Given sphere preserving (M\"obius) transformations in $n$-dimensional Euclidean space one can use the Poincar\'e extension to obtain sphere preserving transformations in a half space of $n+1$ dimensions. The Poincar\'e extension is usually…
It is shown that the two complex Cartesian components of the electric field of a monochromatic electromagnetic plane wave, with a temporal and spatial dependence of the form ${\rm e}^{{\rm i} (kz - \omega t)}$, form a SU(2) spinor that…
We present a constructive framework for designing transformations between structured light fields using birefringent optical elements, formulated in terms of SU(2) operations on polarization. Within this framework, transformations between…
In the framework of optical quantum computing and communications, a major objective consists in building receiving nodes that implement conditional operations on incoming photons, using the interaction with a single stationary qubit. In…
Designing a single element for all polarization transformations on a Poincar\'e sphere is impossible due to practical limitations and hence a combination of few standard wave-plates are used to construct a gadget. With this gadget it is…
We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in…
Poincar\'e-gravity modes described by the shallow water equations in a rotating frame have non-trivial topology, providing a new perspective on the origin of equatorially trapped Kelvin and Yanai waves. We investigate the topology of…
The geometric phase of light is a fascinating phenomenon in optics and arises whenever there is a change in the polarization state of light. It is a fundamentally well-established concept and has recently found extensive applications,…
This article presents a generalization of the notion of \emph{Poincar\'e rotation set} to homeomorphisms of the ad\`ele class group $\mathbb{A}/\mathbb{Q}$ of the rational numbers $\mathbb{Q}$, which is a connected compact abelian group…
We present a simple and convenient method to yield cylindrical vector (CV) beams and realize its polarization evolution on higher-order Poincare sphere based on inhomogeneous birefringent metasurface. By means of local polarization…
We study geodesics on hypersurfaces close to the standard (n-1)-dimensional sphere in n-dimensional Euclidean space. Following Poincar\'e, we treat the problem within the framework of the analytical mechanics, and employ the perturbation…
We study non-resonant and resonant Hopf bifurcation of a rotating wave in SO(3)-equivariant reaction-diffusion systems on a sphere. We obtained reduced differential equations on so(3), the characterization of modulated rotating waves…