Related papers: SU(2) gadget for higher-order Poincar\'{e} sphere
We extend the notion of Poincar\'e duality in KK-theory to the setting of quantum group actions. An important ingredient in our approach is the replacement of ordinary tensor products by braided tensor products. Along the way we discuss…
The angular momentum of light can be elegantly mapped onto high-order Poincare spheres, providing a powerful framework for describing structured light beams. Such beams have shown extraordinary potential across diverse applications,…
The dimension of the third homogeneous component of a matrix quantum bialgebra, determined by pair of quantum spaces, is calculated. The Poincar\'{e} series of some deformations of $GL(n)$ is calculated. A new deformation of $GL(3)$ with…
For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for…
We study Poincar{\'e} series associated to strictly convex bodies in the Euclidean space. These series are Laplace transforms of the distribution of lengths (measured with the Finsler metric associated to one of the bodies) from one convex…
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 a broadband optical device that is capable of rotating the polarization plane of a linearly polarized light at any desired angle over a wide range of wavelengths. The device is composed of a sequence of half-wave plates rotated…
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 comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincar\'e sphere.…
We theoretically suggest and experimentally demonstrate a broadband composite optical rotator that is capable of rotating the polarization plane of a linearly-polarized light at any chosen angle. The device is composed of an even number of…
In polarization optics, various topological constructs, namely Poincar\'e spheres of different orders, are used to represent uniform and structured polarization distributions. Similarly, there are also structured polarization optical…
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…
The $GL_2$ Poincar\'{e} series giving the subconvexity results of Diaconu and Garrett is the solution to an automorphic partial differential equation, constructed by winding-up the solution to the corresponding differential equation on the…
Dynamic manipulation of arbitrary light polarization is of fundamental importance for versatile optical functionalities, yet realizing such full-Poincar\'e-sphere control within compact nanophotonic architectures remains a formidable…
We present an approach to classical polarimetry that requires no moving parts, is compact and robust, and that encodes the complete polarization information on a single data frame, accomplished by replacing the rotation of components such…
We define and study 'non-abelian' Poincar\'e series for the group $G=\mathrm{SU} (2,1)$, i.e. Poincar\'e series attached to a Stone-Von Neumann representation of the unipotent subgroup $N$ of $G$. Such Poincar\'e series have in general…
We derive new Poincar\'e-series representations for infinite families of non-holomorphic modular invariant functions that include modular graph forms as they appear in the low-energy expansion of closed-string scattering amplitudes at genus…
Geometric representation lays the basis for understanding and flexible tuning of topological transitions in many physical systems. An example is given by the Poincar\'{e} sphere (PS) that provides an intuitive and continuous…
Parallel transport of a vector around a closed curve on the surface of a sphere leads to a direction holonomy which can be related with a geometric phase that is equal to the solid angle subtended by the closed curve. Since Pancharatnam…
We show that, under the right conditions, one can make highly accurate polarization-based measurements without knowing the absolute polarization state of the probing light field. It is shown that light, passed through a randomly varying…