Related papers: SU(2) gadget for higher-order Poincar\'{e} sphere
The orbital angular momentum and the polarisation of light are physical quantities widely investigated for classical and quantum information processing. In this work we propose to take advantage of strong light-matter coupling,…
Polarization-resolved control and measurement of the optical field are essential for a wide range of photonic systems, including coherent communication, polarimetric sensing, and quantum information processing. We present a photonic…
A general scheme of construction and analysis of physical fields on the various homogeneous spaces of the Poincar\'{e} group is presented. Different parametrizations of the field functions and harmonic analysis on the homogeneous spaces are…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
We show that polarization states of electromagnetic waves can be manipulated easily using a single thin uniaxial crystal plate. By performing a rotational transformation of the coordinates and controlling the thickness of the plate, we can…
We introduce an alternative approach to the polarization theory of light. This is based on a set of quantum operators, constructed from two independent bosons, being three of them the $su(1,1)$ Lie algebra generators, and the other one, the…
We introduce a notion of Poincar\'e duality for pairs of $\infty$-categories, extending Poincar\'e-Lefschetz duality for pairs of spaces. This categorical extension yields an efficient book-keeping device that affords, among other things, a…
Dielectric metasurfaces with spatially varying birefringence and high transmission efficiency can exhibit exceptional abilities for controlling the photonic spin states. We present here some of our works on spin photonics and spin-photonic…
We have described a novel way to determine the Mueller matrix of any optical element by using projection method. For this purpose, we have used two universal SU(2) gadgets for polarization optics to obtain projection matrix directly from…
We present the realization of a ultra fast shutter for optical fields, which allows to preserve a generic polarization state, based on a self-stabilized interferometer. It exhibits high (or low) transmittivity when turned on (or inactive),…
We propose and experimentally demonstrate a novel type of polarization rotator which is capable of rotating the polarization plane of a linearly polarized light at any desired angle in either broad or narrow spectral bandwidth. The rotator…
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons…
We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…
Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum…
The Poincar\'e polynomial of the complement of an arrangements in a non compact group is a specialization of the $G$-Tutte polynomial associated with the arrangement. In this article we show two unimodular elliptic arrangements (built up…
In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincar\'e algebra. We first give some general properties of Lie superalgebras with some emphasis on the supersymmetric extension of the…
Structured light has proven useful for numerous photonic applications. However, the current use of structured light in optical fiber science and technology is severely limited by mode mixing or by the lack of optical elements that can be…
2-Dim quantum Poincare` Group E_q(1,1) at roots of unity, its dual U_q(e(1,1)) and some of its homogeneous spaces are introduced. Invariant integrals on E_q(1,1) and its invariant discrete subgroup E(1,1\mid p) are constructed.…
We demonstrate an optomechanical platform where optical mode conversion mediated by mechanical motion enables arbitrary tailoring of polarization states of propagating light fields. Optomechanical interactions are realized in a…
The first experimental realization of a photon Bose-Einstein condensate was demonstrated more than a decade ago. However, the polarization of the condensate has not been fully understood and measured in this weakly driven-dissipative…