Related papers: SU(2) gadget for higher-order Poincar\'{e} sphere
Building on Greene's changemaker lattices, we develop a lattice embedding obstruction to realizing an L-space bounding a definite 4-manifold as integer surgery on a knot in the Poincar\'e homology sphere. As the motivating application, we…
A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into…
It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and…
Electrically tunable devices contribute significantly to key functions of photonics integrated circuits. Here, we demonstrate the tuning of the optical index of refraction based on hybrid integration of multi-layered anisotropic GaGeTe on a…
Semiconductor quantum dots are promising candidates for the generation of nonclassical light. Coupling a quantum dot to a device capable of providing polarization-selective enhancement of optical transitions is highly beneficial for…
Recent experimental work has demonstrated the potential to combine the merits of diffractive and on-chip photonic information processing devices in a single chip by making use of planar (or slab) waveguides. Researchers have adapted key…
We present a portable polarimeter capable of real-time visualization of partial and fully polarized light over a broad band of wavelengths. Our system utilizes a Raspberry Pi computer with a low-cost data acquisition "HAT" (DAQ HAT) and an…
We demonstrate a polarization rotator integrated at the output of a GaAs waveguide producing type I second harmonic generation (SHG). Form-birefringent phase matching between the pump fundamental transverse electric (TE) mode near 2.0…
We study the optical properties of a two-axis galvanometric optical scanner constituted by a pair of rotating planar mirrors, focusing our attention on the transformation induced on the polarization state of the input beam. We obtain the…
We give an explicit form of the symplectic groupoid that integrates the semiclassical standard Podles sphere. We show that Sheu's groupoid, whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld…
In any polarimetric measurement technique, enhancing the laser polarization change of a laser beam before it reaches the analyzer can help in improving the sensitivity. This can be performed using an optical component having a large linear…
Birefringent materials or nanostructures that introduce phase differences between two linear polarizations underpin the operation of wave plates for polarization control of light. Here we develop metasurfaces realizing a distinct class of…
Let M be the set of mixed states and S the set of separable states of the two-qubit system, and G = SU(2) x SU(2) the group of local unitary transformations (ignoring the overall phase factor). We compute the multigraded Poincare series for…
Gauge theories with matter fields in various representations play an important role in different branches of physics. Recently, it was proposed that several aspects of the interesting pseudogap phase of cuprate superconductors near optimal…
Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a 2-dim curved space) and mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm W}_0$) are shown to…
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…
Geometric phases play an enormous role in optics and are generally associated with the evolution of light's polarization state on the Poincar\'{e} sphere, or its spin on the sphere of spin directions. Here we put forward a new kind of…
In this paper, we analyze the possible homotopy types of the total space of a principal $SU(2)$-bundle over a $3$-connected $8$-dimensional Poincar\'{e} duality complex. Along the way, we also classify the $3$-connected $11$-dimensional…
The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…