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We propose that the full Poincar{e} beam with any polarization geometries can be pictorially described by the hybrid-order Poincar{e} sphere whose eigenstates are defined as a fundamental-mode Gaussian beam and a Laguerre-Gauss beam. A robust and efficient Sagnac interferometer is established to generate any desired full Poincar{e} beam on the hybrid-order Poincar{e} sphere, via modulating the incident state of polarization. Our research may provide an alternative way for describing the full Poincar{e} beam and an effective method to manipulate the polarization of light.
The goal of this paper is to push forward the study of those properties of log-concave measures that help to estimate their Poincar{e} constant. First we revisit E. Milmans result [40] on the link between weak (Poincar{e} or concentration) inequaliti
We propose and experimentally demonstrate a novel interferometric approach to generate arbitrary cylindrical vector beams on the higher order Poincare sphere. Our scheme is implemented by collinear superposition of two orthogonal circular polarizatio
Function approximation and recovery via some sampled data have long been studied in a wide array of applied mathematics and statistics fields. Analytic tools, such as the Poincare inequality, have been handy for estimating the approximation errors in
We define Poincar{e} profiles of Dirichlet type for graphs of bounded degree, in analogy with the Poincar{e} profiles (of Neumann type) defined in [HMT19]. The obvious first definition yields nothing of interest, but an alternative definition yields
In this paper, we consider a problem in calculus of variations motivated by a quantitative isoperimetric inequality in the plane. More precisely, the aim of this article is the computation of the minimum of the variational problem $$inf_{uinmathcal{W