Related papers: Geometric representation of higher-order optical m…
Generalised Hermite-Gaussian modes (gHG modes), an extended notion of Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function $\alpha$, which can be used to unite conventional HG…
Visual methods are of great utility in understanding and interpreting quantum mechanics at all levels of understanding. The Bloch sphere, for example, is an invaluable and widely used tool for visualising quantum dynamics of a two level…
With increasing interest in using orbital angular momentum (OAM) modes in high-power laser systems, accurate mathematical descriptions of the high-intensity modes at focus are required for realistic modelling. In this work, we derive…
We present an experimental demonstration to manipulate the width and position of the down-converted beam waist. Our results can be used to engineer the two-photon orbital angular momentum (OAM) entangled states (such as concentrating OAM…
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…
We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer…
The rich structure of transverse spatial modes of structured light has facilitated their extensive applications in quantum information and optical communication. The Laguerre-Gaussian (LG) modes, which carry a well-defined orbital angular…
We present higher order polynomial algebras which are the dynamical symmetry algebras of a wide class of multi-mode boson systems in non-linear optics. We construct their unitary representations and the corresponding single-variable…
We explore Majorana stellar representation on the Riemann sphere for optical scalar beams and vector fields, leveraging the spin and orbital angular momentum of light. For scalar beams, the star constellations for the Laguerre-Gaussian beam…
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 deduce a set of circularly polarized Gaussian laser beam modes via a separation-of-variables solution to the Helmholtz wave equation in oblate spheriodal coordinates. On transforming to cylindrical coordinates these become the well-known…
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.…
We propose an interferometric method for statistically discriminating between nonorthogonal states in high dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital…
A generalized family of scalar structured Gaussian modes including helical-Ince--Gaussian (HIG) and Hermite--Laguerre--Gaussian (HLG) beams is presented with physical insight upon a hybrid topological evolution nature of multi-singularity…
The transverse structure of light is recognized as a resource that can be used to encode information onto photons and has been shown to be useful to enhance communication capacity as well as resolve point sources in superresolution imaging.…
Classical beams of light with non-uniform polarization patterns (e.g. radially and azimuthally polarized doughnut beams) may exhibit quantum-like features as, for instance, inseparability. We establish an exact correspondence between…
The geometry of quantum states is well-established as a basis for understanding the response of electronic systems to static electromagnetic fields, as exemplified by the theory of the quantum and anomalous Hall effects. However, it has…
We present a systematic treatment of higher-order modes of vacuum-clad ultrathin optical fibers. We show that, for a given fiber, the higher-order modes have larger penetration lengths, larger effective mode radii, and larger fractional…
Polarization of light signifies transversal, anisotropic and asymmetrical statistical property of electromagnetic radiation about direction of propagation. Traditionally, optical-polarization is characterized by Stokes theory susceptible to…
We propose a geometric hybrid Poincar\'e sphere (GHPS) as a unified geometrical framework for describing structured photon states with independently controllable spin angular momentum (SAM) and orbital angular momentum (OAM). Unlike the…