Related papers: A ray-optical Poincar\'e sphere for structured Gau…
Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536-540) found a paraxial…
The extended Gaussian family is the closure of the Gaussian family obtained by completing the Gaussian family with the counterpart elements induced by degenerate covariance or degenerate precision matrices, or a mix of both degeneracies.…
Spatial characteristics of diffracted beams produced by the "fork" holograms from incident circular Lauerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the…
A light ray in space is characterized by two vectors: (i) a transverse spatial-vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation.…
We construct a frame of complex Gaussians for the space of $L^2(\mathbb{R}^n)$ functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the…
We investigate the waveguiding properties of the optical interference pattern of two counter-propagating Laguerre-Gaussian beams. The number, helicity, radius, pitch, depth and frequencies of transverse confinement of the waveguides are…
We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly-periodic Mathieu functions in…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
The geometrical-optics expansion reduces the problem of solving wave equations to one of solving transport equations along rays. Here we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general…
In this work, a group theory-based formulation that introduces new classes of dihedral-symmetric beams is presented. Our framework leverages the algebraic properties of the dihedral group of rotations and reflections to transform input…
An octant representation of higher-order optical modes that includes Laguerre-Gaussian and Hermite-Gaussian modes is presented. The octant picture captures the high-dimensional nature of three-state optical systems and beyond, with standard…
In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that…
When a phase singularity is suddenly imprinted on the axis of an ordinary Gaussian beam, an optical vortex appears and starts to grow radially, by effect of diffraction. This radial growth and the subsequent evolution of the optical vortex…
We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schr\"odinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into…
We investigate, theoretically and experimentally, the evolution of a paraxial beam propagating in free space when its initial transverse structure is characterized by an asymmetric Gaussian modulation combined with an entire function.…
We explore a degenerate four-wave mixing process induced by transversely structured light beams in a rubidium vapor cell. In particular, we consider the nonlinear interaction driven by optical modes contained in the orbital angular momentum…
We present a description of the evolution of a polarized Gaussian beam in a smoothly inhomogeneous isotropic medium in frame of the eikonal-based complex geometrical optics which describes the phase front and the cross section of the…
A centred system forms the coherent image of the optical field on a spherical cap, taken as an object, on another spherical cap, whose vertex and curvature center are the respective paraxial images of the vertex and center of the object…
Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is…
We demonstrate the transformation of Gaussian input beams into super-Gaussian beams with a quasi flat-top transverse profile by means of the conical refraction phenomenon by adjusting the ratio between the ring radius and the waist radius…