Related papers: Some exact solutions for light beams
A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression…
For the first time exact analytical solutions to the eikonal equations in (1+1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit…
Beam shaping - the ability to engineer the phase and the amplitude of massive and massless particles - has long interested scientists working on communication, imaging and the foundations of quantum mechanics. In light optics, the shaping…
We construct localized beams that are located at the edge of a non-Hermitian Glauber Fock (NGF) lattice made of coupled waveguides and can propagate for a long distance without almost no diffraction. Specifically, we calculate the…
We show that any metallo-dielectric multilayer with a hyperbolic dispersion relation can actually be characterized by a complex effective index. This refractive index, extracted from the complex Bloch band diagram, can be directly linked to…
Wavefront shaping allows for ultimate control of light propagation in multiple-scattering media by adaptive manipulation of incident waves. We shine two separate wavefront-shaped beams on a layer of dry white paint to create two enhanced…
Radially-polarized light beams present very interesting and useful behavior for creating small intensity spots when tightly-focused, and manipulating nanostructures or charged particles. The modeling of the propagation of such vector beams,…
Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles…
A particular case of the Hindman--Galvin--Glazer theorem states that, for every partition of an infinite abelian group $G$ into two cells, there will be an infinite $X\subseteq G$ such that the set of its finite sums…
Lenses are crucial to light-enabled technologies. Conventional lenses have been perfected to achieve near-diffraction-limited resolution and minimal chromatic aberrations. However, such lenses are bulky and cannot focus light into a hotspot…
In this article we formulate and solve the problem of molecular beam diffraction when each molecule consists of two interacting bodies. Then, using our results, we present the diffraction patterns for various molecular sizes employing the…
The orbital angular momentum (OAM) of light holds great promise for applications in optical communication, super-resolution imaging, and high-dimensional quantum computing. However, the spatio-temporal coherence of the light source has been…
In this paper, we present a new mathematical foundation for image-based lighting. Using a simple manipulation of the local coordinate system, we derive a closed-form solution to the light integral equation under distant environment…
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams,…
We study monochromatic, scalar solutions of the Helmholtz and paraxial wave equations from a field-theoretic point of view. We introduce appropriate time-independent Lagrangian densities for which the Euler-Lagrange equations reproduces…
We investigate numerically interactions between two bright or dark incoherent localized beams in an strontium barium niobate photorefractive crystal in one dimension, using the coherent density method. For the case of bright beams, if the…
We introduce a novel technique using closure amplitudes, inspired by radio interferometry, to determine with high angular resolution the two-dimensional profile of a light beam using an interferogram from a non-redundantly masked aperture.…
By a generalized bidirectional decomposition method, we obtain many new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; various of them…
We propose and generate a new class of structured light fulfilling quantum-like coherent states based on a set of circular Airy vortex modes. Such coherent-state wave packets possess strong focus with both radial and angular…
Vortex beams are stable solutions of Maxwell's equations that carry phase singularities and orbital angular momentum, unique properties that give rise to many applications in the basic sciences, optical communications, and quantum…