Related papers: Generalized solution of the paraxial equation
We present a method to obtain explicit solutions of the complex eikonal equation in the plane. This equation arises in the approximation of Helmholtz equation by the WKBJ or EWT methods. We obtain the complex-valued solutions (called…
We demonstrate the fractional Talbot effect of nonpraxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect…
We formulate a multiple scattering theory of light in media spatially disordered along two directions and homogeneous along the third one, without making any paraxial approximation on the wave equation and fully treating the vector…
The Fokker--Planck Equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity…
Orbital Angular Momentum (OAM) waves were first recognized as those specific vortex solutions of the paraxial Helmholtz equation for which the orbital contribution to the total angular momentum of the beam yields an integer multiple of…
Since Schwarzshild discovered the point-mass solution to Einstein's equations that bears his name, many equivalent forms of the metric have been catalogued. Using an elementary coordinate transformation, we derive the most general form for…
A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The…
Spatially accelerating beams that are solutions to the Maxwell equations may propagate along incomplete circular trajectories, after which diffraction broadening takes over and the beams spread out. Taking these truncated Bessel wave fields…
It is shown how the standard forms for the spin and orbital components of the angular momentum of a paraxial wave of electromagnetic radiation are obtained from the general expressions for the angular momentum that have been derived…
On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase…
The parametric representation is given to the multisoliton solution of the Camassa-Holm equation. It has a simple structure expressed in terms of determinants. The proof of the solution is carried out by an elementary theory of…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
In this letter a new formula for light deflection is derived using only physically observable concepts. The general result is specialized to cosmological perturbation theory and expressed in terms of gauge--invariant perturbation variables.…
We consider light propagation through a twisted nematic liquid crystal. At first, an expression for light transmission is obtained using a rather intuitive approach. Secondly, an accurate solution for light transmission based on Maxwell's…
In [18], fundamental solutions for the generalized bi-axially symmetric Helmholtz equation were constructed in $R_2^ + = \left\{ {\left( {x,y} \right):x > 0,y > 0} \right\}.$ They contain Kummer's confluent hypergeometric functions in three…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
We construct 3-D solutions of Maxwell's equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum…
It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Dirichlet boundary conditions, are unique up to multiplication by a positive constant.
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…