Related papers: On Gaussian Beams Described by Jacobi's Equation
Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as…
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…
Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to…
In this work we construct Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source. Under the assumption of non-trapping rays we show error estimates between the exact outgoing solution and…
We consider the propagation of Gaussian beams in a waveguide with gain and loss in the paraxial approximation governed by the Schr\"odinger equation. We derive equations of motion for the beam in the semiclassical limit that are valid when…
We develop the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray-wave tilt and the curvature of materials Fresnel wave surfaces. We obtain solutions of the paraxial equation in the form…
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…
A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…
The Ince-Gauss beams, separable in elliptic coordinates, are studied through a ray-optical approach. Their ray structure can be represented over a ray-Poincar\'e sphere by generalized Viviani curves (intersections of a cylinder and a…
We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which represents a limit on the practical simulation time. The…
This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation of wave equations, semi-discretized in space by finite difference schemes. GB are high-frequency solutions whose propagation can be…
We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
We present the Eulerian Gaussian beam method in anisotropic media. We derive kinematic and dynamic ray tracing equations based on the level set theory and Eulerian theory using the anisotropic eikonal equation. Compared with the traditional…
We conducted a comprehensive study on the robust propagation of the same spot-size Gaussian beam (SSGB), same envelope Gaussian beam (SEGB), Circular Airy beam (CAB) and Circular Pearcey beam (CPB) in complex environments. Our findings…
The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error…
Quantum Gaussian channels play a key role in quantum information theory. In particular, the attenuation and amplification channels are useful to describe noise and decoherence effects on continuous variables systems. They are directly…
There is a study of coherent perfect absorption (CPA) in composite medium (CM) which is made of metal-dielectric composition. The CM, an orthorhombic shaped slab, is illuminated by two identical Gaussian beams (GB) incident at equal angle…
In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane…
A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is invariant upon propagation (except for cycling of the rays and…