Related papers: Paraxial beam propagation from Airy-type initial c…
We present a treatment of the nonlinear matter wave propagation inspired from optical methods, which includes interaction effects within the atom optics equivalent of the aberrationless approximation. The atom-optical ABCD matrix formalism,…
The master equation of quantum optical density operator is transformed to the equation of characteristic function. The parametric amplification and amplitude damping as well as the phase damping are considered. The solution for the most…
The discovery of Berry and Balazs in 1979 that the free-particle Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing…
We investigate, through simulation, the modifications to Bessel and Airy beams during propagation through atmospheric turbulence. We find that atmospheric turbulence disrupts the quasi-non-diffracting nature of Bessel and Airy beams when…
Several applications, such as optical tweezers and atom guiding, benefit from techniques that allow the engineering of optical fields' spatial profiles, in particular their longitudinal intensity patterns. In cylindrical coordinates,…
The interactions between copropagating ring-Airy beams in a (2+1)-dimensional Kerr medium are numerically investigated for the first time. It is shown that two overlapping ring-Airy beams in such a medium produce controllable regions of…
I derive directional wave equations useful for pulses propagating in beam, rod, pipe, and disk geometries by using a cylindrical coordinate system; the scheme works equally well for either long multi-cycle or single-cycle ultrashort pulses.…
We propose a paraxial quantum simulator that requires only widely available optical fibers or metamaterials. Such a simulator would facilitate cost-effective quantum simulation without specialized techniques. We show theoretically that the…
The paper aims at presenting a didactic and self-contained overview of Gauss-Hermite and Gauss-Laguerre laser beam modes. The usual textbook approach for deriving these modes is to solve the Helmoltz electromagnetic wave equation within the…
The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…
We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions,…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the sixth paper, exact analysis of the wave propagation in a beam with rectangular…
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…
We explore a family of paraxial beams constructed by the linear superposition of Laguerre-Gaussian beams, representing an optical analogue to generalized $SU(2)$ Lie group coherent states. A single complex parameter controls a smooth…
We analyse the paraxial field propagation in the realm of classical optics, showing that it can be written as the action of the fractional Fourier transform, followed by the squeeze operator applied to the initial field. Secondly, we show…
Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are…
We present a covariant approach to the problem of light beam propagation in a spacetime. We develop our considerations within the framework of classical geometric optics in general relativity. Using the concept of a screen surface…
We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…