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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…
We have considered the paraxial vector erf-Gaussian beams with field distribution in the form of the error function that are shaped by the cone of plane waves with a fractional step of the azimuthal phase distribution modulated by the…
Utilizing the extended Huygens-Fresnel principle and the Rytov approximation, the analytical formula for the propagation of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam (PCEShVB) in anisotropic atmospheric…
Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2x2…
Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion…
One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…
We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical…
We present a general, Gaussian spatial mode propagation formalism for describing the generation of higher order multi-spatial-mode beams generated during nonlinear interactions. Furthermore, to implement the theory, we simulate optical…
The propagation of Airy beams in free space is characterized by being non dispersive, which warrants the shape invariance of their intensity distribution, and self-accelerating along the transverse direction. These distinctive traits are…
Fresnel reflection has been known for centuries to fundamentally impede efficient transmittance across planar interfaces, especially at grazing incidence. Herein, we present the generalized Huygens' condition (GHC) to resolve such…
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…
In the pursuit of directly imaging exoplanets, the high-contrast imaging community has developed a multitude of tools to simulate the performance of coronagraphs on segmented-aperture telescopes. As the scale of the telescope increases and…
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.…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
This study investigates optical activity and quantum transport in twisted bilayer graphene (TBG) systems, demonstrating that the former results from spatial dispersion effects. The transfer matrix method is used to solve the propagation of…
High power end pumped solid state lasers often operate in regimes where pump induced heating creates a strong refractive index gradient (thermal lensing) that governs resonator stability and mode quality. When the pump is absorbed according…
Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide…
We investigate finite-width optical-beam propagation in a medium with uniform torsion described by the geometric theory of a continuous distribution of screw dislocations. Starting from the Riemann--Cartan framework that yields…
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,…
Gaussian graphical models provide a powerful framework for studying conditional dependencies in multivariate data, with widespread applications spanning biomedical, environmental sciences, and other data-rich scientific domains. While the…