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Miniaturized optical resonators with spatial dimensions of the order of the wavelength of the trapped light offer prospects for a variety of new applications like quantum processing or construction of meta-materials. Light propagation in…
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…
In this paper, a mixed high order finite difference scheme-Pad\'{e} approximation method is applied to obtain numerical solution of the Riesz fractional advection-dispersion equation. This method is based on the high order finite difference…
We study multi-parameter solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation which include oscillating laser beams in a parabolic waveguide, spiral light beams, and other important families of…
The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…
We study a reduced hydrodynamic formulation of paraxial vector beam propagation in which the beam intensity, optical phase, and spatially-dependent polarization are coupled through a nonlinear dispersive system. While prior analytical work…
The scattering of light impacts sensing and communication technologies throughout the electromagnetic spectrum. Overcoming the effects of time-varying scattering media is particularly challenging. In this article we introduce a new way to…
Synthesizing a densely sampled light field from a single image is highly beneficial for many applications. The conventional method reconstructs a depth map and relies on physical-based rendering and a secondary network to improve the…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
We demonstrate cloaking with four lenses of different focal lengths. To achieve this, we compute the separation distances between lenses such that the effective ABCD matrix is equal to just a propagation in free space. Previously,…
In this paper, we propose a systematic approach to design a four-component zoom system with fixed spacing between focal points based on matrix optics. Since the more complex model the higher degree of freedom it has, the task of determining…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
A matrix method for the solution of direct fractional Sturm-Liouville problems on bounded domain is proposed where the fractional derivative is defined in the Riesz sense. The scheme is based on the application of the Galerkin spectral…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation…
When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or…
Band theory for partially coherent light is introduced by using the formalism of second-order classical coherence theory under paraxial approximation. It is demonstrated that the cross-spectral density function, describing correlations…
Rigorous electromagnetic field simulations are an essential part for scatterometry and mask pattern design. Today mainly periodic structures are considered in simulations. Non-periodic structures are typically modeled by large, artificially…
We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used,…