We use Hamiltonian optics to design and analyze beam propagation in two-dimensional (2D) periodic structures with slowly varying nonuniformities. We extend a conventional Hamiltonian method, adding equations for calculating the width of a beam propagating in such structures, and quantify the range of validity of the extended Hamiltonian equations. For calculating the beam width, the equations a...

This thesis describes an implementation of the discontinuous Galerkin finite element time domain (DGTD) method on unstructured meshes to solve acoustic wave equations in discontinuous media. In oil industry people use finite difference time domain (FDTD) methods to compute solutions of time domain wave equations and simulate seismic surveys, the first step to explore oil and gas in the earth’s ...

A new finite-difference time-domain (FDTD) algorithm is introduced to solve two dimensional (2D) transverse magnetic (TM) modes with a straight dispersive interface. Driven by the consideration of simplifying interface jump conditions, the auxiliary differential equation of the Debye constitution model is rewritten to form a new Debye–Maxwell TM system. Interface auxiliary differential equation...

The finite-difference time-domain (FDTD) method is used to simulate three-dimensional (3-D) geometries of realistic ground-penetrating radar (GPR) scenarios. The radar unit is modeled with two transmitters and a receiver in order to cancel the direct signals emitted by the two transmitters at the receiver. The transmitting and receiving antennas are allowed to have arbitrary polarizations. Sing...

Presented is the study of the diffraction properties of transmission holographic polymer dispersed liquid crystal (H-PDLC) grating. We constructed a two-dimensional model of H-PDLC film with cylindrical LC droplets. Director distribution inside LC droplets was calculated using the Monte-Carlo method. To calculate light propagation through the film we have solved numerically the Maxwell equation...

The aim of this paper is to show how 2D approaches, often used to investigate numerically the real devices as they are faster and simpler respect to 3D techniques, may lead to wrong results in modeling Photonic Crystal structures. As a test case, the determination of the so called Mini Stop Band (MSB) for the fundamental mode in a W1 waveguide is considered. A MSB is found when the structure, r...

We analyze the performance of finite-difference timedomain (FDTD) method implementations for 2D and 3D problems. Implementations in Fortran, C and C++ (with Blitz++ library) languages and performance tests on several hardware setups (AMD, Intel i5, Intel Xeon) are considered. The performance of implementations using traditional FDTD algorithm for the largest size of test problem is limited by t...

The paper presents the results of 3D FDTD modeling of a 915 MHz cylindrical structure with a spherical load (fruit). Three different configurations of the loops exciting the TM01l mode are analyzed. The coupling is shown not to be sensitive to the load’s temperature and to the type of the fruit.

This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite-difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump condit...