H. Arda Ulku

MOT Solution of the PMCHWT Equation for Analyzing Transient Scattering from Conductive Dielectrics

Transient electromagnetic interactions on conductive dielectric scatterers are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation with a marching on-in-time (MOT) scheme. The proposed scheme, unlike the previously developed ones, permits the analysis on scatterers with multiple volumes of different conductivity. This is achieved by maintaining an extra temporal convolution that only depends on permittivity and conductivity of these volumes. Its discretization and computation come at almost no additional cost and do not change the computational complexity of the resulting MOT solver. Accuracy and applicability of the MOT-PMCHWT solver are demonstrated by numerical examples.

Transient analysis of electromagnetic wave interactions on plasmonic nanostructures using a surface integral equation solver

Transient electromagnetic interactions on plasmonic nanostructures are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation (SIE). Equivalent (unknown) electric and magnetic current densities, which are introduced on the surfaces of the nanostructures, are expanded using Rao-Wilton-Glisson and polynomial basis functions in space and time, respectively. Inserting this expansion into the PMCHWT-SIE and Galerkin testing the resulting equation at discrete times yield a system of equations that is solved for the current expansion coefficients by a marching on-in-time (MOT) scheme. The resulting MOT-PMCHWT-SIE solver calls for computation of additional convolutions between the temporal basis function and the plasmonic mediums permittivity and Green function. This computation is carried out with almost no additional cost and without changing the computational complexity of the solver. Time-domain samples of the permittivity and the Green function required by these convolutions are obtained from their frequency-domain samples using a fast relaxed vector fitting algorithm. Numerical results demonstrate the accuracy and applicability of the proposed MOT-PMCHWT solver.

Radon transform interpretation of the Physical Optics integral and application to near and far field acoustic scattering problems

The Physical Optics (PO) method is a useful asymptotic technique to solve scattering problems at relatively high frequencies. The main idea of PO is to assume the total field on the scatterer surface as twice of the incident field, roughly. With that assumption, scattered field can be found with the radiation integral over the illuminated surface of the scatterer. In three dimensional numerical scattering problems, modeling the scatterer with triangular patches is widely used. Therefore, the radiation integral, is conventionally calculated with steepest descent method or numerical Gaussian quadrature rule over triangular patches. However these methods have drawbacks, e.g. while using quadrature, the surface patches must be much smaller than the minimum wavelength of the incident wave. Recently, a novel technique to calculate scattered field from the PO source, is developed in [1] in time domain. The radiation integral is evaluated with the Radon transform (RT) interpretation in order to calculate the radar cross section (RCS) in [1]. The type of the transform can be called “planar RT.” Closed-form expressions of the magnetic and electric fields due to an RWG current source, which involves “spherical RT” have been obtained [2] in the past.

Solution of the initial condition problem of the time-domain EFIE

Marching on-in-time (MOT) solution of the time-domain electric-field integral equation (EFIE) can be corrupted with linearly increasing and constant components. This corruption is mainly caused by the inappropriate imposition of the initial conditions to the solution of EFIE. In this study, first- and second-order formulations (FOF and SOF) of the time-domain EFIE to alleviate the linear and constant corruption components will be presented. It will be shown that FOF remedies the linear component problem and SOF remedies both linear and constant component problems.

Transient analysis of scattering from ferromagnetic objects using Landau-Lifshitz-Gilbert and volume integral equations

An explicit marching on-in-time scheme for analyzing transient electromagnetic wave interactions on ferromagnetic scatterers is described. The proposed method solves a coupled system of time domain magnetic field volume integral and Landau-Lifshitz-Gilbert (LLG) equations. The unknown fluxes and fields are discretized using full and half Schaubert-Wilton-Glisson functions in space and bandlimited temporal interpolation functions in time. The coupled system is cast in the form of an ordinary differential equation and integrated in time using a PE(CE)m type linear multistep method to obtain the unknown expansion coefficients. Numerical results demonstrating the stability and accuracy of the proposed scheme are presented.

Correction to “Analytical Evaluation of Retarded-Time Potentials for SWG Bases” [Sep 14 4860-4863]

A missing scaling and a comparison of results post correction thereof are presented.

Transient analysis of electromagnetic wave interactions on high-contrast scatterers using volume electric field integral equation

A marching on-in-time (MOT)-based time domain volume electric field integral equation (TD-VEFIE) solver is proposed for accurate and stable analysis of electromagnetic wave interactions on high-contrast scatterers. The stability is achieved using band-limited but two-sided (non-causal) temporal interpolation functions and an extrapolation scheme to cast the time marching into a causal form. The extrapolation scheme is designed to be highly accurate for oscillating and exponentially decaying fields, hence it accurately captures the physical behavior of the resonant modes that are excited inside the dielectric scatterer. Numerical results demonstrate that the resulting MOT scheme maintains its stability as the number of resonant modes increases with the contrast of the scatterer.

On the reflection and shadow boundaries for a moving line source illumination

ABSTRACT This paper aims to investigate the effect of motion on the reflection and shadow boundaries which occur due to the illumination of a half-plane by a uniformly rectilinear moving infinitely long line source. It is shown that the zeros of the argument of the Fresnel integral function, which appears in the asymptotically uniform expression of the edge-diffracted field obtained through the saddle point technique, yield the time depending reflection and shadow boundaries. The numerical examples that show variations of the corresponding boundaries with respect to velocity at different time parameters are presented.

Radon transform interpretation of retarded-time potentials for SWG bases

The closed-form expression of the retarded-time potentials due to impulsively excited Schaubert-Wilton-Glisson (SWG) basis function is obtained using Radon transform interpretation and observation tetrahedron formulation. It has been shown that the closed-form expressions are yielding to geometric parameters, the solid angle and its gradient, formed during the intersection of the time dependent hyper-cone centered at the observation point and support of the SWG basis function. These geometric parameters are determined analytically using observation tetrahedron formulation. Numerical results that demonstrate the validity of the proposed method are presented.

On the initial condition problem of the time domain PMCHWT surface integral equation

Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced properly. This problem can be remedied by solving the time integral of the surface integral for auxiliary currents that are defined to be the time derivatives of the equivalent currents. Then the equivalent currents are obtained by numerically differentiating the auxiliary ones. In this work, this approach is applied to the marching on-in-time solution of the time domain Poggio-Miller-Chan-Harrington-Wu-Tsai surface integral equation enforced on dispersive/plasmonic scatterers. Accuracy of the proposed method is demonstrated by a numerical example.