Ismail E. Uysal

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.

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.

An MOT-TDIE solver for analyzing transient fields on graphene-based devices

A marching on-in-time (MOT) scheme for analyzing transient electromagnetic wave interactions on devices consisting of graphene sheets and dielectric substrates is proposed. The MOT scheme discretizes time domain resistive boundary condition (TD-RBC) and Poggio-Miller-Chang-Harrington-Wu-Tsai (TD-PMCHWT) integral equation, which are enforced on the surfaces of the graphene and dielectric substrate, respectively. The expressions of the time domain resistivity and conductivity of the graphene sheet are obtained analytically from the intra-band contribution formulated in frequency domain. Numerical results, which demonstrate the applicability of the proposed scheme, are presented.

Analysis of transient electromagnetic wave interactions on graphene-based devices using integral equations

Graphene is a monolayer of carbon atoms structured in the form of a honeycomb lattice. Recent experimental studies have revealed that it can support surface plasmons at Terahertz frequencies thanks to its dispersive conductivity. Additionally, characteristics of these plasmons can be dynamically adjusted via electrostatic gating of the graphene sheet (K. S. Novoselov, et al., Science, 306, 666–669, 2004). These properties suggest that graphene can be a building block for novel electromagnetic and photonic devices for applications in the fields of photovoltaics, bio-chemical sensing, all-optical computing, and flexible electronics. Simulation of electromagnetic interactions on graphene-based devices is not an easy task. The thickness of the graphene sheet is orders of magnitude smaller than any other geometrical dimension of the device. Consequently, discretization of such a device leads to significantly large number of unknowns and/or ill-conditioned matrix systems.

Analysis of transient electromagnetic interactions on nanodevices using a quantum corrected integral equation approach

Analysis of electromagnetic interactions on nanodevices can oftentimes be carried out accurately using “traditional” electromagnetic solvers. However, if a gap of sub-nanometer scale exists between any two surfaces of the device, quantum-mechanical effects including tunneling should be taken into account for an accurate characterization of the devices response. Since the first-principle quantum simulators can not be used efficiently to fully characterize a typical-size nanodevice, a quantum corrected electromagnetic model has been proposed as an efficient and accurate alternative (R. Esteban et al., Nat. Commun., 3(825), 2012). The quantum correction is achieved through an effective layered medium introduced into the gap between the surfaces. The dielectric constant of each layer is obtained using a first-principle quantum characterization of the gap with a different dimension.

Transient analysis of plasmonic nanostructures using an MOT-PMCHWT solver

A marching on in time (MOT) scheme for solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation on plasmonic nanostructures is described. The proposed scheme calls for temporal convolutions of the permittivity and Green function of the plasmonic medium with the temporal basis function. Time domain samples of the permittivity and the Green function required by these convolutions are computed using a fast relaxed vector fitting (FRVF) algorithm. Numerical results demonstrate the accuracy and applicability of the proposed MOT-PMCHWT solver.

Analysis of transient plasmonic interactions using an MOT-PMCHWT integral equation solver

In this work, a marching on-in-time (MOT) scheme is proposed to solve the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) (L. N. MedgyesiMitschang et al., J. Opt. Soc. Am. A, 11(4), 1383-1398, 1994) IE for analyzing transient plasmonic interactions. The MOT-PMCHWT solver calls for convolutions of the spatio-temporal basis functions with the time domain Green function of the dispersive medium. These convolutions are carried out using a semi-numerical procedure. It is shown that Green function consists of a Dirac delta term and a temporal tail. The convolution with the delta term is analytically evaluated. Samples of the temporal tail are computed from frequency domain samples using the Fast Relaxed Vector Fitting (FRVF) algorithm (B. Gustavsen, IEEE Trans. Power Delivery, 21(3), 1587-1592, 2006). FRVF generates a rational function fit to frequency domain samples, which is used in time domain to represent the tail of the Green function in terms of shifted exponentials. Applying this procedure to every source-observer pair during the computation of MOT matrix entries is computationally costly. Therefore, a look-up table consisting of Green function samples at discrete distances and times is generated. Then, an interpolation scheme is used to fill the MOT matrix elements.