Ergun Simsek

Singularity subtraction for evaluation of Green's functions for multilayer media

This paper presents an efficient method to evaluate the two- and three-dimensional multilayered medium Greens functions for general electric and magnetic sources. Without finding any surface poles or steepest descent path, a special subtraction procedure is applied to each term of the Sommerfeld integrands to make them rapidly decreasing functions of krho. The contributions of the subtracted terms are calculated analytically. The remaining integrals are computed adaptively by using Gaussian quadratures. The accuracy of the method has been confirmed by comparison with many examples in literature, and the high efficiency has been verified

Nanoscale patterning of graphene through femtosecond laser ablation

We report on nanometer-scale patterning of single layer graphene on SiO2/Si substrate through femtosecond laser ablation. The pulse fluence is adjusted around the single-pulse ablation threshold of graphene. It is shown that, even though both SiO2 and Si have more absorption in the linear regime compared to graphene, the substrate can be kept intact during the process. This is achieved by scanning the sample under laser illumination at speeds yielding a few numbers of overlapping pulses at a certain point, thereby effectively shielding the substrate. By adjusting laser fluence and translation speed, 400 nm wide ablation channels could be achieved over 100 μm length. Raster scanning of the sample yields well-ordered periodic structures, provided that sufficient gap is left between channels. Nanoscale patterning of graphene without substrate damage is verified with Scanning Electron Microscope and Raman studies.

A spectral Integral method (SIM) for layered media

A spectral integral method is presented for electromagnetic scattering from dielectric and perfectly electric conducting (PEC) objects with a closed boundary embedded in a layered medium. Two-dimensional layered medium Greens functions are computed adaptively by using Gaussian quadratures. The singular terms in the Greens functions and the non-smooth terms in their derivatives are handled appropriately to achieve exponential convergence. Numerical results, compared with the ones obtained by using other methods, demonstrate the spectral accuracy and high efficiency of the proposed method. They also confirm that the spectral integral method (SIM) is applicable to concave objects.

A Spectral Integral Method and Hybrid SIM/FEM for Layered Media

This paper first presents a spectral integral method (SIM) for electromagnetic scattering from homogeneous dielectric and perfectly electric conducting objects straddling several layers of a multilayered medium. It then uses this SIM as an exact radiation boundary condition to truncate the computational domain in the finite-element method (FEM) to form a hybrid SIM/FEM, which is applicable to arbitrary inhomogeneous objects. Due to the high accuracy of the SIM, the sampling density on the radiation boundary requires less than five points per wavelength to achieve 1% accuracy. The efficiency and accuracy of the developed methods have been demonstrated with several numerical experiments for the TMz case. The TEz case can be obtained by duality

Bessel-beam-written nanoslit arrays and characterization of their optical response

Nanoslit arrays are fabricated on thin metal film coated glass slides using femtosecond laser pulses with Bessel beam profiles. The optical properties of the fabricated structures with different periodicities are characterized with transmission spectroscopy. Experimental results reveal the existence of two separate surface plasmon resonance modes occurring at the metal-air and metal-glass interfaces. These two resonance modes cause two minima in the high transmission spectra of the sub-skin depth thick thin films in the visible and near infrared regions. The existence of double surface plasmon resonance modes is verified with additional experiments, theoretical and numerical studies. Due to its relaxed alignment constraints, reduced aberrations, scalability property to shorter wavelengths, and resulting shorter dimensions, nanofabrication with diffraction-free Bessel beams is an easy, cheap, and advantageous alternative to regular lithography techniques to fabricate nanoslit arrays. The shift of the reson...

A 3-D Spectral Integral Method (SIM) for Surface Integral Equations

An efficient 3-D spectral integral method (SIM) has been proposed to speed up the method of moments (MOM) calculation of induced currents on a cuboid. This method utilizes the Toeplitz structure in the impedance matrix and the fast Fourier transform to accelerate the MOM solution. It reduces the memory and CPU time per iteration from <i>O</i>(<i>N</i> ²) in the MOM to <i>O</i>(<i>N</i> ^1.5) and <i>O</i>(<i>N</i> ^1.5log<i>N</i>), respectively. Thus, the SIM can be also used as an efficient radiation boundary condition for the finite element method. Numerical results confirm the effectiveness of this method.

A spectral integral method for layered media

Summary form only given. In order to solve layered-medium problems, various numerical methods have been developed. We are concerned with piecewise homogeneous objects embedded in a layered medium. As such; the surface integral equation (SIE) can be used to reduce the number of unknowns compared with the volume integral equation. The SIE is solved first with the method of moments (MoM) and then with the fast multipole method (FMM) to calculate the electromagnetic fields scattered from a homogeneous scatter with arbitrary geometry in free space. J. Liu and Q. H. Liu (see IEEE Micro. and Wire. Comp. Lett., vol.14, no.3, p.97-9, 2004) developed a spectral integral method (SIM) as an alternative way of solving the surface integral equation more efficiently than MoM for arbitrarily-shaped smooth dielectric cylinders in free space. We extend this method to arbitrarily-shaped smooth perfect electrical conductor (PEC) and dielectric cylinders in a multilayer medium. We have demonstrated the spectral accuracy of the method and the reduced computational cost from that of the MoM. This method can also be extended to three dimensions.

Fast computation of dyadic Green's function for layered media and its application in interconnect simulations

Summary form only given. In order to solve layered-medium problems, such as interconnect simulations, various numerical methods have been developed. We are concerned with piecewise homogeneous objects embedded in a layered medium. The surface integral equation (SIE) can be used to reduce the number of unknowns required in the volume integral equation. For the solution of the SIE, we first develop a fast method to evaluate the Sommerfeld integrals in the dyadic Greens function (GF) for a layered medium. Particular attention is paid to evaluate the GF when the source and observation points are on the same plane parallel to the layer interfaces. The primary and quasi-static field terms are subtracted from the integrand of the dyadic GF and their contribution is calculated analytically. This makes the integrand decay rapidly for large values of k/sub /spl rho//. Since this is an exact method, the whole procedure is robust; the results of this method have been validated by comparison with many examples in the literature, and the high efficiency has been verified. We then apply this dyadic GF in the solution of surface integral equations arising from interconnect simulations.

Influence of Breakouts On Borehole Sonic Dispersions

Borehole breakouts are commonly encountered during underbalance drilling in the presence of large tectonic stresses. The characteristics of borehole sonic data may be affected by strong departures from cylindrical geometry. A finite-difference time domain (FDTD) formulation with a perfectly-matched layer (PML) enables a study of the influence of breakouts on the borehole Stoneley, flexural and quadrupole dispersions. Breakout azimuths are oriented perpendicular to the maximum horizontal stress direction. The FDTD formulation yields synthetic waveforms at an array of receivers produced by a monopole, dipole or quadrupole source placed on the borehole axis. The borehole cross-section can be modified to simulate the breakout geometry. Synthetic waveforms are then processed by a modified matrix pencil algorithm to isolate both non-dispersive and dispersive arrivals in the wavetrain. While the axi-symmetric Stoneley dispersion is marginally affected by the presence of a breakout, there are discernible changes in both the flexural and quadrupole dispersions that can help in the analysis of such borehole failures. Computational results indicate that the presence of a symmetric breakout causes both the flexural and quadrupole wave splitting in the intermediate frequency band similar to the case of an elliptic hole. The two canonical dispersions approximately correspond to the largest and smallest diameters of the distorted borehole cross-section. These characteristic changes in the Stoneley, flexural and quadrupole dispersions can be used as indicators of the presence of breakouts and need to be accounted for in the sonic data inversion and interpretation.

A spectral integral method for the analysis of nano wires

This work presents a spectrally accurate method for electromagnetic scattering from objects with complex permittivity embedded in a layered medium. Two-dimensional (2D) layered medium Greens functions are computed adaptively by using Gaussian quadratures. The singular terms in the Greens functions and the non-smooth terms in their derivatives are handled appropriately to achieve exponential convergence. Numerical results, compared with the ones obtained by using other methods, demonstrate the spectral accuracy and high efficiency of the proposed method.