John D. Rockway

Rough surface Green's function based on the first-order modified perturbation and smoothed diagram methods

Abstract This paper presents an analytical theory of rough surface Greens functions based on the extension of the diagram method of Bass, Fuks, and Ito with the smoothing approximation used by Watson and Keller. The method is a modification of the perturbation method and is applicable to rough surfaces with small RMS height. But the range of validity is considerably greater than for the conventional perturbation solutions. We consider one-dimensional rough surfaces with a Dirichlet boundary condition. The coherent Greens function is obtained from the smoothed Dysons equation using a spatial Fourier transform. The mutual coherence function for the Greens function is obtained by first-order iteration of the smoothing approximation applied to the Bethe-Salpeter equation in terms of a quadruple Fourier transform. These integrals are evaluated by the saddle-point technique. The equivalent bistatic cross section per unit length of the surface is compared with that for the conventional perturbation method and the Watson-Keller result. With respect to the Watson-Keller result, it should be noted that our result is reciprocal, while the Watson-Keller result is non-reciprocal. Included in this paper is a discussion of the specific intensity at a given observation point. The theory developed will be useful for RCS signature related problems and low grazing angle scattering when both the transmitter and the object are close to the surface.

Sommerfeld and Zenneck wave propagation for a finitely conducting one-dimensional rough surface

Starting with Zenneck and Sommerfeld wave propagation over a flat finitely conducting surface has been extensively studied by Wait (see IEEE Antennas Propagat. Mag., vol.40, p.7-24, 1998) and many other authors. We examine propagation over a finitely conducting rough surface, also studied by many people including Feinberg (1944), Bass and Fuks (1979), and Barrick (see Radio Sci., vol.6, p.517-26, and vol.6., p.527-33). This paper extends the multiple scattering theories based on Dyson and Bethe-Salpeter equations and their smoothing approximations. The theory developed here applies to rough surfaces with small root-mean-square (RMS) heights (/spl sigma/<0.1/spl lambda/). We limit ourselves to the one-dimensional (1-D) rough surface with finite conductivity excited by a magnetic line source, which is equivalent to the Sommerfeld dipole problem in two dimensions (x-z plane). With the presence of finite roughness, the total field decomposes into the coherent field and the incoherent field. The coherent (average) field is obtained by using Dysons equation, a fundamental integral equation based on the modified perturbation method. Once the coherent field has been obtained, we determine the Sommerfeld pole, the effective surface impedance, and the Zenneck wave for rough surfaces of small RMS heights. The coherent field is written in terms of the Fourier transform, which is equivalent to the Sommerfeld integral. Numerical examples of the attenuation function are compared to Monte Carlo simulations and are shown to contrast the flat and rough surface cases. Next, we obtain the general expression for the incoherent mutual coherence functions and scattering cross section for rough conducting surfaces.

Signal-to-noise ratio between coupled carbon nanotube dipole antennas

A method of moment procedure for accurately calculating the coupling between two carbon nanotubes dipole antennas is presented. A mixed potential integral equation is used to model the current distribution on a carbon nanotube by representing it as a nano thin-wire antenna. A quantum conductance model was used for the surface impedance. Once the current distribution has been determined, the antenna characteristics can then be evaluated. Using this methodology, the required input power for a carbon nanotube dipole antenna communication system can be calculated for various receive noise figures, bandwidths, and distances between dipoles.

A boundary element based methodology for modeling and simulation of Lab-on-Chip devices

This paper combines lumped circuits, electromagnetic and fluidic models in order to predict dielectrophoretic and fluidic traction forces for biochips. The boundary element method (BEM) is used for solving both electromagnetic (EM) and fluidic domain problems. A coupled circuit-EM methodology is used to model electrical excitations. The resulting simulator accurately predicts the force fields on arbitrarily-shaped bio-species. This integrated computational tool enables the exploration of new design ideas for microfluidic Lab-on-chip devices.

A Fast Computational Method for Particle Dynamics in Dielectrophoretic Lab-on-Chip Systems

An accelerated boundary element method (BEM) is proposed for predicting the motion of bio-particles under combined electromagnetic and fluidic force fields. Many Lab-on-chip (LoC) designs are based on dielectrophoretic (DEP) manipulation of polarized species inside microfluidic channels. The BEM approach presented here relies entirely on modeling the surface of the computational domain, significantly reducing the number of unknowns when compared to volume-based methods. Additionally, the need for re-meshing the whole domain at each time-step of particle movement is prevented. A coupled circuit-EM formulation is presented for accurate prediction of dielectophoretic field distribution due to on-chip electrodes. This allows the circuit control of the resulting electromagnetic fields. Next, BEM formulations for predicting DEP and fluidic traction forces on arbitrarily shaped bio-particles are presented. EM fields produced by the electrodes induce the DEP forces, while the fluid flow is driven by a pressure gradient across the channel. The resultant motion of the subjected particles is studied using a simple time-stepping algorithm. The algorithm has a time complexity of O(N3 ), where N is the number of unknowns), which leads to a large bottleneck during simulation of each time step. This problem is addressed by implementing oct-tree based O(N) multilevel iterative solvers. The methodology is used to study the field distribution due to distributed electrode systems and particle motion in fluidic channels. Evidence of O(N) behavior of the fast solver is presented. The resulting simulator can be used to study complicated distributed structures and explore new LoC design ideas.Copyright

A Combined Circuit-Electromagnetic-Fluidic Computational Methodology for Force Prediction in Lab-on-Chip Environments

This paper focuses on a computational method for the simulation of the motion and manipulation of bio-particles using dielectrophoretic and micro-fluidic forces. The presented method uses surface integral equations for modeling both electromagnetic (EM) and fluidic domains. A coupled circuit-EM methodology is used to model electrical excitations. A steady Stokes flow is assumed for computing the fluidic traction forces. The resulting simulator accurately predicts the fields and forces on arbitrarily-shaped three dimensional particles representing bio-species. The presented methodology is amenable to acceleration with state of the art oct-tree-based fast matrix-vector schemes for rapid linear time iterative solution. This integrated computational approach leads to a pathway for rapid simulation of coupled circuit-EM-fluidic systems for Lab-on-chip (LoC) manipulation of biological species, which provides medical device designers the capability to augment control of bio-species, and explore new system designs

A computational circuit-electromagnetic framework for force prediction on explicitly modeled nanoparticle surfaces in a lab-on-chip environment

A numerical technique for manipulation of nanoscale ionized and neutral particles in a lab-on-chip environment is discussed. The underlying Laplace solver used for modeling dielectric particle surfaces is coupled with a 3D circuit-electromagnetic field solver in order to predict the forces on the particles under arbitrary circuit excitation.

Green's function for rough surface with Dirichlet, Neumann, and impedance boundary conditions

This paper presents an analytical theory of rough surface Greens functions based on the extension of the diagram method of Bass and Fuks (1979), and Ito (1985) with the smoothing approximation used by Watson and Keller (1983, 1984). The method is a modification of the perturbation method and is applicable to rough surfaces with small RMS height. But the range of validity is considerably greater than the conventional perturbation solutions. We consider one-dimensional rough surfaces with Dirichlet, Neumann, and impedance boundary conditions. The coherent Greens function is obtained from the smoothed Dysons equation by using a spatial Fourier transform. The mutual coherence function for the Greens function is obtained by the first-order iteration of the smoothing approximation applied to the Bethe-Salpeter equation in terms of a quadruple Fourier transform. These integrals are evaluated by the saddle-point technique. The equivalent bi-static cross section per unit length of the surface is compared to the conventional perturbation method and Watson-Kellers result. With respect to Watson-Kellers result, it should be noted that our result is reciprocal while the Watson-Keller result is nonreciprocal. Included in this paper is a discussion of the specific intensity at a given observation point. The theory developed will be useful for the RCS signature related problems and LGA (low grazing angle) scattering when both the transmitter and object are close to the surface.

Propagation and scattering of low grazing skimming waves over conducting rough surfaces

If both the transmitter and the observation points are located close to the rough conducting surface, the wave incident upon a point on the surface is a mixture of the coherent and incoherent waves and is no longer the incident plane or spherical wave in free space. If the surface is flat, this is the Sommerfeld problem which has been studied extensively. This paper considers the Sommerfeld problem for rough surfaces. First, the authors consider the coherent field over the one-dimensional rough surface which satisfies the Dyson equation. Using the flat surface Greens function, the coherent field is expressed in a spatial Fourier transform which is equivalent to the Sommerfeld integral. From the complex reflection coefficient in the Fourier domain, the authors obtain the Sommerfeld pole and the final expressions are given for the attenuation function. Numerical examples are given for rough ocean and land surfaces showing the additional attenuation due to the scattering. The results are then compared with Monte Carlo simulations showing good agreement. Next, the incoherent field is formulated based on the Bethe-Salpeter equation. The first-order solution indicated that the coherent wave propagates to a point on the surface where the incoherent wave is excited and is propagated to the observation point. The total incoherent field is a sum of contributions from all scattering points on the surface.

Linear frequency-angular correlation function (FACF) imaging of targets buried in the presence of clutter

A novel correlation imaging technique called frequency angular correlation function imaging (FACF) was investigated to determine its role in clutter suppression imaging. A strong response from clutter in small angle and frequency separation between correlated scattered fields has been observed. By providing larger angular and frequency separation between scattered fields in the imaging process, FACF becomes an inherent clutter suppression algorithm. Experimental microwave studies for FACF were conducted and compared to confocal SAR imaging to determine the range of clutter suppression over other techniques.