Single Integral Equation Formulation Research Articles

A SEMI-ANALYTICAL METHOD TO CALCULATE THE ENTRIES OF THE METHOD OF MOMENTS MATRIX FOR THE MIXED POTENTIAL INTEGRAL EQUATION OF A SOURCE RECONSTRUCTION PROBLEM

In this article, the mixed potential integral equation is discretized using the Rao-Wilton- Glisson basis functions in order to obtain a method of moments matrix equation for a source reconstruction problem. The weighting functions used in the setup of the moments equation are Dirac delta functions. The entries of the moments matrix are computed using a semi-analytical method which is applicable to any method of moments problem with point matching. The analytical calculation is made possible by employing a differentiation property of the scalar Green function and the properties of the mesh elements of the source plane. The semi-analytical method makes it easier to increase the accuracy of the moments matrix elements. The accuracy of the method is shown by comparing the results obtained using the semi-analytical method to those obtained by a fully numerical procedure. The source reconstruction for a specific electromagnetic field distribution is the procedure of either setting up equivalent electromagnetic problems in order to determine equivalent sources or determining the actual sources by solving the related integral equations. The source reconstruction method is used in several areas which can be mentioned as near-field to far-field (NF-FF) transformation, microwave imaging, antenna design, antenna characterization, antenna diagnostics, electromagnetic interference estimation in electronic circuits, corrections in antenna measurements, radome defect localization. The most important aspect of the source reconstruction method is that it takes the electromagnetic problem into consideration just as it is, with all of the real world factors included through the electromagnetic field measurement results. The literature on the source reconstruction method can be divided into two parts with respect to the type of the integral equation formulation for the problem. In the first group, a single integral equation formulation is done whereas in the second group, a dual-integral equation formulation is preferred. In the single equation formulation, the equivalent sources obtained using the equivalence principle are related to the field measurement results using the radiation integrals. In the dual equation formulation, an extra equation is set up using the Love's equivalence principle at the measurement surface. Some of the articles in the single equation formulation group are to be cited now. In (7-30), several NF-FF transformation formulations using the source reconstruction method and the related applications are studied. In (7), equivalent magnetic currents are constructed on a plane including the aperture of an antenna using the near electric field data on a plane. These currents are then used to calculate the far-field. In (8), equivalent magnetic currents are built on a plane including the aperture of an antenna again. However, the near electric field data is not necessarily to be obtained on a plane and can be gotten from a surface with an arbitrary geometry. In (9), an equivalent electric current is set up on a

Parallel analysis of electromagnetic scattering from random rough surfaces

An efficient approach for simulation of random rough surface scattering is developed based on using a single integral equation formulation and a multilevel sparse-matrix canonical-grid method. Merits of the scheme are demonstrated using two wind-driven ocean surfaces, one which is very rough and the other large in size.

Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation.

Use of Rigorous Three-Dimensional Electromagnetic Simulation to Evaluate the Effectiveness of Optical Proximity Correction for Nonplanar Lithography

ABSTRACTA rigorous three-dimensional lithography simulator based on a recently developed single integral equation formulation for electromagnetic scattering is used in a simulation study of the effectiveness of using pre-distortions of mask patterns to compensate for linewidth variations in the resist patterns on nonplanar substrate topography. An efficient simulation methodology is used to reduce the number of required scattering calculations. Simulation results for different mask shapes and defocus conditions are presented.