John L. Visher

Scalar and Tensor Holographic Artificial Impedance Surfaces

We have developed a method for controlling electromagnetic surface wave propagation and radiation from complex metallic shapes. The object is covered with an artificial impedance surface that is implemented as an array of sub-wavelength metallic patches on a grounded dielectric substrate. We pattern the effective impedance over the surface by varying the size of the metallic patches. Using a holographic technique, we design the surface to scatter a known input wave into a desired output wave. Furthermore, by varying the shape of the patches we can create anisotropic surfaces with tensor impedance properties that provide control over polarization. As an example, we demonstrate a tensor impedance surface that produces circularly polarized radiation from a linearly polarized source.

Holographic artificial impedance surfaces for conformal antennas

We have developed a method for generating arbitrary radiation patterns from antennas on complex objects. The object is coated with an artificial impedance surface consisting of a lattice of sub-wavelength metal patches on a grounded dielectric substrate. The effective surface impedance depends on the size of the patches, and can be varied as a function of position. Using holography, the surface impedance is designed to generate any desired radiation pattern from currents in the surface. With this technique we can create antennas with novel properties such as radiation toward angles that would otherwise be shadowed

A study of combined field formulations for material scattering for a locally corrected Nystro/spl uml/m discretization

A study of the error convergence and condition number of three integral-equation formulations derived for penetrable material scattering objects-the Poggio, Miller, Chang, Harrington, Wu and Tsai (PMCHWT), the Mu/spl uml/ller, and the PMCHWT(-) formulations-is presented for a variety of problems when discretized via a locally corrected Nystro/spl uml/m method. The PMCHWT formulation is a first-kind integral equation with a hypersingular operator. The Mu/spl uml/ller formulation leads to a second-kind equation consisting of a diagonal term plus a compact operator. This form is both frequency and mesh stable. However, unlike the PMCHWT formulation, the error grows with the refractive index. The PMCHWT(-) formulation is in the form of a second-kind equation, but has a hypersingular term.

Numerical solution of 2-D scattering problems using high-order methods

We demonstrate that a method of moments scattering code employing high-order methods can compute accurate values for the scattering cross section of a smooth body more efficiently than a scattering code employing standard low-order methods. Use of a high-order code also makes it practical to provide meaningful accuracy estimates for computed solutions.

Polarization controlling holographic artificial impedance surfaces

We have demonstrated the necessary components for designing and constructing polarization controlling holographic tensor artificial impedance surfaces. Applications using the tensor impedance holographic method and tensor impedance characterization are currently being developed.

Efficient high-order discretization schemes for integral equation methods

A high-order method is a method that provides extra digits of accuracy with only a modest increase in computational cost. A number of method of moment (MoM) techniques based on high-order basis and testing functions have been presented in the literature. Characteristically, these methods result in a substantial increase in precomputational cost principally due to the expensive numerical integration required for near interactions. This can be accelerated through the use of specialized quadrature schemes when available. Unfortunately, performing the double integration numerically over high-order functions can still be quite computationally intensive. A novel high-order technique based on a locally-corrected Nystrom scheme combined with advanced quadrature schemes is presented. It is shown that this method truly demonstrates high-order convergence for the solution of electromagnetic scattering problems with comparable computational cost to low-order schemes. The elegance of this technique is in its simplicity and ease of implementation. However, the power of the method is its ability to inexpensively provide true high-order convergence.

Scattering computation using the fast multipole method

The fast multipole method (FMM) computes scattering cross sections from large targets with several orders of magnitude reduction in the CPU time and memory storage compared to traditional method of moments (MoM) techniques. The authors compare the memory usage and CPU times for FMM with traditional MoM results using both direct and iterative solvers. It is shown that dramatic reductions in CPU and memory requirements can be realized by using the FMM to compute scattering and radiation from large objects. In the test cases considered, 2D objects with perimeters longer than about 12 wavelengths required less memory than using traditional MoM techniques. Using the FMM to compute scattering from objects with perimeters larger than about 30 wavelengths required less CPU time than using iterative solvers with a dense Z matrix.<<ETX>>

3D method of moments scattering computations using the fast multipole method

The fast multipole method (FMM) dramatically reduces the time and memory required to compute radar cross sections and antenna radiation patterns compared to dense matrix techniques. We have implemented the FMM in a method of moments (MoM) program to compute electromagnetic scattering from large bodies of arbitrary shape. We compare the memory and time required using the FMM to that for direct and iterative solutions using a dense impedance matrix.<<ETX>>

Electromagnetic scattering computations using high-order basis functions in the method of moments

Using high order basis functions in Galerkin method of moments calculations permits a significant reduction in the number of unknowns needed to achieve a given accuracy in modeling a scatterer or antenna [Hamilton et al., 1993]. The present authors have developed a set of vector valued basis functions of arbitrary order with a sparse overlap matrix. They demonstrate the reduction of computational effort for a given accuracy by computing the scattering from a sphere.

The importance of accurate surface models in RCS computations

The authors investigate the magnitude of the errors in the scattering cross section made by approximating 2-D targets by flat segments and by quadratic splines. These results were compared to computations using exact representations of the surface. A research program for scattering computation called Fast Scat was instrumental in computing the results. The importance of precise surface models for computing accurate scattering amplitudes and radiation patterns is shown. For the particular example of TM (transverse magnetic) scattering from an infinite PEC (perfectly electrically conducting) circular cylinder, the error made in approximating the surface by linear segments or quadratic splines was computed.<<ETX>>