Exact Full Wave Research Articles

An Efficient Electromagnetic Scattering Optimization Scheme for Multiscale Problems Using Green's Functions of Arbitrary Scatterers

An efficient optimization methodology is developed and exemplified for electromagnetic scattering problem of structures with multiscale features. We have developed a scheme to efficiently derive the exact full wave scattering solution from a large scatterer with localized modifications by using the Green's function of the original scatterer. The Green's function of the original scatterer and the free-space Green's function are used to formulate coupled surface integral equations (SIEs) on a virtual boundary that separates the localized modifications from the original scatterer. The unknowns of the SIEs are only on this virtual boundary, on the deformed part of the boundary of the original scatterer, and on any inhomogeneities within the virtual boundary. The resulting matrix equations are of marginal sizes, and can be readily manipulated to improve its condition number by representing all other unknowns in terms of the surface fields on the virtual boundary. Thus, by solving the scattering problem associated with the original scatterer once to derive its Green's function, we can make use of this result to compute the scattering solutions of similar structures for as many times as needed with minimal computing cost. These new scattering solutions, when necessary, can be used as a new starting point as we introduce further modifications to the structure. The approach turns out extremely effective in numerous engineering designs when we iterate the shape of the design for optimal performances.

Thermal State for the Capacitance Coupled Mesoscopic Circuit with a Power Source

The Schrodinger equation of the mesoscopic capacitance coupled circuit with an arbitrary power source is solved by means of two step unitary transformation. The original Hamiltonian transformed to a very simple form by unitary operators so that it can be easily treated. We derived the exact full wave functions in Fock state. By making use of these wave functions and introducing the Lewis--Riesenfeld invariant operator, the thermal state have been constructed. The fluctuations of charges and currents are evaluated in thermal state. For T→ 0, the uncertainty products between charges and currents in thermal state recovers exactly to that of Fock state with n, m=0.

Scattering at a nonchiral-chiral interface in a coaxial waveguide

A formally exact full-wave solution is presented for the problem of scattering at a nonchiral-chiral interface in a coaxial waveguide. The field components for the axisymmetric modes in a coaxial chirowaveguide are initially obtained. A new orthogonality relation for the modes is then proposed and used to find expansion coefficients for the electromagnetic fields in the coaxial chirowaveguide. The scattering matrix for the nonchiral-chiral dielectric discontinuity in a coaxial waveguide is finally derived by enforcing the continuity conditions of the tangential field components across the interface. Numerical results for the reflection and transmission coefficients at the nonchiral-chiral interface in a coaxial waveguide are presented.

A comparison of exact and quasi-static methods for evaluating grounding systems at high frequencies

Recently, it has been suggested that traditional quasi-static methods for evaluating power network grounding systems are not valid at high frequencies. However, the conditions under which exact full wave theory must be used have not been established. In this paper, exact full wave and quasi-static methods are used to evaluate touch and step potentials of a simple ground stake. It is shown that a sufficient condition for quasi-static theory to be valid is if the size of the buried electrode is less than one-tenth of a wavelength in the earth.

A numerically exact full wave packet approach to molecule–surface scattering

A numerically exact spectral method for solving the time-dependent Schrödinger equation in spherical coordinates is described. The angular dependence of the wave function is represented on a two-dimensional grid of evenly spaced points. The fast Fourier transform algorithm is used to transform between the angle space representation of the wave function and its conjugate representation in momentum space. The time propagation of the wave function is evaluated using an expansion of the time evolution operator as a series of Chebyshev polynomials. Calculations performed for a model system representing H2 scattering from a rectangular corrugated surface yield transition probabilities that are in excellent agreement with those obtained using the close-coupling wave packet (CCWP) method. However, the new method is found to require substantially more computation time than the CCWP method because of the large number of grid points needed to represent the angular dependence of the wave function and the variation in the number of terms required in the Chebyshev representation of the time evolution operator.