Jaehoon Jeong

The time domain Green's function and propagator for Maxwell's equations

The free space time domain propagator and corresponding dyadic Greens function for Maxwells differential equations are derived in one-, two-, and three-dimensions using the propagator method. The propagator method reveals terms that contribute in the source region, which to our knowledge have not been previously reported in the literature. It is shown that these terms are necessary to satisfy the initial condition, that the convolution of the Greens function with the field must identically approach the initial field as the time interval approaches zero. It is also shown that without these terms, Huygens principle cannot be satisfied. To illustrate the value of this Greens function two analytical examples are presented, that of a propagating plane wave and of a radiating point source. An accurate propagator is the key element in the time domain path integral formulation for the electromagnetic field.

Corrections to “The Time Domain Green's Function and Propagator for Maxwell's Equations” [Nov 04 3012-3018]

In the above titled paper (ibid., vol. 52, no. 11, pp. 3012-3018, Nov 04), there were several typographical errors and mistakes. Corrections are presented here.

The Time Domain Propagator Method for Lossless Multiconductor Quasi-TEM Lines

A time domain propagator method is developed to solve telegraphers equations for coupled lossless multiconductor quasi-TEM transmission lines. The resulting expression is obtained in a form in which the propagator operates on the line voltage and current. Examples are presented showing that exceptionally accurate results are obtained for uniform and nonuniform coupled microstrip lines. The lack of numerical dispersion with the propagator method is demonstrated through an examination of two coupled microstrip lines.

Microwave Simulation of Grover's Quantum Search Algorithm

An analog of a quantum search method, known as Grovers algorithm, is modeled without entanglement on the macroscopic level, using numerical simulation of microwave devices and methods. An array of microstrip annular-ring resonators simulates a quantum bit array. An oracle that performs a test to determine which element in the array is the answer to the search algorithm is provided by a microwave-frequency plane wave, modulated by a Gaussian pulse. A single annular ring with a resonant frequency identical to the frequency of the incident pulse serves as the answer to the search. It is shown that the number of Gaussian pulses needed to identify the answer element is equal to the radicN iterations predicted by the Grover algorithm. The decay in a microwave-resonator element is used to show that the quantum dual - a spontaneous decay of the excited energy level of a quantum bit, also described as its decoherence - can be a serious obstacle to the development of large quantum-bit data arrays

Time Domain Coupled Field Dyadic Green Function Solution for Maxwell's Equations

The free space time domain coupled electric and magnetic field integral equation solution for Maxwells differential equations is derived. The coupled field integral equation solution is expressed as a vector containing the electric and magnetic fields found in terms of a surface integral over the equivalent surface currents on a boundary, an integral over the electric and magnetic current sources in the region enclosed by the boundary, and a volume integral over the initial field in the bounded region. Because of the irreversibility of the vector differential equation and the lack of spatial symmetry in the corresponding free space dyadic Green function, as a starting point the Green differential equation is replaced by the reciprocal (adjoint) equation and the dyadic Green function is replaced by its transpose. These replacements plus identities that relate the components of the Green function to its transpose lead in a straightforward way to the coupled field solution. The general dyadic expression derived here provides a framework for developing source current, boundary integral, and propagator methods that are based on the interaction between the electric and magnetic vector field components in the time domain.

Novel time domain analysis technique for lossy nonuniform transmission lines

The nonuniform transmission line is traditionally modeled and analyzed in the frequency domain. However, it is difficult to characterize and simulate nonuniform lossy transmission lines accurately in the time domain. A highly accurate and general approach for time domain analysis of lossy inhomogeneous transmission lines is described. The propagator method presented is an exact solution to the lossy telegraphers equations based on the modal matrix technique. Simpsons rule is applied to produce a remarkably accurate numerically compatible result. An exponentially tapered transmission line example shows that this method is not only simple and efficient, but also an accurate technique for analyzing lossy nonuniform transmission lines with minimal numerical dispersion. Multiple sectioned transmission lines can be handled by a straightforward application of the presented equations.

The time domain dyadic integral equation for the electromagnetic field

The purpose of this paper is to present a derivation of the free space time domain dyadic integral equation that includes both electric and magnetic current as well as the surface and volume electromagnetic fields. The lack of spatial symmetry in the dyadic Greens functions and the irreversibility of the Maxwell vector differential equation prove to be major hurdles.

Closed-Form Time Domain Solutions for Multiconductor TEM Lines

Time domain closed-form analytical solutions to the coupled telegrapher`s equations for the voltage and current on a lossless multiconductor transmission line are presented. The resulting expressions are obtained in the form of exact time domain propagators operating on the line voltage and current. Time domain numerical methods are developed and examples showing exceptionally accurate results are obtained for uniform and nonuniform; symmetric and asymmetric strip lines.

The electromagnetic field in a 1-D lossy medium based on a Maxwell equation propagator

A propagator has been derived for the electromagnetic field in a 1D lossy region. The solution is exact, and does not require the evaluation of a differential or integral equation. In the limit as /spl sigma/ /spl rarr/ 0 the result is seen to reduce to the DAlembert solution for coupled equations in a homogeneous lossless medium. Good agreement with the ADS CAD program has been demonstrated. Because we get an exact solution, it is expected to be more accurate than integral or differential equation methods, not subject to numerical dispersion and simple to evaluate. By using the methods described here, derivations of the 2D and 3D cases should be straightforward.