A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a smooth convex surface excited by a general time impulsive astigmatic ray field. This TD-UTD impulse response is obtained by employing an analytic time transform (ATT) for the inversion in time of an available and accurate corresponding frequency domain UTD (FD-UTD) solution. The ATT is employed because it overcomes the difficulties that occur when inverting FD-UTD fields associated with rays that traverse line or smooth caustics. Furthermore, the TD-UTD response to a general pulsed astigmatic wave excitation may be found by a convolution of the general excitation with the TD-UTD impulse response which can be performed in closed form. Some numerical examples illustrating the utility of this TD-UTD are presented.

A Time Domain Formulation of the Uniform Geometrical Theory of Diffraction for Scattering From a Smooth Convex Surface

A time-domain formulation of the uniform geometrical theory of diffraction (TD-UTD) is developed for predicting the transient radiation and surface fields of elemental pulsed antennas placed directly on a smooth perfectly conducting, arbitrary convex surface. The TD-UTD solution is obtained by employing an analytic time transform (ATT) for inverting into time the corresponding frequency domain UTD (FD-UTD) solution. An elemental antenna on the convex surface is excited by a step function in time and a TD-UTD solution is obtained first. The TD-UTD response to a more general pulsed excitation of the elemental current is then found via an efficient convolution of the TD-UTD solution for the step function excitation with the time derivative of the general pulsed excitation. In particular, this convolution integral is essentially evaluated in closed form after representing the time derivative of the general pulsed excitation by a small sum of simple signals whose frequency domain description is a sum of complex exponential functions. Some numerical examples are presented to illustrate the utility of these TD-UTD solutions for pulsed antennas on a convex body.

TD-UTD Solutions for the Transient Radiation and Surface Fields of Pulsed Antennas Placed on PEC Smooth Convex Surfaces

: A time domain (TD) version of the uniform geometrical theory of diffraction which is referred to as the TD-UTD is developed to analyze the transient electromagnetic scattering from perfectly conducting objects that are large in terms of pulse width. In particular, the scattering from a perfectly conducting arbitrary curved wedge and an arbitrary smooth convex surface are treated in detail. These TD-UTD solutions are obtained in the form of relatively simple analytical expressions valid for early to intermediate times. The geometries treated here can be used to build up a transient solution to more complex radiating objects via space-time localization, in exactly the same way as is done by invoking spatial localization properties in the frequency domain UTD. The TD-UTD provides the response due to an excitation of a general astigmatic impulsive wavefront with any polarization. This generalized impulse response may then be convolved with other excitation time pulses, to find even more general solutions due to other excitation pulses. The formulation of an analytic time transform (ATT), which produces an analytic time signal given a frequency response function, is given here. This ATT is used because it provides a very efficient method of inverting the asymptotic high frequency UTD representations to obtain the corresponding TD-UTD expressions even when there are special UTD transition functions which may not be well behaved at the low frequencies; also, using the ATT avoids the difficulties associated with the inversion of UTD ray fields that traverse line or smooth caustics. Another useful aspect of the ATT is the abffity to perform an efficient convolution with a broad class of excitation pulse functions, where the frequency response of the excitation function must be expressed as a summation of complex exponential functions. (AN)

Time Domain Version of the Uniform Geometrical Theory of Diffraction.

An analytical study of the early-time current response of a perfectly conducting circular cylinder to a cylindrical electromagnetic wave, produced by a parallel filament carrying a unit-step current, is presented. Surface current density expressions for both the shadow and illuminated regions are obtained by applying the Watson transformation to the frequency-domain solution and then evaluating the corresponding integrals separately, in the shadow region by a residue series and in the illuminated region by using the saddle point technique. Analytical results obtained by using a double Laplace transform approach for the shadow region and the Luneberg-Kline expansion approach for the illuminated region are given. Numerical results illustrate the variation of the distribution of current density with time for different locations of the line current with respect to the cylinder, and also allows a comparison of the alternate methods applied by the authors, showing their corresponding range of validity. The response to an impulsive plane wave is derived as a special case. >

/pdf/early-time-currents-induced-on-a-cylinder-by-a-cylindrical-5062zskuzj.pdf

Early-time currents induced on a cylinder by a cylindrical electromagnetic wave

Early-time current response of a conducting cylinder to a step-function electromagnetic plane wave has been already thoroughly studied [l]-[4]. In this paper, we consider the early-time response of a perfectly conducting circular cylinder to cylindrical electromagnetic waves generated by a parallel filament carrying a unit-step current. The geometry of the problem is shown in Fig. 1. The mathematical technique utilized in this paper is different from that in our previous work [5], where the Watson transformation is employed to obtain the solution for the shadow region and the physical optics approximation for the illuminated region. The new approach consists in applying a double Laplace transform of the wave equation for the vector potential with respect to time and angle. From the solution of the ordinary differential equation satisfied by the transformed vector potential, the transformed current density induced on the surface of the cylinder is derived. To obtain the real time surface current density we perform first the inversion of the angle transform for large values of the time transform variable, by using the theorem of residues for the shadow region and the saddle point technique for the illuminated region. A second inverse Laplace transform yields the time dependent early-time solution.

Robert Henry Schafer

Papers

Transient currents on a perfectly-conducting cylinder illuminated by unit-step and impulsive plane waves /