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Time Domain Version of the Uniform Geometrical Theory of Diffraction.

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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

Subject Categories:

  • Optics
  • Electromagnetic Pulses

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