Time-domain uniform geometrical theory of diffraction for a curved wedge

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 perfectly conducting, arbitrarily curved wedge excited by a general time impulsive astigmatic wavefront. This TD-UTD impulse response is obtained by a Fourier inversion of the corresponding frequency domain UTD solution. An analytic signal representation of the transient fields is used because it provides a very simple procedure to avoid the difficulties that result when inverting frequency domain UTD fields associated with rays that traverse line or smooth caustics. The TD-UTD response to a more general transient wave excitation of the wedge may be found via convolution. A very useful representation for modeling a general pulsed astigmatic wave excitation is also developed which, in particular, allows its convolution with the TD-UTD impulse response to be done in closed form. Some numerical examples illustrating the utility of these developments are presented.