Radio pulse diffraction in terms of the wave catastrophe theory

Abstract

This report delivers to investigation of diffraction of a frequency-modulated (FM) pulses on a conductive screen in dispersive media. The problem has an important significance in non-stationary diffraction processes of FM signals on conductive elements of antenna systems and space constructions. There are different analytical and numerical methods calculating a space-time distribution of wave fields caused by diffraction processes under consideration. In this paper we shall consider the problem of diffraction of a semi-infinitive radiopulse on a conductive screen by means of methods of a space-time (ST) geometry theory of diffraction (GTD). The propagation of a radio signal with increasing frequency is known to result in the compression of signal and forming a ST caustic of cuspoid types (AN) which may be interpreted as envelope of ST geometric-optical (GO) rays. An account of space-time boundary rays connected with the beginning of radiopulse lead to utilizing of BN+~=(AN,A~) edge catastrophes. As follows the field in the neighborhood of limiting ST GO ray is described by the incomplete Airy's functions. In diffraction problem with the metal screen besides ST GO rays and ST boundary rays two additional rays families generated on a boundary of the screen by rays listed above must be confederated: a family of ST diffraction rays generated by ST GO rays and ST corner rays generated by ST boundary rays. Then in the neighborhood of limiting ST GO ray the (AN,A~ ,AN,A~) corner catastrophe arise. If the screen boundary is a straight line and the signal frequency is not modulate, then N=l and all rays diverge and don't form caustics. If the radiopulse is modulated which frequency increase linearly, then N=2 and in addition to the focusing of ST GO rays the same type focusing (A$ of ST diffraction rays arises. In the case when the frequency modulation law besides linear term has also quadratic one it is possible to arise the (A3,Ai ,A3,Al) and so on. The problem will be more complex if we shall take into account a curvature of screen boundary and nonhomogeneity of medium. In the paper we shall also present the uniform asymptotic describing space-time structure of radiosignal in the neighborhood of limiting ST rays and results of numerical simulation of amplitude-phase field structure. '