Applications of the incremental theory diffraction to the scattering by planar configurations

The electromagnetic scattering from some planar structures is investigated to demonstrate the validity of the incremental theory of diffraction (ITD). First, the scattering from a disc illuminated by a scaler plane wave, is considered. Next, the bistatic echo area of a disc and a square plate are analyzed and compared with either the exact solution or other techniques. Finally, the diffracted field of a perfectly conducting circular disc which is illuminated by a short electric dipole is calculated by different methods and discussed.<<ETX>>

I. INTRODUCTION.The description of high-frequency electromagnet,ic scatt,ering by complex struct,ures is of inkrest in many practical applications, such as reflector antennas pattern and RCS prediction, analysis of radiat,ing characteristics in a complex environment,.et,c..As is well known.two leading high-frequency theories have provided very effective tools for most engineering purposes, namely the Geometrical Theory of Diffract,ion (GTD) [l].especially in it.suniform ext,ension (UTD) [2], and the Physical Theory of Diffraction (PTD [3].complex object, in terms of rays emanating from isolated "flash point,s".However, still there are some difficulties in applying this ray method close and at caustics.Furthermore.there is an inherent limitation, at least, from a conceptual point of view, due to the fact t,hat in several cases GTD is able to predict a non-vanishing field in rest,ricted angular regions.It should be noted.however?that this latter inconvenience, may be alleviated by introducing diffracted field contributions from rertices. Within the framework of the original PTD pioneered by Ufimtsev [3].several formulations for a wedge [4][5][6] have been presented to asympt,otically describe fringe current contributions.that may occur whenever an edge discontinuity introduces a relevant distort,ion of t.he Physical Optics (PO) currents.The major attempt of these t,echniques, besides eliminating caustic singularities, is that of providing an extension for observation angles which are not on the diffraction cone.
Recent,ly, an Incremental Theory of Diffraction ITD) ['i] has been phenomena.The procedure essentially consist,s of a localization process.based on a rigorous Fourier transform analysis of canonical problems.The solution of a cylindrical canonical configuration is thought of as a superposit.ion of an infinite uniform distribution of incremental field contributions.that are localized along a directrix of the cylinder.The pertinent element fact,or may be extracted by establishing a Fourier transform pair relationship between t.he incremental contribution and the solution of the cylindrical canonical problem.Next.t.hese increment,al field contributions are adiabatically dist,ributed and integrated along the actual shadow boundary line (SBL).The t,otal scattered field is represent.edas the sum of a generalized Geometrical Opt,ics (GO) field plus incremental diffraded fields.This method is applicable t,o any local shape, where a uniform.cylindrical, local canonical configuration with arbitrary cross-section is appropriate.Also, its formulat,ion is uniformly valid at any incidence and observation aspect,s.including caustic of the corresponding ray-field representation.
In this paper, t,he electromagnetic scattering from some planar struct,ures is investigated.to demonstrate the validity of the ITD.First,, the scatt,ering from a disc illuminated by a scalar plane wave, is considered.Next.. the bist.at,icecho area of a disc and a square plate are analyzed and compared The GTD 1 eads to a very attractive picture of the scattering from a developed which provides a unified framework for descri r, ing high-frequency 0-7803-2009-3/94/$4.00 0 1994 IEEE.610 with either the exact solution or other techniques.Finally. the diffracted field by a perfectly conducting circular disc which is illuminated by a short electric dipole is calculated by different methods and discussed.

XI. WEDGE SHAPED CONFIGURATION.
Let us consider first an edge discontinuity and its relevant infinite.local canonical wedge problem.Let us introduce at Q' a cylindrical coordinate system ( p . 4 .z ) with the z axis at the edge of the wedge.and a spherical (r, B, 4 ) coordinate system.with its origin at Q' (Fig. 1).Also, let us denote by (/?',d') the local direction at Q' of an arbitrarily polarized incident plane wave.and by nx the exterior wedge angle.
The high-frequency incremental diffracted field contribution at any point P arising from Q' on the edge. is where E ' is the electric field of the incident plane wave.and where b, = (-l)', b, = 1, 'Pl = (4-(-lid'), GJ[Ka] is the UTD transition function, and ai 2(9) is the same as a -' Next.let 'us consider a finite surface with an edge.A first order approximation of the high-frequency scattered field may be obtained by resorting to the PO approximation.The PO integration process asymptotically contams information from both stationary phase contributions and end-point contributions at the SBL.These latter contributions are inaccurate because they do not contain the correct local information at the edge of the SBL.Thus.they should be taken out and replaced by proper incremental diffracted field contributions.An estimate of the above end-point contribution is deduced from a pertinent local canonical problems.which consists of a half-lit infinite (y=O) plane with an infinite straight SBL (2) locally tangent to the actual SBL at Q'. r( Q') at any point P from Q' on the edge. is The high-frequency incremental end-point PO contribution ..

-jkr
in which E ' is the electric field of the incident plane wave.and with (4) (5) where 9 ' = (4*6').and 9 is the UTD transition function.Both the incremental fields in (1) and (4) are adiabatically distributed and then integrated along the actual SBL.In subtracting the latter contribution from that of the PO surface integration.a field is obtained which is referred to as a generalized GO field.This is expressed as Then, the total scattered field is represented as in which Ed is the generalized diffracted field V. NUMERICAL RESULTS.Only the numerical example of the bist,atic echo area of a perfectly conducting 6Xx6X square plate is present.edhereinaft,er.Further numerical results will be shown and discussed during the oral present,ation.Fig. 2b-e shows t,he four component of the scattering matrix for the direction of incidence and the range of observation which are depicted in Fig. 2a.In this range, the PO field is zero at all directions of Observation.The result,s calculat,ed by the method of moments (MOMcontinuous line.[8]) and by first order PTD (dashed line, [SI) are compared with t,hose obtained by the first order ITD coefficients in eq.s (1).It is found that, both asymptot,ic met,hods are in the same very good agreement with Moh4 near and at, t,he caustic.This is expected since the two theories provide the same prediction at the first, order diffraction cones.At other aspects the two asymptotic met,hods predict different results.Close and at.grazing aspects, both first order asympt,ot,ic results deviat.esfrom MOM.
This is a consequence of neglecting higher order interactions mechanisms.A PTD estimat,e of second order mechanisms is available in [8].However, as will also be shown during the oral presentation, simple first order descriptions of scattering phenomena are in general much more satisfactory, for most.ractical purpose, than in t,his specific example.This was indeed selected in PSI in order to emphasize t,he importance of including high order scattering mechanisms.

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Breinbjerg. "Higher order equivalent edge currents for fringe ware radar scattering by perfectly conducting polygonal plates.IEEE Trans.

Fig. 1 :Fig
Fig. 1: Geometry at a locally v-edge Fig. 2a: Direction of incidence and shaped configuration range of observation