Elektromagnetik dalgaların paralel tabakalı dalga klavuzundan kırınımı
Başlık çevirisi mevcut değil.
- Tez No: 75228
- Danışmanlar: PROF. DR. EREN ERDOĞAN
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1998
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Elektrik-Elektronik Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 48
Özet
ÖZET Bu çalışmada; Oxyz bir kartezyen koordinat sistemi olmak üzere y=0 düzlemi ve ye(a,b), x
Özet (Çeviri)
SUMMARY PLANE WAVE DIFFRACTION BY AN OPEN PARALLEL PLATE WAVEGUIDE 1. Introduction: The scattering of plane waves by a series of parallel plates constitutes an important class of canonical problem in diffraction theory and has been studied for many years. The scattering by a parallel plate wavequide [1,2] and by an infinite grating [3,4], [5] was resolved in the early days but other configurations such as three parallel half-planes have long defied analysis. The reason is that the solution rests on the Wiener-Hopf technique. The diffraction of plane waves by three parallel infinitely thin soft half-planes has been considered first by D.S. Jones who formulated the problem as a three dimensional matrix Wiener-Hopf equation [6]. The three parallel half-planes problem has been also considered by Abrahams [7] who presented a more simples approach to achieve the Wiener-Hopf factorization of the Kernel matrix. The aim of the present work is to generalize the analysis to the case where the semi-infinite plates are neither infinitely thin nor thick empedance. To this and, we consider the diffraction of Ez-polarized plane waves by an open parallel plate wavequide. The traditional formulation of this problem leads to Wiener-Hopf equation which can not be solved by considering the known techniques. A numerical solution of this system is obtained for various values of the wave number of dielectric region plate thicknesses and distance between the plates, through which the effect of these parameters on the diffraction phenomenon are studied. A time factor e'iu“ with co being the angular frequency is assumed and suppressed throughout the paper. VIFig.l. Geometry of the problem. 2. Formulation of the Problem: Let us consider first the configuration depicted in Fig.l. Since in this case the field is symmetrical about the plane y=0 the normal derivative of the total electric field must vanish for y=0, xe(-oo,oo) (electric wall). For analysis purposes, it is convenient to express the total field as follows: u W) +”r(*o0 +«1(^y) ; y>b u-jix,y)=\ u2(x,y) ; 00 (1) Here, u * is the incident field given by u Xx,y)=exp(-ik(xcos^0+ysm^) (2a) Vllwhile ur denotes the field reflected from the plane y=b, namely w r(x,y) = -exp(ifc(xcos(J)0 -(y -2fe)sin), its Fourier transform with respect to x gives d2 +(*2-«2) dy> F(a,y)=0 (5a) with where F(a,y)=F+(a,y)+F_(a,y) (5b) F±(aj)=ful{xj)etm*dx (5c) o By taking into account the following asymtotic behaviours of w1 for x-»±°° ^1o(e^ ;*-+-/ (6) One can show that F+(ot>,y) and F_(a,y) are regular functions of a in the half planes Imia}>Im{kcos^ and TmiaK/into:}, respectively. The general solution of (5a) satisfying the radiation condiction for y-»» reads F+(a,y) +F_(a,y) M(a)e **?.*-*> (7a) with K(a.)=\lk2-a.2 (7b) The square-root function is defined in the complex a-plane cut along a=k to a=k+ioo and a=-k to a=-k-ioo, such that K(0)=k In the Fourier transform domain (4a) takes the form F(a,2>)=0 (8) By using the derivative of (7a) with respect to y and (8), we get, ixA(a)=F+(a,fc) (9) In the region 0 < y < b and x > 0, u$(x,y) satisfies the Helmholtz equation * +-“+Au,(x,y)=0 \dx2 dy2, The half-range Fourier transform of (10) yields with dy' +K\a) (10) (Ha) f(y)=-u3(0,y), g(y)=u3(0,y) dx (Hb,c) G+(a,y), which is defined by G+(a,y)=±fu3(x,y)eiaxdx (12) is a function regular in the half-plane Im{a}>Im{-k}. The general solution of (1 la) satisfying the Dirichlet boundary condition at y=0 reads GSu,y)=B(a)smK(a)y+- ±- f{M-i«g(t)] smiK(a)(y-t))dt (13) 2nK(a)J0 Combining (4e) and (4f), we get FXa,b)=G.(a,b) and B(a.) can be solved uniquely to give (14) B(a) FM^)--^[[Âtyiag(t)]sm{K(a)(b-t))dt 2nK(a)J0 sm[K(a)b] (15)Replacing (15) into (13) we get _, x sinAT(a)y, + sm[K(a)b] FMM--^-J\At)-^8(t)]smiK(a)(b-t)}dt 2nK(a)J0 1 ”r + ', J[^(?)-/ag(0]sin{^(a)(y-0}^ 27ttf(a) J (16) Although the left-hand side of (16) is regular in the upper half-plane Im{a}>Im{-k) the regularity of the right-hand side is violated by the presence of simple poles occuring at the zeros of sm[Kmb] namely at a=am satisfying sinful =0, lm{a)>lm{-k), m = 1,2,.. (17) These poles can be eliminated by imposing that their residues are zero This gives (~Dm+1 h 2*Km 2 (18a) where K^f^, fm 8" hJ b Ât) sm[KJ]dt (18b,c) Consider now the region 0,*)-G>,Z>)= -e it (a -fccoscl),)) (26) where the dot (.) specifies the derivative with respect to y. Taking into account xn(7a), (9) and (16), one obtains v -F+(a,Jb)+F_(a»= -iAfcin0) 2usin[.K(a)&] J J{t)sm[K(a)t]dt-iaf g(f)sm[K(a)t] (27) d* Substituting (21) in (27) and evaluating the resultant integral, one obtains the following Wiener-Hopf Equation of the second kind valid in the strip Imikcos^0e -ikbsin$0 fm-iasm ^(a-fcos^o) 2% m=1 (a+am)(a-aj sin(Kb) (28) with (?(a) = ^^, a=Jkz-K. sm[K(a)b] m v (29) Here Q+(a) and Q_(a) are the split functions, regular and free zeros in the half- planes Imia}>Im{-k} and Im{a}b can be obtained by taking the inverse Fourier transform of F(a,y) ux(x,y) =-fA(a)e ««)&-«e ~iaxda (32a) 2rc L Here L is a straight line parallel to the real a-axis lying in the strip Im(kcos) m=1 am(?_(-am) (am-&cos) gttp (32b) u0=e-ikb^ (32c) DCW^^ ~^ ^ ' 06d),J2^ QXkco&bf) (cos^+cos^ Q+(-kcos) are the cylindrical polar coodinates defined by x=pcos=psüi(|> and u0 is the expression of the incident field at y=b,x=0. The results here applied to some numerical examples which permit us grasp the effect of various parameters on the diffraction phenomena. xiv
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