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Wave Propagation 2011 Part 6

Tham khảo tài liệu 'wave propagation 2011 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Application of Media with Negative Refraction Index to Electromagnetic Imaging. Fundamental Aspects. 137 1 z 2 e2 - 1 1C1 - n S1 nỉứ k1- g 1 f e r3h 2 g2 i ii Ỵ ctg y2h Ci-iiyu Y C3-n S1 n Q k2 -g I sin Yh 40 Finally the boundary condition for the electric field on the boundary z -h is expressed as 1 1 k. sin y2h C1 i3 ll Y. ctg ĩ2h e r3hC3 I -A A I 41 k2 k ưAC -nỉeiY3hS3 I i hY 1 V The system of equations 38 - 41 can be represented in the matrix form as A T B where the matrix of the problem is given by A11 A12 A13 A14 A A A A ZA21 22 ZA23 ZA24 A31 A32 A33 A34 A41 A42 A43 A44 Ĩ1V1 where f 1 1 A11 An k2-ệ2 k22 -A j A 0 A fcỉ - A k2A . Y ctg Ĩ2h A41 . A12 0 A22 - k e A jaụi71 A _ f M l A Ag Ĩ2h Vl. k22 A sin y2h A42 k2-A2 k22-A2 I A 2gYi fe2Y 2ctg r2h I A - iaejY 1 Í-.Ắ 1 1 j A n A ime2V2 eir3h A33 n 1.2 g2 1.2 rt I A43 0 A14 2 e2 Í I k2 - A k2- j k2- sin y2h A2. 4k A j3 A 0 A. i k 1 1 . I ev3h k - A2 J The right-hand side of the matrix equation and the vector of unknown coefficients are given by Bt f - T Q -ĩ ĩĩYry Hjtf k Q 0 Tt C1 C3 S1 s3 . 138 Wave Propagation in Materials for Modern Applications From the equation A T B one can determine the column of coefficients T A-1 B and as a particular case C3 T2 and S3 T4 then the components of the electric and magnetic fields in domain 3 are determined by the formulas E3x S3 e- ĩ3Z B 3x Cẽ Ĩ31 1 r .-d- i 1 _iY z Ẽ3y j 2 I nếẼ3x r B3x I j 2 nếS3 Y3 ft.3C3 e 3 k3 V dz J k3 ế B3 p rI i . Ẽ3x ếyẼ3x I -2 Ỵ S ếnC3 ẽ k3 ế V dz J k3 ế ỊÍ 1 M n . 1 1 _ _ivz Ẽ3z 2 V x anB3x J k2 2 ế3S3 n 3C3 e Y B 7 I Ì - ẼK ếỊ-Ẽ3X 1 - - WS3S3 yC . k2 ế V dz J k Knowing the Fourier components of the fields one can determine the field components themselves by applying the inverse Fourier transformation. As a result for example the formula for the electric field component Ẽ3x x y z in domain 3 is given by TO TO Ẽ3X x y z 2n 2 J đệ J dn e ếx ny a 1 b 4 e Y3Z . 42 TO TO In the special case of a Hertzian dipole parallel to the boundary of a half-space .