tailieunhanh - Wave Propagation 2011 Part 3

Tham khảo tài liệu 'wave propagation 2011 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Uniform Asymptotic Physical Optics Solutions for a Set of Diffraction Problems 49 in which k2 is the propagation constant in the double-negative metamaterial 02 is the negative refraction angle and . kcos 9 - k cos 0 _. k cos 9 - k cos 0 j J i 7 c Rij i c i j c j 11 kj cos 0i ki cos 0j ki cos 0i kj cos 0j 61 Tl 2ki cos 0i kj cos 0i ki cos 0j Tjj 2ki cos 0i ki cos 0i kj cos 0j 62 In 61 and 62 ki k3 k0 01 03 and the superscripts i and j refer to the left and right media involved in the propagation mechanism. Comparisons with COMSOL MULTIPHYSICS results are reported in Figs. 14 and 15 with reference to Ộ 45 . As can be seen the UAPO diffracted field guarantees the continuity of the total field across the two discontinuities of the GO field in correspondence of the incidence and reflection shadow boundaries and a very good agreement is attained. Accordingly the accuracy of the UAPO-based approach is well assessed also in the case of a lossless double-negative metamaterial layer. Anisotropic impedance layer A layer characterised by anisotropic impedance boundary conditions on the illuminated face is now considered. Such conditions are represented by an impedance tensor Z Zx X x ZZ Z Z having components along the two mutually orthogonal principal axes of anisotropy X and Z . The structure is opaque so that the transmission matrix does not exist and according to Gennarelli et al. 1999 the elements of R can be so expressed Fig. 14. Amplitude of Ep if Ep 1 Eộ 0 and P 90 Ộ 45 . Circular path with p 5 -0 . Layer characterised by sr -4 pr -1 and d -0 . 50 Wave Propagation in Materials for Modern Applications Fig. 15. Amplitude of Eộ if Ep. 0 Eộ. 1 and p 90 Ộ 45 . Circular path with p 5 -0 . Layer characterised by sr -4 pr -1 and d -0 . -A 1 AC B2 cosei -Ccos2 ei 11 A 1 - AC - B2 cos ei - Ccos2 ei 63 2B cos9i R12 R21 . i . _ _ 2 A 1 - AC - B2 cos 0i - C cos2 0i 64 A 1 AC B2 cos ei Ccos2 ei A 1 - AC - B2 cos 9i - Ccos2 9i 65 in which if X is the angle between X .