Negative Refraction by a Multilayered Mushroom-type Metamaterial

Transcription

1 29 IEEE AP-S International Smposium June 5, 29, Charleston, South Carolina Negative Refraction b a Multilaered Mushroom-tpe Metamaterial Mário G. Silveirinha, Department of Electrical Engineering, Universit of Coimbra, Portugal Aleander B. Yakovlev, Department of Electrical Engineering, Universit of Mississippi, USA 25, it - instituto de telecomunicações. Todos os direitos reservados.

2 Motivation: Negative refraction with indefinite media D. R. Smith and D. Schurig, Phs. Rev. Lett. 9, 7745 (23) D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Re, APL 84, 2244, 24 2

3 Negative refraction with arras of nanorods in the visible: J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stac,and X. Zhang, Science 321, 93, 28. 3

4 Can a similar effect be observed at microwave frequencies? P.A. Belov, R. Marqués, S. I. Maslovski, I.S. Nefedov, M. Silveirinha, C. R. Simovsk, S. A. Tretakov, Phs. Rev. B 67, (23). An arra of parallel rods does not behave as a local uniaial ENG material at microwaves 4

5 Taming the spatial dispersion A Demetriadou and J B Pendr, J. Phs.: Condens. Matter 2 (28) O. Luukkonen, M. G. Silveirinha, A. B. Yakovlev, C. R. Simovski, I. S. Nefedov, and S. A. Tretakov, Effects of Spatial Dispersion on Reflection from Mushroom-tpe Artificial Impedance Surfaces, ariv: v1 A. B. Yakovlev, M. G. Silveirinha, O. Luukkonen, C. R. Simovski, I. S. Nefedov, and S. A. Tretakov, Homogeniation Models for the Characteriation of Surface-Wave Propagation on Mushroom Structures. 5

6 Hpothetical equivalence Multilaered Mushroom Local uniaial ENG periodicall loaded with patch grids uˆ uˆ uˆ uˆ uˆ uˆ t k h k 2 p 2 6

7 Geometr: E i h a g 7

8 Scattering problem: Analtical model E H All the field components can be obtained from H We use a transfer matri approach to characterie the reflected/transmitted waves Transfer Matri: Q Transfer Matri: M Global Transfer Matri: Mglobal Q av.m...q.m.q.m.q av 8

9 Transfer matri for the patch grid: a E E Q. a H H g g h h 1 g 1 Y 2a g ln csc 2 2a g h h Q with g jk Y 9

10 Transfer matri for the wire medium slab: E E M. H H h Field in WM-slab is written in terms of TM and TEM modes (coming from the nonlocal dielectric function) H A e A e B e B e TM TM TEM TEM TM TM TEM TEM 1 TM TM TEM TEM E j A e A e j B e B e TM TM TM TEM TEM TEM hk TEM jk k k k h TM p h 1

11 Transfer matri for the wire medium slab (contd.): Because the wires are actuall connected to the patches, the amplitudes of the TEM and TM modes are not independent! H A e A e B e B e TM TM TEM TEM TM TM TEM TEM Additional boundar condition: de k d dh k d h and h M. Silveirinha, C. A. Fernandes, J. R. Costa, "Additional Boundar Condition for a Wire Medium Connected to a Metallic Surface", New J. Phs., 1, 5311(1-17), 28 O. Luukkonen, M. G. Silveirinha, A. B. Yakovlev, C. R. Simovski, I. S. Nefedov, and S. A. Tretakov, Effects of Spatial Dispersion on Reflection from Mushroom-tpe Artificial Impedance Surfaces, ariv: v1 11

12 Transfer matri for the wire medium slab (contd.): E E M. H H h m m TM TM h TM sinh TM hcosh TEM h TEM cosh TM hsinh TEM h TM TM h TM sinh TM h TEM sinh TEM h m 12 sinh 1 j TEM TM sinh TM h TEM h k h h TM TM h TM sinh TM TEM sinh TEM m jk 21 TM TM TM 2 2 TM TM TEM 2 h 1 cosh TM hcosh TEM h sinh TEM hsinh TM h h TEM TM TM TM h TM sinh TM h TEM sinh TEM h 2 k TM p h k k p 12

13 Numerical validation E H Analtical model CST Microwave Studio a 2 mm, 1.2, g.1 a, h a, r.25 a, 45 deg, N 2 3 h i plates 1. T f GH p 15.8 arg T f GH f GH 13

14 Characteriation of negative refraction Etraction of equivalent parameters from scattering data???? There is a simpler and more general solution! i tan t 1 L L Meta-material t 14

15 Characteriation of negative refraction (contd.) i tan t 1 L L t Meta-material i inc Incident field (plane wave decomposition): jk H, H k e d Transmitted wave: o inc jk H, L T, k H k e d Transfer function of the slab (for plane wave incidence) 15

16 Characteriation of negative refraction (concl.) L i t Meta-material tan t 1 L inc o jk H, L T, k H k e d inc Quasi-plane wave: H k, ecept for k k / csin i j,, T k T e T k T e d j kk dk jk inc,, H L T k e H o d dk Negative refraction occurs when the phase of transfer function decreases with the incident angle! M. G. Silveirinha, PHYSICAL REVIEW B 79, 15319, 29 16

17 Negative Refraction in the Mushroom structure a 2 mm, 1.2, g.1 a, h a, r.25 a, N 2 3 h Analtical model CST Microwave Studio f a c plates 11GH /.46; 2.3 T 1. argt º i k / k sin i k / k sin i 17

18 Negative spatial shift a 2 mm, 1.2, g.1 a, h a, r.25 a, N 2 3 h plates f 11GH a / c.46; 2.3 k / k sin i d dk º i i L t Mushrooms 18

19 Negative angle of transmission a 2 mm, 1.2, g.1 a, h a, r.25 a, N 2 3 h plates i f 11GH a / c.46; 2.3 f.8 f t f.9 f i f f L t Mushrooms 19

20 Dependence with the number of laers a 2 mm, 1.2, g.1 a, h a, r.25a h Δ L i t.22λ.74 λ.45λ.148 λ.7λ.22λ 1λ.29λ 1.3λ.364 λ 1.73λ.438 λ 2

21 Full wave simulations with CST Microwave Studio (incoming beam) I will add here a slide with the incoming beam (without the slab) 21

22 Full wave simulations with CST Microwave Studio (contd.) a 2 mm, 1.2, g.1 a, h a, r.25 a, N 2 3 f 11GH, 33º i h plates -component H

23 Conclusion A multilaered mushroom structure behaves as a local uniaial ENG material periodicall loaded with patch grids Strong negative refraction ma occur at an interface with air at microwave frequencies This phenomenon can be accuratel described using homogeniation techniques. 23