NEGATIVE REFRACTION BY A TWO-SIDED MUSHROOM STRUCTURE WITH LOADED VIAS

Size: px

Start display at page:

Download "NEGATIVE REFRACTION BY A TWO-SIDED MUSHROOM STRUCTURE WITH LOADED VIAS"

Sydney Perry
5 years ago
Views:

1 NEGATIVE REFRACTION BY A TWO-SIDED MUSHROOM STRUCTURE WITH LOADED VIAS Candra S. R. Kaipa, Alexander B. Yaovlev Mário G. Silveirina, and Stanislav I. Maslovsi Metamaterials : Te Fift International Congress on Advanced Electromagnetic Materials in Microwaves and Optics Barcelona, SPAIN October -5,

2 Outline Introduction and Motivation Homogeniation Metods Uniform Loading Nonlocal Model Local Model Discrete Loading Negative Refraction Results Conclusion

$Negative Refraction Hypotesied te existence of a pysical material in wic bot ε and μ are$ Demonstrated tat te existence of LH propagation does not violate any nown pysical law. V. G.

Demonstrated tat te existence of LH propagation does not violate any nown pysical law. V. G.

3 Negative Refraction Hypotesied te existence of a pysical material in wic bot ε and μ are simultaneously negative. Demonstrated tat te existence of LH propagation does not violate any nown pysical law. V. G. Veselago, Sov. Pysics Solid State, 8, 854, 967 Veselago s Prediction Reversal of Snell s law Negative refraction Transformation of a point source into point image 3

4 Indefinite Media Indefinite material slab Local response xx yy Complementary electric resonator structure 4 D. R. Smit et. al., APL, 84, 44, 4 Q. Ceng et.al., Pys. Rev. B, 78, (R), 8

5 Array of Metallic Nano Rods J. Yao et.al., Science, 3, 93, 8 P. A. Belov et.al., Pys. Rev. B, 67, 33, 3 Effective only in te optical domain Strong spatial dispersion at lower infrared and microwaves does not beave as a local uniaxial ENG material at microwaves 5

Pys.: Condens. Matter,, 95, 8 O. Luuonen et.al., IEEE Trans. Microwave Teory Tec.

6 Taming te Spatial Dispersion Spatial Dispersion (SD) can be significantly reduced by increasing Capacitance of wires Inductance of wires A. Demetriadou et al., J. Pys.: Condens. Matter,, 95, 8 O. Luuonen et.al., IEEE Trans. Microwave Teory Tec., 57, Nov. 9 A. B. Yaovlev et.al., IEEE Trans. Microwave Teory Tec., 57, Nov. 9 6

Residual SD effects are observed for wide incident angles M. G.

7 Suppressed Spatial Dispersion a Periodic loading of wires wit square metallic patces Significantly reduces te SD effects! Residual SD effects are observed for wide incident angles M. G. Silveirina and A. B. Yaovlev, Pys. Rev. B, 8, 335, 7 C. S. R. Kaipa, A. B. Yaovlev, and M. G. Silveirina, J. Appl. Pys., 9, 449,

8 Loaded Uniaxial Wire Medium Homogeniation Models 8

9 Musroom Structure wit Loaded Vias a Loads Loads (Inductive) Increase te Inductance of wires Significantly Reduce te SD effects 9

10 Continuously loaded WM Dielectric function of continuously loaded WM t I t p j n ˆˆ y x t transverse permittivity due to patces n slow-wave factor accounts for impedance insertions Quasi-static approac Formulated in terms of te effective capacitance (C) and te effective inductance (L) per unit lengt of a wire Taes into account te SD effects Does not tae into account te granularity of te structure along Accurate only for a bul medium S. I. Maslovsi and M. G. Silveirina, Pys. Rev. B, 8, 45, 9

11 Uniform Loading Model () t I t p j n ˆˆ Ignoring te Loading by Patces t y x Assuming tat eac period is uniform loaded wit an Inductive load (L ) j L Z w L is te effective inductance per unit lengt of a wire Zw L Effective permittivity of te inductively loaded WM ~ It S. I. Maslovsi and M. G. Silveirina, Pys. Rev. B, 8, 45, 9 L log a 4 r a r p n~ ˆˆ

12 Uniform Loading Model () I t ~ p n~ ˆˆ ~ L p p L Effective plasma wavenumber n~ n L L n LC Effective slow-wave factor slow-wave factor C r a r log a 4 Effective Capacitance per unit lengt of a wire Increase in te value of te Inductive load L Reduction in SD effects Decrease in plasma frequency

13 Uniform Loading Model (3) H y E r a y x a g x Tangential electric and magnetic fields across te patc interfaces are related via te seet admittance Y g j a ln Requires additional boundary condition at te connection of wires to metallic patces csc! Does not tae into account te position of te load g a O. Luuonen et al., IEEE Trans. Antennas Propagat., 56, 8 S. I. Maslovsi et al., New J. Pys.,, 347, 3

14 Local Model y x Local model for Inductively loaded WM slab Anisotropic material caracteried by tensor effective permittivity Quasi-static approximation No spatial dispersion I t ~ p ˆˆ ~ L p p L p a log a 4r a r Plasma wavenumber Does not require additional boundary conditions Taes into account only frequency dispersion Accurate wen SD effects are significantly reduced 4

15 Discrete Loading Model () E H y x x y I t p Field in WM-slab in terms of TM and TEM modes ˆˆ H y A TM e TM A TM e TM B TEM e TEM B TEM e TEM E x j TM A TM e TM A TM e TM TEM B TEM e TEM B TEM e TEM TEM j TM p x 5

16 Discrete Loading Model () y = x = - = = -!! Additional boundary conditions Z L I() Z L a () C patc Z L j C patc Z L I C di Additional potential j C d C patc a g log sec g a Effective capacitance of patc 6 S. I. Maslovsi et al., New J. Pys.,, 347,

17 Discrete Loading Model (3) Generalied additional boundary condition for microscopic current: at te connection of lumped load to patc ( ) In terms of field components de dh di d C C C patc y x j CZ L E x H y d d C patc j CZ L I Generalied additional boundary condition: at te connection of metallic wire to te patc ( ) In terms of field components de dh di d C C patc y x E x H y d d C patc S. I. Maslovsi et al., New J. Pys.,, 347, C I 7

18 Results Uniform loading model Discrete loading model Local model HFSS a = mm, g =. mm, = mm, r =.5 mm, ϵ =., θ i = 6 deg, and Load =. nh Plasma frequency witout loads =.4 GH Plasma frequency wit. nh load =.6 GH 8

19 Negative Refraction a = mm, g =. mm, = mm, r =.5 mm, ϵ =., θ i = 6 deg, and Load =. nh f GH i 4. L i t Material slab d t tan L dx Negative refraction occurs wen te pase of transfer function decreases wit te incident angle! 9 M. G. Silveirina, Pys. Rev. B, 79, 539, 9

20 All-Angle Negative Refraction & Ultra Tin Structure

21 Ultra Tin Structure Discrete loading model HFSS a = mm, g =. mm, = mm, r =.5 mm, ϵ =, θ i = 6 deg, and Load = 5nH Hig Transmission 66% decrease in plasma frequency wen compared to te structure witout loads Electrical ticness at te frequency of operation 5

$Negative Refraction f GH i 33 i Discrete loading model HFSS$

22 Negative Refraction f GH i 33 i Discrete loading model HFSS Angle of transmission corresponding to incidence angle t 65.4 i 33

23 Negative Refraction 9 GH GH Hig transmission as a function of Incidence Angle All-angle negative refraction 3

24 Gaussian Beam Simulation a = mm, g =. mm, = mm, r =.5 mm, ϵ =, Load = 5nH and f = GH Angle of transmission t

25 Gaussian Beam Simulation a = mm, g =. mm, = mm, r =.5 mm, ϵ =, Load = 5nH and f = GH Widt of te array along x, W x = 9 a 5

26 Conclusions Loading te WM slab wit inductive loads decreases te plasma frequency and reduces te SD effects. Strong negative refraction over a wide frequency band at microwaves is observed. Te observed penomena is accurately predicted by te omogeniation models. Ultra-tin structure exibits ig transmission and allangle negative refraction. Te proposed structure can be used for focusing of waves and in te design of planar lenses. 6

Cherenkov emission in a nanowire material

Cherenkov emission in a nanowire material Lisboa 16/11/2012 Cerenkov emission in a nanowire material David E. Fernandes, Stanislav I. Maslovski, Mário G. Silveirina Departamento de Engenaria Electrotécnica e de Computadores Instituto de Telecomunicações