Electromagnetic wave propagation through ultra-narrow channels filled

Transcription

1 31st October, HKUST, Hong-Kong Electromagnetic wave propagation through ultra-narrow channels filled with an ENZ material Mário G. Silveirinha

2 How to have ε-nearε zero (ENZ) Media? 2 ω p ε r ~1 ω ω ( + iγ) Metal near ~ 0 ε r ε r 2 2 p ω p ω ε m < 0 ω Γ ε > 0 d αε 1 1+ αε α1+ α2 εt 0 0 αε 1 1+ αε 2 2 ε = ε 0 0 εt 0 = ε0 0 0 α1 α2 0 0 ε + z ( α 1+ α2) ε1ε αε 2 1+ αε 1 2 2

3 How to have ε-nearε zero (ENZ) Media? (contd.) 3

4 What if ε is near zero? 2-D Scenario with TE z polarization H int z (, ) = H x y uˆ z 1 E= H iωε ε o r 1 1 ˆ iωε ε u int = H z z o r The magnetic field must be constant inside id a connected ENZ region 4

5 Magnetic field inside the ENZ material Applying Faraday s law to the ENZ contour: E.dl A =+ iωμ μ H A int 0 r, p z p The magnetic field inside the ENZ material can be written in simple form in terms of the electric field evaluated at the outer side of the boundary 5

6 Formal solution of a scattering problem involving ENZ objects (Object is replaced by PMC) int Hz = Hz = const. + (Dirichlet problem) 6

7 Formal solution of a scattering problem involving ENZ objects (contd.) The total magnetic field outside the object can thus be written as: PMC int?s H z =ψ + H z ψ 1 The electric field is given by:? 1 1 ˆ PMC int s E = ψ H ψ1 iωε u + z z z 0 iωε u 0 ˆ (Object is replaced by PMC) + (Dirichlet problem) H z = ψ PMC H z = ψ s 1 7

8 Formal solution of a scattering problem involving ENZ objects (contd.) Calculation of the magnetic field inside the ENZ material: E.dl =+ iωμ μ H A A int 0 r, p z p E 1 u 1 ˆ u ˆ = PMC int s ψ z H z ψ1 z iωε + 0 iωε 0 H int z = A A s 1 ψ n PMC dl ψ 2 dl + k0 μr, p A n p 8

9 Formal solution of a scattering problem involving ENZ objects (conclusion) It is possible to completely determine the field scattered by an ENZ object by solving two external problems! PMC int s H z =ψ + H z ψ 1 H int z = A A s 1 ψ n PMC dl ψ 2 dl + k0 μr, pa n p 9

10 Application to the theory of parallel plate waveguides 10

11 General waveguide transition a 1 H inc E inc PEC PEC PEC PEC PEC E inc H inc PEC a 2 11

12 General waveguide transition a 1 H inc E inc PEC PEC PEC PEC PEC ε 0 E inc H inc a 2 PEC 12

13 Calculation of the scattering parameters (Object is replaced by PMC) + (Dirichlet problem) These problems have a trivial solution!!! 13

14 The scattering parameters for an ENZ channel with arbitrary geometry ρ = ( ) ( ) a a + ik μ A r, p a + a ik μ A r, p p p τ = 1+ ρ 14

15 Tunneling EM energy through tight ENZ channels If a=a 1 =a 2 the reflection coefficient is: ρ = k0 μr, pap i a k0 μr, pa 2 i a p The reflectivity can be made very small provided: k μ 0 r, p a A p << 1 15

16 Tunneling EM energy through tight ENZ channels (contd.) k μ Possibilities: 0 r, p a A p << 1 Very low frequency (static-like behavior). Permeability of the ENZ material is near zero. The channel is very tight so that t A p /a is small 16

17 Tunneling EM energy through tight ENZ channels (contd.) Despite the huge wave impedance contrast, in the ε=0 lossless limit it is possible to squeeze more and more energy through an ENZ channel by making the channel tighter and tighter! 17

18 U-shaped Waveguide Transition & EM Squeezing ρ = ( ) ( ) a a jk μ A a + a + jk μ A r r D D where A = al + al + a L D ch 18

19 U-shaped Waveguide Transition & EM Squeezing (contd.) a1 = a2 = L a L1 = L2 = ach = 0.1a = 1 μ r 2 ω p ε = 1 ω ω ( jγ) ω a p / c = π /2 19

20 Field concentration in the ENZ channel a = a = L a 1 2 L1 = L2 = 0.1a = 1 μ r E E inc a a ch 20

21 Poynting vector a1 = a2 = L a L1 = L2 = 0.1a μ r = 1 Γ / ω p =

22 Field concentration and confinement in a small air cavity a1 = a2 = L a L1 = L2 = ach = 0.1a = 1 μ r

23 Waveguide with 90-deg Bend μ r = 1 aimp = 0.9a ω a / c = p 3 π /4

24 Experimental Demonstration of Energy Squeezing at Microwaves

25 Artificial plasma emulated by a waveguide below cut-off 2 π = ωεμε b TE10 mode: 2 γ d ε eff γ = ω μ b π b ω / c = ε0 εd 2 a ε d W. Rotman, IRE Trans. Antennas Propag. AP-10, R. Marqués, J. Martel, F. Mesa, and F. Medina, Phys. Rev. Lett. 89,

26 Artificial plasma emulated by a waveguide below cut-off (contd.) The plasma frequency is controlled by the H-plane width, b. ε = 1 d b L 1 L L 2 How to emulate the free-space regions in the waveguide scenario?

27 Emulation of the free-space regions in the waveguide scenario ε = 1 d b L 1 L L 2 ε eff 2 π = ε 0 1 = 0 bω / c (at the plasma freq.) ε d = π ε eff = ε 0 2 = ε0 b ω / c (at the plasma freq.) The waveguide sections that emulate the free-space regions are filled with a dielectric i with ε diel =2.0 20

28 Emulation of the 2D-problem using a waveguide setup Incident wave is TEM Incident wave is the TE10 mode ε = 1 d ε = d 2.0 ε d = 2.0 b L 1 L L 2

29 Simulation of an ENZ filled channel a1 = a2 a L1 = L2 = ach = 0.1a ω a / c p = π /2 Artificial plasma Artificial plasma L L = = 3.0a a a 2D setup 2D setup

30 Simulation of an unfilled channel a1 = a2 = L a L1 = L2 = ach = 0.1a 3D waveguide uniformly filled with ε diel =2.0. 2D setup with unfilled narrow channel.

31 Experimental Demonstration

32 Experimental Demonstration (contd.)

33 Experimental Demonstration (contd.)

34 Tunneling oblique waves through an ENZ material

35 Oblique Incidence Total reflection ENZ n=0 How Since can the we magnetic make a field wave is that constant t impinges i inside idon the ENZ interface medium off the phase variation normal at the tunnel air side through cannot the be reproduced ENZ slab? inside the slab

36 Idea: Convert the incident EM wave into TEM modes Provided d a is much smaller than the wavelength, the incident id field can be sampled and propagated through different channels

37 Transmission as a function of the extension of the metallic plates LENZ = λ 0 ε = a = 0.03λ L = L 0 1ef 2ef When the total thickness L 1 +L 2 is a odd multiple of 0.5λ 0, the wave can tunnel through the ENZ medium, even for wide incident angles

38 Compression of the modal fields of a dielectric waveguide

39 Geometry ε s = Standard dielectric waveguide Array of 10 waveguides filled with ENZ material Standard dielectric waveguide

40 Poynting vector ε i LENZ = 0.75λd L1 = L2 = 0.25λd ach = 0.1a hs = 0.87λd

41 Electric Field (movie)

42 Transmission of modal fields in a dielectric waveguide 42

43 Transmission of an image through sub-λ aperture D h = W s /2.5 W = λ 0 /2 s M. Silveirinha, N. Engheta, Phys. Rev. Lett., 102, ,

44 Transmission of an image through sub-λ aperture (contd.) 44

45 Summary ENZ media have interesting wave guiding properties; EM waves may be squeezed through very tight and narrow channels, with great electric field enhancement. These structures may enable bending and compressing waves in the subwavelength scale.

46 Thank you! 46