Understanding the Electromagnetic Characteristics of Real Metamaterials via Rigorous Field...
-
Upload
randolph-booth -
Category
Documents
-
view
229 -
download
4
Transcript of Understanding the Electromagnetic Characteristics of Real Metamaterials via Rigorous Field...
Understanding the Electromagnetic Characteristics
of Real Metamaterials via Rigorous Field Simulation
Raj MittraElectromagnetic Communication LaboratoryPenn State UniversityE-mail: [email protected]
Why Metamaterials?
• Combine expertise from fields of electrical engineering and materials science.
• Artificial Dielectrics and their Applications:– Explore metamaterials and – Investigate their viability in
enhancing antenna performance.
• Antennas:– Size Reduction– Other Improvements.
Metamaterial Terminology
Loughborough Antennas and Propagation Conference – 2006 F. Bilotti – Potential Applications of Matamaterials in Antennas
Re[ ]
Re[ ]
DPSk
DNGk
ENG
k MNG
kMNZ
MNZ
EN
ZE
NZ
RegularDielectricsDPS
Interpretations of Metamaterials
• Various interpretations of metamaterials have led to different names:
– MTM - Metamaterial– DNG – Double negative (negative ε
and μ)– LHM – Left-Handed Materials– NIR – Negative Index of Refraction
• Dielectric Resonator Approach1
– High-k dielectric resonators in low-k matrix
• Transmission Line Approach2
– Lumped element circuit theory creates left-handed transmission line
+ve n
Image appears closer
-ve n
Image focuses on other side
1E. Semouchkina et al, “FDTD study of the resonance processes in metamaterials,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, Apr. 2005, pp. 1477-1487, Apr. 2005.2A.K. Iyer et al, “Planar negative index media using periodically L-C loaded transmission lines,” IEEE Trans. Microw. Theory Tech., vol. 50, no. 12, Dec. 2002, pp. 2702-2712, Dec. 2002.
Loughborough Antennas and Propagation Conference – 2006 F. Bilotti – Potential Applications of Matamaterials in Antennas
A Plethora of Applications
DPS
ENG
Ziolkowski’s group:resonant sub- dipole
antennas
Roma Tre group: resonant sub-
patch and leaky wave antennas
DPS DNG
Miniaturized circular patch antennas with metamaterial loading 4/4
Loughborough Antennas and Propagation Conference – 2006 F. Bilotti – Potential Applications of Matamaterials in Antennas
Vertical electric field distribution
Implementation of the MNG medium through SRR inclusions
Matching features
Metamaterial Design using SRRs and Dipoles
• Front view • Top view
• Top view of a metamaterial prismLe-Wei Li, Hai-Ying Yao, and Wei XuLe-Wei Li, Hai-Ying Yao, and Wei Xu
National University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQun WuQun WuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore
Why Metamaterials?
• Combine expertise from fields of electrical engineering and materials science.
• Artificial Dielectrics and their Applications:– Explore metamaterials and – Investigate their viability in
enhancing antenna performance.
• Antennas:– Size Reduction– Other Improvements.
Simulation Results
• Distribution of electric field component Ez(r,t) in rectangular linear around a metamaterial prism at f=16.21 GHz
Le-Wei Li, Hai-Ying Yao, and Wei XuLe-Wei Li, Hai-Ying Yao, and Wei XuNational University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQun WuQun WuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore
Simulation Results
• Electric field component Ez(r,t) distribution due to a metamaterial prism
Le-Wei Li, Hai-Ying Yao, and Wei XuLe-Wei Li, Hai-Ying Yao, and Wei XuNational University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQun WuQun WuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore
Scattering Pattern
• Distribution of electric field component Ez(r,t) in polar plot due to a metamaterial prism at f=16.21 GHz
Le-Wei Li, Hai-Ying Yao, and Wei XuLe-Wei Li, Hai-Ying Yao, and Wei XuNational University of Singapore, Kent Ridge, SingaporeNational University of Singapore, Kent Ridge, SingaporeQun WuQun WuHarbin Institute of Technology, Harbin, ChinaHarbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore
Candidates for Metamaterial Superstrates
◈ Periodic structures such as FSSs and EBGs act as spatial angular filters with transmission and reflection pass and stop bands, and can be used to enhance directivity of a class of antennas being placed above them.
Woodpile EBGStacked
dielectric layerDielectric rod
EBG FSS
◈ Two approaches for the analysis of antennas with metamaterial superstrates
1. Fabry-Perot Cavity (FPC) Antenna Partially Reflecting Surface (PRS)
2. Leaky Wave Antenna
20×10 Thin FSS Superstrate
Antenna over AMC Ground
2010 Thin FSS Composite Superstrate
r = 2.2,
t = 2.0828 mm
< top view > < back view >
< side view >
The design parameter valuesFSS array size: 10 20
a = 12, b = 6
dl_l = 8.7, dl_u = 11.2
dw_l =1, dw_u = 4
h = 16, Lg=2.0828
h = 13
8.41 and 11.67 GHz
Two FSS layer are etched in same substrate whose thickness is only 2.0828 mm
Extraction of constitutive effective parameters from S-parameters for
normal incidence
Equations used in the inverse approach
• Compute Z:
• Compute n:
• Compute effective and :
221
211
221
211
)1(
)1(
SS
SSZ
Conditions used: Z’ > 0 and <= 1-
})]'[ln(]2)]"{[[ln(1
00 dinkdink
oeime
dkn
210 XiXe dink Y =
( 2 different roots )
( 2 different roots )
221
211
21
11
SSS
X 2
(branches with different m)
Conditions used: n”<=0, ”<= 0 and ” <= 0
Iterative approach to pick n such that n is continuous
zneff / nzeff and
Example 1: 2-D infinite array of dipoles for normal incidence
X
Y
Z
Plane wave source EY
Plane of reflection
Plane of transmission
Unit cellBC usedX and Y: PBC
Z: PML
Ei, Et and Er are the contributions from the zeroth Floquet mode measured on the corresponding planes.
(1) By enforcing ” <0 and ” <0, only m=0 can be solution.
(2) By enforcing n”<0, the correct root can be determined.
(1)(1)
(2)
Solutions for all branches ( m=0, -1 and +1) and 2 roots
Determine the solutionby using ref. (1):
Extracted parameters: 2-D infinite array of dipoles
X
Y
Z
Plane wave source EY
Plane of reflection
Plane of transmission
Unit cellBC usedX and Y: PBC
Z: PML
Example 2: 2-D infinite array of split-rings for normal incidence
Extracted parameters: 2-D infinite array of split-rings
Note: The shaded area represents the non-physical region, where ” or ” > 0. In this region, we choose the branch that best connect n just before and after this band.
X
Y
Z
Plane wave source EY
Plane of reflection
Plane of transmission
Unit cellBC used
X and Y: PBCZ: PML
Example 3: 2-D infinite array of split-rings + dipoles for normal incidence
Extracted parameters: 2-D infinite array of split-rings+dipoles (1-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.
2-D Infinite array of split-rings + dipoles ( 2-layer )
Note: The shaded area represents the non-physical region, where ” or ” > 0.
Note: The shaded area represents the non-physical region, where ” or ” > 0.
Extracted parameters: 2-D infinite array of split-rings+dipoles (2-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.
2-D Infinite array of split-rings + dipoles ( 3-layer )
Note: The shaded area represents the non-physical region, where ” or ” > 0.
Extracted parameters: 2-D infinite array of split-rings+dipoles (3-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.
2-D Infinite array of split-rings + dipoles ( 4-layer )
Extracted parameters: 2-D infinite array of split-rings+dipoles (4-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.
Comparison of effective parameters for 1 to 4-layer split-ring + dipole
Note: The effective parameters for 1-4 layers are almost the same, except that more resonant peaks can be seen for more layers.
Realization of Conventional Metamaterial
Negative ε• Thin metallic wires are arranged periodically• Effective permittivity takes negative values below plasma frequency
Negative μ• An array of split-ring resonators (SRRs) are arranged periodically
( Koray Aydin, Bilkent University, Turkey Sep 6 , 2004 )
Question?
Images?
Can we resolve two sources placed along the longitudinal direction with a DNG lens?
DNGDNG
LensLens
Imaging with DNG Lens
Field distribution along z in the RHS of Lens
or ?
0 ZIsource
DNG LENS
Field Distribution
0 ZI 0 I Z
Field Distribution
Effective Parameters
Inversion Method
• Can be applied to both simple and complicated structures
• Can use both numerical and experimental data
• S-parameters for metamaterials are more complex
• Ambiguities in the inversion formulas
Equivalent Medium ApproachIt is a common practice to replace an artificial dielectric with its equivalent ε and μ perform an analysis of composite structures (antenna + medium) using the equivalent medium.
But this can lead to significant errors and wrong conclusions
Single layer
R T...
Multiple layers
Exit angle?
.
.
.
.
.
.
.
.
.
Floquet harmonics
Negative Refraction in a Slab
Plane wave
θ ??DNGDNG
SLABSLAB
Comprising Comprising of Periodicof Periodic
Structures Structures
AMC Ground Designs
Response of AMC Ground
AMC Ground
Antenna over AMC Ground