1. Understanding the Electromagnetic Characteristics of Real Metamaterials via Rigorous Field Simulation
Raj Mittra
Electromagnetic Communication Laboratory
Penn State University

2. 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.

3. Metamaterial Terminology
Loughborough Antennas and Propagation Conference – 2006
F. Bilotti – Potential Applications of Matamaterials in Antennas
DPS
DNG
ENG
MNG
MNZ
ENZ
Regular
Dielectrics

4. 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 , Apr
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 , Dec

5. A Plethora of Applications
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-l dipole antennas
Roma Tre group:
resonant sub-l patch and leaky wave antennas

6. Vertical electric field distribution
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

7. Metamaterial Design using SRRs and Dipoles
Front view
Top view
Top view of a metamaterial prism
Le-Wei Li, Hai-Ying Yao, and Wei Xu
National University of Singapore, Kent Ridge, Singapore
Qun Wu
Harbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore

8. 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.

9. 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 Xu
National University of Singapore, Kent Ridge, Singapore
Qun Wu
Harbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore

10. Simulation Results
Electric field component Ez(r,t) distribution due to a metamaterial prism
Le-Wei Li, Hai-Ying Yao, and Wei Xu
National University of Singapore, Kent Ridge, Singapore
Qun Wu
Harbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore

11. 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 Xu
National University of Singapore, Kent Ridge, Singapore
Qun Wu
Harbin Institute of Technology, Harbin, China
IWAT’05, March 7, 2005, Singapore

12. Stacked dielectric layer
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.
Stacked dielectric layer
Dielectric rod EBG
FSS
Woodpile EBG
Two approaches for the analysis of antennas with metamaterial superstrates
Fabry-Perot Cavity (FPC) Antenna Partially Reflecting Surface (PRS)
Leaky Wave Antenna

13. 20×10 Thin FSS Superstrate

14. Antenna over AMC Ground

15. 2010 Thin FSS Composite Superstrate
Two FSS layer are etched in same substrate whose thickness is only mm
The design parameter values
FSS 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
< top view >
< back view >
r = 2.2,
t = mm
h = 13
8.41 and GHz
< side view >

16. Extraction of constitutive effective parameters from S-parameters for normal incidence

17. Equations used in the inverse approach
Compute Z:
Compute n:
Compute effective  and :
( 2 different roots )
<= 1 -
Conditions used: Z’ > 0 and 2
Y =
( 2 different roots )
(branches with different m)
Conditions used:
n”<=0, ”<= 0 and ” <= 0
Iterative approach to pick n such that n is continuous
and

18. Example 1: 2-D infinite array of dipoles for normal incidenceZ
Unit cell
BC used
X and Y: PBC
Z: PML
Plane of transmission
Ei, Et and Er are the contributions from the zeroth Floquet mode measured on the corresponding planes.
Plane of reflection X
Plane wave source EY Y

19. Solutions for all branches ( m=0, -1 and +1) and 2 roots
Determine the solution
by using ref. (1):
By enforcing ” <0 and ” <0, only m=0 can be solution.
By enforcing n”<0, the correct root can be determined.
(2)
(1)
(1)

20. Extracted parameters: 2-D infinite array of dipoles

21. Example 2: 2-D infinite array of split-rings for normal incidenceZ
Unit cell
BC used
X and Y: PBC
Z: PML
Plane of transmission
Plane of reflection X
Plane wave source EY Y

22. 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.

23. Example 3: 2-D infinite array of split-rings + dipoles for normal incidenceZ
Unit cell
BC used
X and Y: PBC
Z: PML
Plane of transmission
Plane of reflection X
Plane wave source EY Y

24. Extracted parameters: 2-D infinite array of split-rings+dipoles (1-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.

25. 2-D Infinite array of split-rings + dipoles ( 2-layer )
Note: The shaded area represents the non-physical region, where ” or ” > 0.

26. Extracted parameters: 2-D infinite array of split-rings+dipoles (2-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.

27. 2-D Infinite array of split-rings + dipoles ( 3-layer )
Note: The shaded area represents the non-physical region, where ” or ” > 0.

28. Extracted parameters: 2-D infinite array of split-rings+dipoles (3-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.

29. 2-D Infinite array of split-rings + dipoles ( 4-layer )
Note: The shaded area represents the non-physical region, where ” or ” > 0.

30. Extracted parameters: 2-D infinite array of split-rings+dipoles (4-layer)
Note: The shaded area represents the non-physical region, where ” or ” > 0.

31. 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.

32. 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
Pendry suggested that the so-called SRRs exhibit negative permeability and the microwave-plasma thin-wire structure exhibits a negative permittivity below the plasma frequency. The first metamaterial having simultaneously negative permeability and permittivity was made by combining SRRs and thin wires.
( Koray Aydin, Bilkent University, Turkey Sep 6 , 2004 )

33. Question?
DNG
Lens
Images?
Can we resolve two sources placed along the longitudinal direction with a DNG lens?

34. or ? Imaging with DNG Lens Z IZ I
source
DNG LENS
Field distribution along z in the RHS of Lens I Z
Field Distribution
Field Distribution Z I
or ?

35. 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

36. But this can lead to significant errors and wrong conclusions
Equivalent Medium Approach
It 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

37. Comprising of Periodic
Negative Refraction in a Slab
θ ??
DNG
SLAB
Comprising of Periodic
Structures
Plane wave

38. AMC Ground Designs

39. Response of AMC Ground

40. AMC Ground

41. Antenna over AMC Ground