Raj Mittra Electromagnetic Communication Laboratory Penn State University

Understanding the Electromagnetic Characteristics

of Real Metamaterials via Rigorous Field Simulation

Raj MittraElectromagnetic Communication LaboratoryPenn State UniversityE-mail: [email protected]

mailto:[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.


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


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


Simulation Results

• Electric field component Ez(r,t) distribution due to a metamaterial prism



Scattering Pattern

• Distribution of electric field component Ez(r,t) in polar plot due to a metamaterial prism at f=16.21 GHz



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 of reflection


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 of reflection


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 )












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

Documents

Raj Mittra Electromagnetic Communication Laboratory Penn State University