Understanding the Electromagnetic Characteristics of Real Metamaterials via Rigorous Field Simulation Raj Mittra Electromagnetic Communication Laboratory Penn State University E-mail: rajmittra@ieee.org

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 DPS DNG ENG MNG MNZ ENZ Regular Dielectrics

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 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

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

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

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

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

20×10 Thin FSS Superstrate

Antenna over AMC Ground

2010 Thin FSS Composite Superstrate Two FSS layer are etched in same substrate whose thickness is only 2.0828 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 = 2.0828 mm h = 13 8.41 and 11.67 GHz < side view >

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

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

Example 1: 2-D infinite array of dipoles for normal incidence Z 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

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)

Extracted parameters: 2-D infinite array of dipoles

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

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.

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

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.

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 ) Note: The shaded area represents the non-physical region, where ” or ” > 0.

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 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 )

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

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

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

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

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

AMC Ground Designs

Response of AMC Ground

AMC Ground

Antenna over AMC Ground