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Raj Mittra Electromagnetic Communication Laboratory Penn State University

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?.

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Raj Mittra Electromagnetic Communication Laboratory Penn State University

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

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

  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. 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.

  5. A Plethora of Applications Ziolkowski’s group: resonant sub-ldipole antennas ENG DPS Roma Tre group: resonant sub-lpatch and leaky wave antennas Loughborough Antennas and Propagation Conference – 2006 F. Bilotti – Potential Applications of Matamaterials in Antennas

  6. Miniaturized circular patch antennas with metamaterial loading 4/4 Implementation of the MNG medium through SRR inclusions Vertical electric field distribution Matching features Loughborough Antennas and Propagation Conference – 2006 F. Bilotti – Potential Applications of Matamaterials in Antennas

  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. 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 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 < back view > < top view > r = 2.2, t = 2.0828 mm h = 13 8.41 and 11.67 GHz < side view >

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

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

  18. 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 Plane wave source EY X 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 incidence Z Unit cell BC used X and Y: PBC Z: PML Plane of transmission Plane of reflection Plane wave source EY X 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 incidence Z Unit cell BC used X and Y: PBC Z: PML Plane of transmission Plane of reflection Plane wave source EY X 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 ( 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. source 0 I Z DNG LENS Field Distribution Field Distribution 0 I Z 0 I Z Imaging with DNG Lens Field distribution along z in the RHS of Lens 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. R T Exit angle? . . . . . . . . . . . . Single layer Multiple layers Floquet harmonics 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

  37. 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

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