DNG and SNG Metamaterial Designs and Realizations for Practical Applications

Transcription

1 DNG and SNG Metamaterial Designs and Realizations for Practical Applications Richard W. Ziolkowski Department of Electrical and Computer Engineering The University of Arizona XI School on Metamaterials Distributed European Doctoral School on Metamaterials Marrakesh, Morocco May 6, 008 Metamaterials ( MTMs ) Artificial materials that exhibit electromagnetic responses generally not found in nature Lycurgus Cup, 300AD Chartres, France, 1400AD Inclusions In a host medium can alter its Electromagnetic Properties Sir Jagadish Chandra Bose, 1893 Artificial Chiral Materials F

2 Metamaterials ( MTMs ) Why all the renewed interest in artificial materials?? The possibility that one can tailor the permittivity and permeability values Positive or Negative to match any application Cloaking Negative Refraction Highly Subwavelength Resonators Perfect Lens n = +1 d n = -1 n = +1 Scattering n = -1 Source ξ Size ξ ~ λ/100 d-ξ Negative New Physics and New Engineering Possibilities Lorentz: The Debye, Lorentz, and Drude linear polarization models produce well-known material responses t e t 0 = 0 p ωp χα ( ) = ω + j Γ e ω+ ω0 P+Γ P+ ω P ε ω χ E χω Drude: t +Γe t p ω χα ω χα χω ( ) = = ω + j Γe ω ω ( ω j Γ e ) Debye: t e 0 e 0 p p P P= ε ω χ E P+Γ P= ε ω χ E ωp χ χω ( ) = jω +Γ α α Standard α α + ε0 ωpχβ te + ε0 χγ t E jωp χβ ω χγ ω j e ω+ ω0 ω + j Γ e ω+ ω Γ p 1TD-LM TD-LM P( ω) χω ( ) = ε E ( ω) 0

3 Lorentz: χ The Debye, Lorentz, and Drude linear polarization models produce well-known material responses t + Γe t + ω0 = ε0 ωp ωp χα ( ω) = ω + j Γ e ω P P P χα E Drude: Debye: t e tp ε0 ωp ω p α ω + j Γ e ω P+Γ = Standard 0 + ω χ E χ ω χα χω ( ) = = ω ( ω j Γ ) P+ Γ P = ε ω χ E t e 0 p ωp χ χ( ω) = jω +Γ α e α α p 1TD-LM + ε0 ωpχβ te jω χ + ω + Γ ω + ω p β j e 0 e TD-LM ε χ E + 0 γ t ω χγ j e 0 + ω + Γ ω + ω P( ω) χω ( ) = ε E ( ω) 0 Where do the negative values appear? Lorentz real part is negative just above the resonance Drude real part is negative for all frequencies below the plasma frequency Lorentz behavior = narrow bandwidth Drude behavior = broad bandwidth REAL MTMs ARE DISPERSIVE AND LOSSY 3

4 ENG versus MNG realizations Easier to achieve MNG ENG Harder to achieve ENG MNG Frequency 1-10 GHz Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) UA Unit Cell Lumped element ~ λ / 100 Z load UA Electric and Magnetic Molecules for RAMs Z load Zero-index DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) ε UA Low Loss DNG and SNG X-band elements UA CLL AMC at X-band S1, Composite planar structure ~ -0.3dB/cm Magnitude ( db) Frequency -10 5E+09 7E+09 9E E E E+10 4

5 Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) Z load Z load UA Electric and Magnetic Molecules for RAMs Zero-index DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) ε EM Properties of aggregates of atoms / molecules are typically characterized by their electric and magnetic dipole moments E + - Dielectric Dipoles p P = Σ i p i / V = ε 0 χ e E ε = ε 0 ( 1 + χ e ) χ e = electric susceptibility H Magnetic Dipoles m M = Σ i m i / V = χ m H μ = μ 0 ( 1 + χ m ) χ m = magnetic susceptibility 5

6 Artificial electric and magnetic molecules have been designed that produce novel material responses Electric molecule: Small Loaded Dipole Antenna Magnetic molecules: Small Loaded Loop Antenna Z load Z load Tailored Polarization Behavior Tailored Magnetization Behavior F. Auzanneau (CEA-CESTA, France) & R. W. Ziolkowski,

7 Several material models had been developed and studied. They produce a variety of novel electromagnetic responses. Lorentz material t e t 0 0 p P+Γ P+ ω P= ε ω χ E Time derivative Lorentz material (TDLM) t P e tp ω0 P ε0 ωp χα E ε0 ωp χβ t +Γ + = + Two time derivative Lorentz material (TDLM) α t +Γ e t ω0 P= ε0 ωp χα E+ ε0 ωp χβ t E + ε0 χγ t P P+ E E These models have been implemented and tested in our 1D, D, and 3D FDTD simulators The TDLM model has been used to achieve ABCs for lossy media The TDLM model produces a causal MTM response t e t 0 0 p P+Γ P+ ω P= ε ω χ E ω χω ( ) = ω 0 p α + jωωχβ ω ω + j Γ e ω+ ω0 χ 0 p β t E 0 γ t 0 [ + ] εω ( ) = ε 1 χω ( ) ω p ε = 1 χ α 0 ω0 ω ε0 εω ( ) ( ω) lim + lim = 1+ χ ε α + ε ω χ + ε χ This implies controllable low and high frequency limits DC limit High freq limit χ γ E γ 7

8 Uniaxial TDLM medium was designed to act as a (Maxwellian) Perfectly Matched Layer for FDTD ABCs R = 0 Incident Wave P M L Independent of * frequency * angle of incidence ABCs Stealth EMI/EMC PCS Anechoic Chambers Electromagnetic absorbers have many useful applications Considered bi-anisotropic molecules 8

9 Considered active molecules Curve Shaper Molecule Volumetric 3D metamaterial realized as a stack of D planar metamaterial realizations Ziolkowski Bi-Anisotropics Meeting Ghent, Belgium 004 Potential how to realize any type of 3D metamaterial 9

10 HP-ADS layout of an elementary D-3D metamaterial molecule Input Matching Circuits DNG Circuits Output Matching Circuits Antenna Load Term1 Num=1 Z=73+j4.5 Ohm Antenna Load Term Num= Z=73+j*4.5 S-PARAMETERS S_Param SP1 Start=1 GHz Stop=4 GHz Step=1 MHz Preliminary results were promising (circa 004) SMT_Pad SMT_Pad Pad1 W=50 mil L=50 mil PadLayer="bond" SMO=5.0 mil SM_Layer="solder_mask" PO=0 mil MSub MSUB MSub1 H=31 mil Er=. Mur=1 Cond=4.1e7 Hu=3.9e+034 mil T=35 um TanD= Rough=8 um Recent considerations 10

11 Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) Zero-index DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) ε UA CLL AMC at X-band The scattering properties of PEC and PMC slabs are different Out-of-Phase Reflection E tan = 0 Γ = +1 φ Γ = π k ref E ref H ref E inc k inc H inc Perfect Electric Conductor (PEC) In-Phase Reflection H tan = 0 Γ = +1 E ref E inc H ref k inc k ref H inc Perfect Magnetic Conductor (PMC) φ Γ = 0 11

12 Artificial Magnetic Conductors (AMCs) AMCs are high-impedance surfaces often generated by a) incorporating a special texture on host surfaces, or b) artificially fabricated inhomogeneities embedded in host media Two important parameters, electrical permittivity ε and magnetic permeability μ, determine the response of the material The physical structure of -D or 3-D array of inclusions are much smaller than the wavelength Split Ring Resonators (SRRs) Capacitively Loaded Loops (CLLs) 7 th ESA Antenna Technology Workshop on Innovative Periodic Antennas: EBG, DNG, Fractal and FSSs Santiago de Compostella, Spain March 004 High-Impedance Electromagnetic Surfaces Mushroom Surface Many Thanks to Dr. Dan Sievenpiper, HRL, for this slide 1

13 η The reflection and transmission coefficients for the scattering of a normally incident plane wave from a slab are readily derived Incident wave Reflected wave d Transmitted wave Wave impedance Reflection S 11 = ( η η0 ) ( η+ η ) 0 μ η = ε jkd 1 e η η 1 ( ) e η+ η 0 jkd 0 11 η lim S = 1 η Independent of d Transmission S = 4ηη 0 1 ( η+ η0 ) jkd e η η 1 ( ) e η+ η 0 jkd 0 lim S = 0 η 1 PMC Surface Realization Using UC-PBG UC-PBG PEC Equivalent Circuit Model Reflection coefficients measured for PBG structure and PEC surface Phase difference = GHz Magnitude = 1 at all frequency Many Thanks to Prof. Tatsuo Itoh, UCLA, for this slide 13

14 H E SRR Design with Dimensions k W a t g L1 W 1 g g L One element unit cell b g g t L 1 W 1 L W a b 10 mils 10 mils 55 mils 55 mils 95 mils 95 mils 5 mils 0 mils 100 mils =.54 mm HFSS calculated S 11 values for the SRR MTM with a depth of 1,, 3, 4 SRR elements show complete reflectivity near the design frequency of 10GHz Magnitude ( db ) SRR SRRs 3 SRRs 4 SRRs Frequency ( GHz ) 14

15 HFSS calculated S 11 values for the SRR MTM with a depth of 4 SRR elements show that it acts as a PMC near the design frequency of 10GHz S11 Magnitude ( db ) S11 Phase ( degrees ) Frequency ( GHz ) H E CLL Design with Dimensions k t g b a s W One element unit cell L b t G s W L a b 10 mils 10 mils 17. mils 80 mils 10 mils 40 mils 40 mils 100 mils =.54 mm 15

16 HFSS calculated S 11 values for the SRR MTM with a depth of 1,, 3, 4 CLL elements show complete reflectivity near the design frequency of 10GHz CLL CLLs 3 CLLs 4 CLLs Magnitude ( db ) Frequency ( GHz ) HFSS calculated S 11 values for the CLL MTM with a depth of 4 CLL elements show that it acts as a PMC near the design frequency of 10GHz Frequency ( GHz ) S11 Magnitude ( db ) S11 Phase ( degrees ) 16

17 HFSS calculated S 11 values for the CLL MTM with a depth of 4 CLL elements show that it acts as a PMC near the design frequency of 10GHz Frequency ( GHz ) S11 Magnitude ( db ) S11 Phase ( degrees ) zoom Final CLL Metamaterial Structure Precisely cut, aligned and assembled of 161 strips 17

18 The CLL MTM was measured with a free space measurement system Measure the CLL MTM with its designed orientation Measure the CLL MTM with a 90 rotation HP 870C network analyzer to measure the S-parameters MUT X-band rectangular horn Measured magnitude of S 1 for the CLL MTM slab 0-10 Magnitude ( db ) Frequency ( GHz ) 18

19 Measured magnitude of S 11 for the CLL MTM slab 0-5 Magnitude ( db ) Frequency ( GHz ) Phase Reference Plane measurement was achieved with a reference copper plate A copper plate is placed over the mouth of the flange of the transmit antenna 19

20 Measured phase of S 11 for the CLL MTM slab and for the reference plate S11 Magnitude ( db ) S11 Phase ( degrees ) S11 Rel. Phase ( degrees ) Frequency ( GHz ) Measured magnitude and phase of S 11 for the CLL MTM slab verifies the predicted PMC behavior Frequency ( GHz ) S11 Magnitude ( db ) S11 Phase ( degrees ) S11 Rel. Phase ( degrees ) 0

21 Measured magnitude of S 11 for the CLL MTM slab in 90 o fixed rotatation demonstrates the expected anisotropy Magnitude ( db ) Frequency ( GHz ) MTM MTM Rotated 90 Found that imperfections had a critical impact on the overall AMC performance 1. Alignment errors reduce the bandwidth and increase losses because there is more incoherent scattering. Maintaining precision of smoothness/uniformity of all exterior surfaces of slab decreased losses 3. Need enough copper in the reference to achieve a an adequate reference plane 1

22 An artificial magnetic conductor has been realized with Capacitively Loaded Loops (CLLs) Dimensions of each CLL element W = 160 mils L = 100 mils U = 65 mils S = 49 mils T = 18 mils 100 mils =.54mm < λ 0 / 10 CLL elements have been used successfully in U Arizona DNG metamaterial studies A. Erentok, P. Luljak, and R. W. Ziolkowski, IEEE Trans. Antennas and Propagat., vol. 53, pp , Jan 005 Metamaterial-based AMC block has been designed, fabricated and measured Acts like PMC No Ground Plane CLL-based AMC block Two CLL-deep unit cell geometry G1= 40 mils = mm G=0 mils =0.508 mm Unit cell size 31 mils x 800 mils x 60 mils ( mm x 0.3 mm x mm ) Acts like PEC

23 Finite versions of the HFSS designs were simulated, fabricated and measured. The AMC block was formed with a stack of 31 unit cells. Block diagram Symmetry Plane z Waveguide Port x Radiation Box MTM Block The HFSS simulation space closely modeled the experimental setup: the MTM block was sandwiched between two X-band waveguides y WG Port The phase of the AMC block was measured in reference to a PEC plate PEC Reference The S-parameters were measured with an HP-870C network analyzer AMC Block 3

24 Volumetric AMC block without ground plane designed and tested X-band Waveguide AMC Blocks Zero 9.75 GHz Measured Zero Phase crossing is 1.0% different from the predicted value Erentok, P. Luljak, and R. W. Ziolkowski, IEEE AP Special Issue on AMCs, IEEE Trans. Antennas and Propagat., vol. 53, pp , January 005. A 4x4 CLL unit cell was also used in HFSS simulations Acts like PMC Acts like PEC Four CLL-deep unit cell geometry G1= 40 mils G=0 mils Unit cell size 31mils x 800mils x 50 mils 4

25 Several 4x4 CLL-deep unit cell structures were investigated using HFSS simulations AMC AEC The magnitudes and phases of the HFSS predicted S 11 values for the four CLL-deep unit cell The zero phase crossing of the HFSS predicted S 11 value for the cases A and B occurs at 9.73 GHz 5

26 The magnitudes and phases of the experimentally measured S 11 values for the finite four CLL-deep MTM blocks show the predicted high reflectivity over the X-band frequencies The zero phase crossing of the measured S 11 values for the cases A and B occurs at GHz, % different from the predicted value Single CLL Unit Cell was simulated with HFSS to extract the permittivity and permeability Port Port 6

27 The matching permeability indicates a TDLM behavior; the matching permittivity indicates a Drude behavior Permeability Permittivity resonance zero crossing χαmωpm + jχβmωpmω χγ mω μω ( ) = μ0 1+ ω j mω ω + Γ + 0m f = 0.97GHz 0m ω = ω χ = χ = 5 pm 0m, αm 0.3, βm 10, χ = 0.5, Γ = 10 ω 5 γ m m 0m Fit by brute force ω pe εω ( ) = 9ε0 1+ ω j e ω + Γ f = 0.97GHz 0e ω = ω, Γ = 10 ω 5 pe 0e e pe There is reasonable agreement between the matched models and the corresponding S-parameters The magnitude is easier to fit than the phase Thus, at the target frequency the AMC block has: μ, ε 0 so that η 7

28 TDLM and Drude models were used is a model-based parameter estimation to match the HFSS-predicted magnitude and phase values of the S 11 and S 1 parameters for a unit cell CLL element TDLM (Permeability) χα : (variable) [0.1,] χγ : (variable) (-1,1] χβ : (fixed) 1e-4 Lm : (variable) [0,10] Background weighting Γm :(fixed) 1e-5 * ωpm ωom : (variable) [9,11] GHz * π ωpm : (fixed) 10 * π GHz Drude Model (Permittivity) ωpe : (variable) [9,11] GHz * π Γe : (fixed) 1e-5 * ωpe Background weighting Le : (variable) [0,10] The total number of variables are 6 The initial parameter values are randomly selected between [0,1], and these values normalized to the defined boundaries. The TDLM and Drude model parameters were optimized by fitting the S 11 and S 1 values to the corresponding HFSS simulation results The optimization results were obtained using 001 discrete frequency points between 9 and 11 GHz Permeability Values Permittivity Values 8

29 MATLAB Optimization Toolbox default values were modified to obtain the most accurate results MATLAB optimization toolbox default settings were modified, e.g., maximum error tolerance = 1e-1, maximum function error tolerance = 1e-1 The number of the function iterations is increased from 1e4 to 1.5e6 The obtained fitness value is (Best Result) The best fit was obtained using S 11 values only Brute Force vs. MATLAB Optimization Toolbox Results shifted to 9.70 GHz resonance and zero crossing 9

30 Modeled-based Parameter Estimation CONCLUSIONS It is difficult to obtain a perfect match for both S 11 and S 1, magnitude and phase values using the TDLM and Drude Models. The best convergence value is obtained using only S 11 values to fit the TDLM and Drude models. The S 11 phase values required f pm and f om frequencies to be 10 GHz for best match. The S 1 magnitude & phase values required f pm and f om to be 9.70 GHz for best match. The optimization scenarios using TDLM model for both permittivity and permeability values did not converge (to the correct values) The S 11 phase values strictly depend on Γ β. The optimization results suggest that the upper value of the Γ β should be restricted to The proportionality constant of the Drude model also had a big impact on the matched S 11 phase and magnitude values. The optimization results showed that the proportional constant should be restricted to the small numbers, e.g., [0,15] to prevent S 11 values from becoming flat and equal to 1. Artificial Magnetic Conductors ( AMCs ) provide important advantages for antenna applications AMC PEC AMC doubles a nearby electric dipole rather than shorting it out Electric Dipole Antenna Image Potential antenna applications include - Low-profile antenna design - Improved radiation pattern ( both in near- and far-field ) - Reduced mutual coupling in multiple antenna systems E-Plane Pattern H-Plane Pattern h = λ 0 / 5 f = GHz Free-space dipole Dipole antenna / CLL-block front-to-back ratio! A. Erentok, P. Luljak, and R. W. Ziolkowski, IEEE Trans. Antennas and Propagat., vol. 53, pp , Jan

31 The resonance between the dipole and the AMC block also produces enhanced near field performance GHz E-plane H-plane Erentok, P. Luljak, and R. W. Ziolkowski, IEEE AP Special Issue on AMCs, IEEE Trans. Antennas and Propagat., vol. 53, pp , January 005. Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) UA Unit Cell Lumped element ~ λ / 100 Zero-index DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) ε 31

32 Re-discovery of bed-of-nails medium for ENG effects Walter Rotman,, 1961; Pendry et al 1996 Two-dimensional anisotropic lattice Three-dimensional anisotropic lattice Three-dimensional isotropic lattice ωp ωp Γ ω εp = ε0 1 + j Γ + ω Γ + ω ω p Γ ε 0 is the plasma frequency is the collision frequency permittivity of free space NOTE: infinite wires required Finite Element Simulator Source1 PMC Walls Slab x PEC Walls Source z E H k y Deembedded distance Extract material parameters from reflection and transmission results Pascal Imhof, MS Thesis, 006, EPFL, LEMA 3

33 Cylindrical and rectangular PEC wire medium models that exhibit the desired effective medium properties z Drude behavior y Cylindrical wire medium x z Rectangular wire medium x y Wire structures Surface area of the inclusions and the spacing between them govern the plasma frequency Extracted permittivities Cut wires do not produce ENG properties at low frequencies Pascal Imhof, MS Thesis, 006, EPFL, LEMA 33

34 Pascal Imhof, MS Thesis, 006, EPFL, LEMA Pascal Imhof, MS Thesis, 006, EPFL, LEMA 34

35 Design of highly subwavelength ENG unit cells Pascal Imhof, MS Thesis, 006, EPFL, Supervisors Profs. J. Mosig and R. W. Ziolkowski Meander line ε r GHz λ 0 /100 x λ 0 /100 PEC d Lumped element - S line ε r = -.96 j 430 MHz λ 0 /331 x λ 0 /681 RO310 RO310 ε r =10. PMC E H k Recommend pattern by Vishay Inductor w l w=1.046mm l=.108mm mm mm 4mm 4mm 4mm Pascal Imhof, MS Thesis, 006, EPFL, LEMA 35

36 Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) Zero-index DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) ε UA Low Loss DNG and SNG X-band elements S1, Composite planar structure ~ -0.3dB/cm Magnitude ( db) Frequency -10 5E+09 7E+09 9E E E E+10 DNG MTMs are achieved by combining MTMs with ENG and MNG effects in the same frequency regime UCSD Experiments David Smith, Shelly Schultz, et al. 36

37 UA DNG MTM was designed to achieve a matched medium at 10 GHz E Electric dipole metamaterial ENG H k Capacitively Loaded Strip ( CLS ) Unit element E Magnetic dipole metamaterial MNG H k Split Ring Resonator ( SRR ) Unit element R. W. Ziolkowski, IEEE Trans. AP, vol. 51, pp , July 003 Compact metamaterials having negative index of refraction have been designed, fabricated and tested experimentally All structures constructed with Rogers Corporation 5880 Duroid ( ε r =., μ r = 1.0, tan d = ) 31 mil ( 100 mil =.54 mm ) thick, 15 mil polyethylene spacers S-parameters measured with a free space measurement system at X-band frequencies Experimental results confirm the realization of DNG MTMs that are matched to free space Very good agreement between numerical and experimental results 37

38 The CLS- and SRR-based MTMs were measured separately Dipoles Only Split rings only MTM block covers the aperture of an X-band rectangular horn HFSS was used to design each MTM structure CLS-only MTM SRR-only MTM 38

39 Measurements confirmed the HFSS simulation results showing the DNG medium effects for the planar structure Dipoles, split rings, & composite planar structure Free space measurement system MTM block X-band horn The S 1 experimental data shows the predicted reflection bands for the electric and magnetic dipole metamaterials MNG band ENG band 39

40 UA DNG MTM was designed to achieve at 10 GHz a matched-to-free-space medium Electric dipole metamaterial Finite everything d ~ λ/10 Magnetic dipole metamaterial H H E E k k Capacitively Loaded Strip ( CLS ) Unit element Split Ring Resonator ( SRR ) Unit element DNG Unit Cell Set Integrated Planar R. W. Ziolkowski, IEEE Trans. AP, vol. 51, pp , July 003 HFSS / FDTD Simulation Region 40

41 The composite planar MTM S-parameters were calculated with Ansoft s HFSS The composite planar MTM S-parameters were calculated with Ansoft s HFSS Matched frequencies Matched frequencies 41

42 The composite planar MTM exhibits matching to free space in two frequency regions ( and nearly three ) The S 1 experimental data shows the predicted transmission bands for the matched DNG medium S1, Composite planar structure Loss < 0.3dB/cm Magnitude ( db) E+09 7E+09 9E E E E Frequency S1, Split rings only Magnitude ( db ) E E+09 9E E E E Freqeuncy 4

43 DNG What is more fundamental: ε, μ or n, η???? ω k = ω ε μ = n c μ η ε n = ε ε μ μ = 0 0 r r r r r r ( r )( r ) n = ε μ = ε μ = j ε j μ = ε μ Index, wave impedance are derived quantities Can you get negative refraction without DNG media? Yes with EBG/PBG media Effective permittivity and permeability parameters are commonly extracted from S-parameter (calculated/measured) values using the Nicolson, Ross, and Weir approach V1 = S1 + S11 V = S1 S11 1+ V1V X = V1 + V 1 V = 1V Y V1 V Ζ = exp( ikd) = X ± Γ = Y ± Y 1 X 1 ω k0 = c ln( Z) ε rμr = jk d r 1+ Γ ln( Z) μr = 1 Γ jk d 0 μr 1+ Γ = ε 1 Γ 0 1 Γ ln( Z) ε r = 1+ Γ jk d 0 43

44 The effective permittivity and permeability parameters were extracted from the S-parameter values using a modified version of the Nicolson, Ross, and Weir approach V1 Γ exp( ikd) = 1 ΓV exp( ikd) V Γ = 1 V exp( ikd) (1 V1 )(1 + Γ) 1 exp( ikd) = 1 ΓV V μr jk d 1+ V ε r 0 k k 0 1 μr μr 1 exp( ikd) 1 V = ε 1+ exp( ikd) 1+ V r 1 (1 V1 )(1 + Γ) ε rμr jk d 1 ΓV 0 1 n = ε r μ ε r μr S jk d r 0 11 Enhanced Result when S 11 ~ 0 A simplified MTM was designed to isolate the electric and magnetic elements and the corresponding effects 44

45 CLS-only MTM S-parameters, Ansoft s HFSS Extracted effective permittivity SRR-only MTM S-parameters, Ansoft s HFSS Extracted effective permeability 45

46 Composite MTM structure S-parameters, Ansoft s HFSS Extracted effective permittivity and permeability The effective permittivity extraction can be improved near the frequency points matched to free space Without enhancements With enhancements 46

47 The effective index of refraction of the simplified MTM is negative in the frequency region were matching occurs The effective permittivity and permeability of the composite planar MTM were extracted from the HFSS S-parameter calculations 47

48 A negative effective index of refraction was extracted from the HFSS S-parameter calculations and from the FDTD calculations HFSS results FDTD results Confirmation that negative index of refraction MTMs was realized Enhancement of the power radiated by a dipole antenna at boresight by means of a left handed superstrate, E. Sáenz, I. Ederra, R. Gonzalo, P. de Maagt IWAT 006 Aperture efficiency with and without superstrate Radiation patterns Aperture efficiency is larger than one field at edges of the superstrate make the effective aperture area larger than the physical area 48

49 Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) UA Unit Cell Lumped element ~ λ / 100 Z load UA Electric and Magnetic Molecules for RAMs Z load Zero-index DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) ε UA Low Loss DNG and SNG X-band elements UA CLL AMC at X-band S1, Composite planar structure ~ -0.3dB/cm Magnitude ( db) Frequency -10 5E+09 7E+09 9E E E E+10 Recent metamaterial research efforts (lumped element-based ENG, MNG and DNG realizations) at UHF frequencies Maximum Cell Size ~ λ / 75 ENG MNG ( not to scale ) This work was supported in part by DARPA Contract number HR C

50 n = 3.11 with a loss of 0.91 db/cm at 400 MHz for 10mm, λ /75 unit cell real Lumped-element based unit cells have achieved the smallest, lowest frequency ENG, MNG, DNG (NIM) materials to date MNG portion Rohacell TM spacer ENG portion Complete NIM slab ( ~ 900 Unit Cells ) ( not to scale ) This work was supported in part by DARPA Contract number HR C Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) UA Unit Cell Lumped element ~ λ / 100 Z load UA Electric and Magnetic Molecules for RAMs Z load Zero-index n = 3.11 real loss = 0.91 db/cm at 400 MHz for 10mm, λ /75 unit cell DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) UA CLL AMC at X-band ε 50

51 Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) Zero-index DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) ε Zero-Index MTMs Highly directive beams FDTD-predicted electric field distributions show that a line source in a zero-index slab creates a uniform aperture field leading to a narrow beam profile Line source ε(ω 0 )=0, μ(ω 0 )=0 Zero-index slab Ziolkowski, Phys. Rev. E, vol. 70, , October, 004 Aperture loaded with field having constant, uniform phase leads to most directive output beam 51

52 Dr. Steve Franson PhD Dissertation, November 007 Motorola MMW Divsion Manuscripts in review Highly directive antennas desired for 1km WLAN systems at 60GHz Zero-n superstrate leads to enhanced antenna gain Patch antenna driven 3 layer grid superstrate structure 17.dB Bare Patch ~ 3.dB 5

53 Fabricated 60 mil Period Dipole Fabricated 40 mil Period Dipole 53

54 Fabricated 30 mil Period Ring Does the grid have Zero N? Matlab code verified a zero index of refraction for a layer infinite grid The simulated phase of the transmitted wave was consistent with Zero N 54

55 Dipole Superstrate Gain = 13.7dBi Operating well below resonance Acting similar to high dielectric Grid Superstrate Nearly 19dBi of simulated Gain First Simulated in CST to find best configuration Simulated and tuned in XFDTD for high accuracy 55

56 Fabricated Grid Dimensions match well with designs Curvature The material is very flexible When adhesive backing is removed, significant curvature occurs Tape is used to tune spacing and curvature 56

57 Antenna Construction 68 mil period design used a 70 mil thick rigid foam spacer (shown) 70 mil period design used layers of flexible foam (not shown) Measured Results Information All measured results are the system gain of the entire antenna structure, including the feed transmission line Tuning was only possible for system gain Unlike other antennas, the best system gain frequency was not typically the same as the best gain frequency All results are tuned for best performance. Tape affects spacing, thickness, and curvature 57

58 70 mil Measured Results 1 layer worked well, but as the layers increased, the expected gain enhancement was not present (max=10dbi) 68 mil measured results Similar Result for 68 mil Structure Best System gain = dbi 58

59 Thickness Variation Thickness was less than expected Thickness variation was greater than expected Grids became nonplanar Multi-layer structures don t perform well, when all layers are not the same thickness 4 layer Thickness Measurement 1 st 3 layers averaged 38 mils, 4 th layer measured 35 mils All layers had at least 3 mil variations at edge This does not even include the curvature effect 59

60 60GHz WLAN Experiments Calibrated Horn 1.5Gb/s Pattern Triggered 1.5 Gb/s Eye Diagram Actual 1.5 Gigabit/s Ethernet data was transmitted wirelessly between two computers using this high gain antenna structure System gain = dbi Why the interest in electrically small antennas (ESAs)? Wireless technologies have become ubiquitous ESAs are one of their enabling technologies λ/4 monopole L = 50mm for 300MHz Typical antenna UAVs Embedded RFID tags Wireless sensor networks FOMs: Efficient High BW Multi-freq Low cost Light weight Easy fab 60

61 Efficient Electrically Small Antennas Electrically small electric dipole = highly capacitive element Source λ/4 resistance transformer Inductor a X ind = X * ant X total = 0 Input impedance matched to the source Γ = 0 Max Accepted Power MTM thing-a-ma-jigger Desire: Source a No matching circuit Efficient ESA Center-fed dipole-eng shell example: Using a highly subwavelength resonator to achieve a metamaterial-based efficient electrically-small antenna (ESA) Free Space radius ~ λ/5 ka ~ 0.1 OE ~ 100% R. W. Ziolkowski and A. Erentok, IEEE Trans. Antennas Propagat., vol. 54, pp , July 006 E-plane and H-plane patterns 61

62 DARPA Sponsored, Boeing Phantom Works led project PI: Minas Tanielian Electrically Small Hemispherical Antenna Many thanks to Bob Greegor for his program review slides 6

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65 ~17dB improvement over bare loop Possible ENG shell meander-line realization 65

66 We have successfully developed several metamaterial-inspired efficient electrically-small antennas EZ Magnetic EZ Electric D A. Erentok and R. W. Ziolkowski IEEE Trans. Antennas Propagat. vol. ka ~ pp , OE > March 90% ~ db FBW VSWR ~ 1-4% 3D -34dB Optical Metamaterials and Applications Based on Resonant Coated Nano-Particles (CNPs) k CNP Laser Gain overcomes MTM Losses Dielectric Gain core (QDs) core R μ 1 ε 1 R 1 ε μ Excited by 500nm visible light 10nm, 30nm radius CNPs Metal coating Pixel containing resonant CNP particles CNP Based Tunable Pigment Three CNP layers generates the entire NTSC and RGB Gamuts? CNP Laser-based Localized Nano-Sensors: Bio, Chem -markers Active Optical Metamaterials: Overcome loss issues J. A. Gordon and R. W. Ziolkowski Opt. Exp., Vol. 15, Issue 5, pp , March

67 Metamaterials ( MTMs ) have exotic properties that may have a high impact on a wide variety of practical applications ENG (ε < 0, μ > 0) μ DPS (ε > 0, μ > 0) UA Unit Cell Lumped element ~ λ / 100 Z load UA Electric and Magnetic Molecules for RAMs Z load Zero-index n = 3.11 real loss = 0.91 db/cm at 400 MHz for 10mm, λ /75 unit cell DNG (ε < 0, μ < 0) MNG (ε > 0, μ < 0) UA CLL AMC at X-band ε Thank you for listening Any questions?? 67