Road Map Potential Applications of Antennas with Metamaterial Loading Filiberto Bilotti Department of Applied Electronics University of Roma Tre Rome, Italy The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading Leaky wave antennas with metamaterial loading Conclusions
The history of metamaterials What are metamaterials? Why to use metamaterials? The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading Leaky wave antennas with metamaterial loading Conclusions Metamaterials are artificially engineered materials exhibiting unusual properties that cannot be found in nature. Metamaterials allows going beyond the classical physical restrictions and limitations of electrodynamics. 3 4
From natural materials to complex materials / First Stage: observation and investigation of the physical phenomena in nature From natural materials to complex materials / Second Stage: design of artificial materials to imitate the nature at lower frequencies n c = c, r c, r Natural materials The arrangement of atomes and molecules determines the physical behavior Optical frequencies n = h h, r h, r Composition Alignment Arrangement Density Geometry Host medium 5 6 3
From complex materials to metamaterials Third Stage: design of artificial materials that exhibit unusual (anomalous, surprising, ) features that cannot be found in nature Microwave applications of metamaterials Fourth Stage: investigate the exciting features of metamaterials to propose novel concepts for microwave components electronic circuits radiating components DNG 7 8 4
Come back to the nature Fifth Stage: design of nanostructures to bring back to the nature the unusual properties discovered at microwave frequencies Natural optical materials Artificial dielectrics Nanotructures Complex materials Exotic shapes Meta materials wave applications of metamaterials Metamaterial terminology The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading Leaky wave antennas with metamaterial loading Conclusions 9 5
Metamaterial terminology / Metamaterial terminology / MNZ MNZ ENG k I DNG k R Re[ ] ENZ ENZ k R MNG k I Regular Dielectrics Re[ ] ENG MNG DNG k =ω p r opagation evanescent evanescent propagation β jα jα β wave 6
Complementary metamaterial pairs Complementary metamaterial pairs /6 The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading Leaky wave antennas with metamaterial loading Conclusions DNG SNG H H = jω n jω n, tan, tan Interface E E = jω n jω n, tan, tan Interface H H = jω n + jω n, tan,tan Interface E E = jω n + jω n, tan, tan Interface Interface Interface Interface Interface 3 4 7
Complementary metamaterial pairs /6 Complementary metamaterial pairs 3/6 DNG DNG The resonance condition for a D cavity filled by / pairs imposes a minimum thickness. (k d +k d ) = m π, m = = d d Pendry, PRL, Oct. Engheta, IEEE AWPL,, -3, k d k d k = k d d m + =, m λ λ d λ + d = 5 6 8
Complementary metamaterial pairs 4/6 Complementary metamaterial pairs 5/6 k d DNG k d kd i i tan(k d )+ tan(k d ) = k k < d + d = d = d Field distribution in metallic cavities filled by / and /DNG slabs (size reduction). Normalized electric field,,8,6,4, Standard resonator DNG resonator, -,8 -,7 -,6 -,5 -,4 -,3 -, -,,, Stratification axis y / λ 7 8 9
Complementary metamaterial pairs 6/6 Compact scatterers and compact antennas / A metallic cavity filled by a (or ENG)/MNG pair works as a cavity filled by a /DNG pair. ENG MNG α d i i tanh( α d )- tanh( α d ) = α α E inc H inc E inc H inc SNG Resonant compact bilayer scatterers RECIPROCITY k d k d d d = d = d SNG Resonant compact bilayer antennas 9
Compact scatterers and compact antennas / Patch Antennas with Metamaterial Loading ENG Ziolkowski s group resonant sub-λ dipole antennas The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading DNG Roma Tre UPenn resonant sub-λ patch and leaky wave antennas Leaky wave antennas with metamaterial loading Conclusions
Brief introduction on Patch Antennas /4 Patch antenna: standard configuration Brief introduction on Patch Antennas /4 Patch antennas: feeding techniques substrate patch ground plane coaxial cable microstrip line aperture coupling 3 4
Brief introduction on Patch Antennas 3/4 Patch antennas: pros and contra Brief introduction on Patch Antennas 4/4 Patch antennas: applications Pros Low cost Low profile Low weight Small volume Conformability Easy fabrication Easy integration with printed circuits Contra Narrow bandwidth Low polarzation purity Spurious radiation Low power Low gain Low radiation efficiency Tolerances 5 6 3
Radiation mechanism and design /3 Radiation mechanism and design /3 Standard rectangular patch Surface wave contribution (degraded radiation pattern and poor efficiency) W L Standard dielectric z y d X Substrate thickness: λ/ λ/ The electric field may be assumed vertically directed The magnetic field does not have the vertical component (TM z modes) 7 8 4
Radiation mechanism and design 3/3 Fringing effect is responsible for the radiation The electric field must be out of phase at the two radiating edges of the patch. L=λ/ Cavity model for analyzing patch antennas / Cavity model (since the substrate is very thin, only TM z modes are present) W The modes of the patch may be calculated as the modes of the PEC-PMC cavity PEC L Imposing the boundary conditions the calculation of the resonant frequencies is straightforward f [m,n,] TM r r c mπ nπ = + π L W PMC 9 3 5
Cavity model for analyzing patch antennas / The dominant mode along x is the TM The magnetic currents at the radiating edges are responsible for the radiation Rectangular patch antennas with metamaterial loading W L z z y d x Is it possible to apply the same concept to microstrip antennas? z y x DNG y x Electric current density distribution of the dominant mode on the patch surface DNG DNG 3 3 6
Cavity model for patch antennas with MTMs /6 Cavity model for patch antennas with MTMs /6 TM m W ηl,, z ( -η) L L Dispersion Equation for TM m modes ω k tan L k tan L k k ω [ η ] = [( η) ] d x L Filling Factor η The dispersion equation may be written with the explicit presence of the filling factor η. η η When L is very small compared to λ, if the two materials have Re[]>, the dispersion equation cannot be satisfied for any value of η. As in the D-cavity, when L is small compared to λ, the total length L is not relevant for the dispersion equation to be satisfied: the only relevant quantities are the filling factor η and the permittivities of the two materials. 33 34 7
Cavity model for patch antennas with MTMs 3/6 Cavity model for patch antennas with MTMs 4/6 Resonant Frequency [ GHz ] Also in this case there is no need for a DNG material: an ENG medium is enough..8.7.6.5.4.3... -.5 -.4 -.3 -. -. -. ENG /, f =.44 GHz r =. W L/ L = 5 mm L/ ENG, η η d Permeability variations do not affect the resonant frequency., W L/ L = 5 mm L/ ENG, d Resonant Frequency [ GHz ].8.7.6.5.4.3.. ωp = ω Drude dispersion model ENG = ENG = 3 DNG = - DNG = -3..5.3.45.6.75.9.5. Plasma Frequency [GHz] 35 36 8
Cavity model for patch antennas with MTMs 5/6 Cavity model for patch antennas with MTMs 6/6 75 E z component. H x component Radiation from this kind of antenna is very poor. Electric Field E z [ V / m ] 6 45 3 5-5 =., f =.44 GHz = -., f =.5 GHz -3....3.4.5 y [ m ] Magnetic Field H x [ A / m ].8.6.4. =., f =.44 GHz = -., f =.5 GHz.....3.4.5 y [ m ] ENG f =.5 GHz f =.44 GHz 37 38 9
Full wave simulations for the rectangular patch /7 Full wave simulations for the rectangular patch /7 W = 5 mm L = 4 mm 3 Lorentz Model for the permittivity db Return Loss as a function of frequency Input Impedance as a function of frequency, W/ W/ ENG, Probe Impedance: 5 Ohm d =.5 mm Probe Location: x p = W/4, y p = Relative Permittivity 5 5 5-5 - Re[ ] Im[ ] Return Loss [db] -5 db - db -5 db - db -5 db Input Impedance [Ohm] 5 5-5 - Input Reactance Input Resistance Probe Radius:.3 mm -5.3.4.5.6.7.8.9. Frequency [GHz] -3 db..5..5..5 3. Frequency [GHz] -5.3.6.9..5.8..4.7 3. Frequency [GHz] 39 4
Full wave simulations for the rectangular patch 3/7 Full wave simulations for the rectangular patch 4/7 E z component E z E x f =.48 GHz f =.44 GHz f =.48 GHz f =.44 GHz 4 4
Full wave simulations for the rectangular patch 5/7 Directivity Full wave simulations for the rectangular patch 6/7 The variation of the electric field under the patch is responsible for the poor radiation of a rectangular patch loaded with -ENG media. f =.48 GHz f =.44 GHz 43 44
Full wave simulations for the rectangular patch 7/7 Plasmonic Resonances Cavity model for patch antennas with MTMs /7 Geometry of a circular patch antenna with - loading. ẑ ŷ ˆx ŷ a a ˆx 45 46 3
Cavity model for patch antennas with MTMs /7 Cavity model for patch antennas with MTMs 3/7 ˆx ẑ ŷ PEP PEP PMP a = mm d =.5 mm a = mm r =.33 ˆx ẑ ŷ Dispersion Equation for TM mn modes [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Jn ka Jn ka Yn ka Yn ka Jn ka = J k a J k a Y k a Y k a J k a n n n n n Resonance Frequencies f = χ c π [m,n,] mn TM a r r TM TM TM f χ c = =.88GHz [,,] TM π a r r f χ c = = 4.77 GHz [,,] TM π a r r f χ c = = 5.99GHz [,,] TM π a r r 47 48 4
When the patch radius is smaller compared to λ, the dispersion equation can be written in terms of the: filling factor η mode order n permittivities or permeabilities Dispersion Equation for TM mn modes [ ] [ ] Cavity model for patch antennas with MTMs 4/7 [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Jn ka Jn ka Yn ka Yn ka Jn ka = J ka J ka Y ka Y ka J ka n n n n n a η Filling factor η= a a η = n η n +η > n n Cavity model for patch antennas with MTMs 5/7 Depending on the materials we use to load the antenna, we may choose the dominant mode of the cylindrical patch resonator. η = η n η > n +η n n 49 5 5
Cavity model for patch antennas with MTMs 6/7 Cavity model for patch antennas with MTMs 7/7 n = n = n = E z E z E z f =.5 GHz f =.88 GHz 5 5 6
Full wave simulations for the circular patch /6 Full wave simulations for the circular patch /6 Lorentz Model for the permittivity Return Loss as a function of frequency Input Impedance as a function of frequency a p = 5 mm a = mm MNG a = mm Probe Impedance: 5 Ohm Probe Location: a p =.75 a, φ p = -π Probe Radius:.3 mm Relative Permittivity 3 5 5 5-5 - Re[ ] Im[ ] -5.3.4.5.6.7.8.9. Frequency [GHz] Return Loss [db] db - db - db -3 db -4 db.4.45.45.475.5.55.55.575.6 Frequency [GHz] Input Impedance [Ohm] 8 7 6 Input Reactance 5 Input Resistance 4 3 - - -3-4 -5.4.45.45.475.5.55.55.575.6 Frequency [GHz] 53 54 7
Full wave simulations for the circular patch 3/6 Full wave simulations for the circular patch 4/6 E z @ f =.88 GHz Current Density and Directivity @ f =.88 GHz 55 56 8
Full wave simulations for the circular patch 5/6 Full wave simulations for the circular patch 6/6 E z and E x @ f =.473 GHz Current Density and Directivity @ f =.473 GHz 57 58 9
Leaky wave antennas with metamaterial loading The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading Leaky wave antennas with metamaterial loading Conclusions d, Natural Modes of a Grounded Slab / ŷ ( k k ) I: β > max, ky, ky I Suraface waves (only with negative constitutive parameters) II: k < β < k ky R, ky I Regular surface waves ˆx ( ) ( ) ( ) ( ) TE: k cos k d + j k sin k d = y y y y TM: k cos k d + j k sin k d = y y y y 59 6 3
d, III: k < Re[ ] < Natural Modes of a Grounded Slab / ŷ β k y y Leaky waves (only with anomalous constitutive parameters) with high leakage factor. Low directivity. ( ) IV: Re[ ] < min k, k Leaky waves (only with anomalous constitutive parameters) with low leakage factor. High directivity. ˆx Re[ k ] > k, Re[ k ] < k β y y ( ) ( ) ( ) ( ) TE: k cos k d + j k sin k d = y y y y TM: k cos k d + j k sin k d = Re[ k ] < k, Re[ k ] < k y y y y θ sin (Re[ β ]/ k) 6 ENZ-MNZ metamaterials for high directivity LW radiators ( ) IV: Re[ ] < min k, k Re[ k ] < k, Re[ k ] < k β y y An almost real solution may be found if the two terms of each equation become sufficiently small. By inspection, it is easy to derive the conditions for both the constitutive parameters and d. ( ) ( ) ( ) ( ) TE: k cos k d + j k sin k d = y y y y TM: k cos k d + j k sin k d = y y y y ( N ) π, d k β N π, d k β 6 3
Grounded bi-layers planar uniform LW antennas /7 Grounded bi-layers planar uniform LW antennas /7 Grounded metamaterial bi-layer dispersion equations TE: TM: TE TE TE TE f f ky = j ky ( f + f ) TM TM TM TM ( + ) = ( ) TE fi = kyi cot ( kyidi) / i TM fi = kyi tan ( kyidi) / i Grounded metamaterial bi-layer ky f f jky f f ky Sub-λ thickness condition High directivity conditions Retardation effects are not significant: depending on the polarization, only one constitutive parameter is involved. max ky d, ky d [ β ] Im ( ) ( ) TE: max, TM: max, ( ky ) ( ky ) TE: dd / TM: dd / 63 64 3
Grounded bi-layers planar uniform LW antennas 3/7 Grounded bi-layers planar uniform LW antennas 4/7 d d = = =.6 = 3 d =λ /5 d =λ /35.5 m ŷ db db db 3dB 4dB,,, 8 3 ˆx 3 TE : d d 34 θ = 55 ( ) / k y D 4 = db 6 8 d d db -db -db -3dB -4dB ŷ m 3 8 3,,, 34 ˆx Material dispersion ( ω ) = F ω ω ωm ω =.998 ω ω =.999 ω 4 ω = ω ω =. ω 6 ω =. ω ω =.3 ω 8 65 66 33
Grounded bi-layers planar uniform LW antennas 5/7 Grounded bi-layers planar uniform LW antennas 6/7 d d m ŷ,,, ˆx Material losses F ω ( ω ) = ω ωm jωγm d d m ŷ,,, ˆx Material losses F ω ( ω ) = ω ωm jωγm.86.8 db -db -db -3dB -4dB 8 3 3 34 4 6 8 γ m = γ m = ω / 5 γ m = ω / ( 5 4 ) γ m = ω / ( 4 ) γ m = ω / 4 γ m = ω / ( 5 3 ) Re [ β ].84.8.8.88.86.84.8.8.88. 5.x -5.x -4.5x -4.x -4.5x -4 3.x -4 3.5x -4 Im [ β ].6.4...8.6.4... 5.x -5.x -4.5x -4.x -4.5x -4 3.x -4 3.5x -4 γ m / ω γ m / ω 67 68 34
Grounded bi-layers planar uniform LW antennas 7/7 Compact cylindrical leaky wave antennas /5 d d =.5 = 4 = = d =λ /7 d =λ /3 p ŷ db db db 3dB 4dB 8,, 3, 3 ˆx 34 TM : d d ( ) / k y θ = D 4 = 7dB 6 8 H E TM jβ z jω β c J( k ) ˆ t ρ e φ ρ < ain TM TM jβ z = jω β c J( k ρ ) + c3 Y( k ρ ) ˆ < < ( ) ( ) e φ a ρ a TM jβ z jω ˆ β c4 H k β ρ e φ ρ > aout TM t t in out TM We are interested here in the modal solutions that do not exhibit field variations along φ. β β ( ) ˆ ( ) ˆ t ρ ρ + β t t ρ z ρ < in β ( ) + ( ) tρ tρ ρˆ + TM TM jβ z β ( ρ) 3 ( ρ) zˆ ρ ( ) β ( ( ) ˆ ) β ρ ρ + β ( ρ) zˆ ρ > TM j z TM j z jc J k e k c J k e a TM TM j z j c J k c3 Y k e = + k c J k + c Y k e a < < a TM j z TM j z jc4 H kt e c4 kth kt e aout t t t in out 69 7 35
Compact cylindrical leaky wave antennas /5 Compact cylindrical leaky wave antennas 3/5 ( t in) ( ) ( t in) ( ) ( t in) ( ) ( ) ( ) ( / ) ( ) ( / ) ( ) ( ) ( ) J k a / J k a / Y ka ktj ktain kj t ka t in ky t ka t in J k a Y k a H k a kj ka ky ka H k a ka t k a out t out [ β ] Im ( ) ( ) ( ) ( ) t out t out t in t t out t t out t out Sub-λ thickness condition High directivity conditions Re [ β ] / = ain ln aout / ain ( ) Electric and magnetic field distribution of the leaky mode ain = λ / 4 = θ = 6 Re [ β ] Exact value of the propagation constant of the leaky mode / ain ln aout / ain ( ) a out =.3a in ( j ) β = k.5 + 5.764 4 7 7 36
Compact cylindrical leaky wave antennas 4/5 Compact cylindrical leaky wave antennas 5/5 db db db db db db 7 3 4 33 fo = GHz 4 = 8 a D out = 3 5 6 Elevation Azimuth 9 =.83mm 69.5dB 4dB db db db db 4dB 7 3 4 33 8 3 5 6 9 f = GHz f =.5 GHz f = GHz f = 3 GHz f = 4 GHz The beam angle scans with frequency in a very smooth way (quasi-static resonance) Material dispersion is added through Drude dispersion formula ω p = ω The result is a fine tuning of the beam direction with the frequency 4dB db db db db 4dB 7 3 4 33 8 3 5 6 9 ω p =.9999 ω* ω p =.99995 ω* ω p = ω* ω p =. ω* 73 74 37
Compact cylindrical leaky wave antennas 6/5 Compact cylindrical leaky wave antennas 7/5 Material losses are added in Drude dispersion formula ω = ωω p j τ ( ω ) 6dB 5dB 4dB 3dB db ω τ = -5 ω* ω τ = -4 ω* ω τ = ain = λ / = θ = 6 Re [ β ] Exact value of the propagation constant of the leaky mode / ain ln aout / ain ( ) a out =.87 a in ( j ) β = k.5 + 4.56 The result is the reduction of the directivity, while the beam direction is almost not affected db db -db 9 5 35 5 65 8 Electric and magnetic field distribution of the leaky mode 75 76 38
Compact cylindrical leaky wave antennas 8/5 Compact cylindrical leaky wave antennas 9/5 db db db -db db 7 3 33 3 db Elevation Azimuth db 6 db 9 -db db 7 3 33 3 6 9 f = GHz f =.5 GHz f = GHz f = 3 GHz f = 4 GHz Material dispersion is added through Drude dispersion formula ω p = ω db db db -db 7 3 33 3 6 9 ω p =.99 ω* ω p =.995 ω* ω p = ω* ω p =. ω* ω p =.5 ω* db db 4 fo = GHz = 8 a D out = 5 = 7.8mm 7.46 db db db 4 8 The transverse dimensions are larger than in the previous case and there is a stronger dependence on the frequency. 5 The result is a fine tuning of the beam direction with the frequency db db db 4 8 5 77 78 39
Compact cylindrical leaky wave antennas /5 Compact cylindrical leaky wave antennas /5 Material losses are added in Drude dispersion formula ω = ωω p j τ ( ω ) db 5dB db 5dB db ω τ = - ω* ω τ = - ω* ω τ = L = 75 cm Drude dispersion for The near field is dominated by the TM LW whose E field is almost radially directed. This is a good hint for both feed and inclusion design. The result is the reduction of the directivity, while the beam direction is almost not affected -5dB -db -5dB 9 5 35 5 65 8 CST Microwave Studio FW simulations 79 8 4
Compact cylindrical leaky wave antennas /5 Compact cylindrical leaky wave antennas 3/5 The electric field is radially directed The amplitude of the Poynting vector decays along the antenna axis Scanning features of the cylindrical leaky wave antenna as a function of frequency f =.975 GHz 6 55 5 Beam Direction [degrees] 45 4 35 3 5 5 f =.975 GHz f =.975 GHz 5.96.965.97.975.98.985 Frequency [GHz] 8 8 4
Compact cylindrical leaky wave antennas 4/5 Compact cylindrical leaky wave antennas 5/5 The 3D radiation patterns show that the structure is long enough not to have back-radiation. f =.96 GHz f =.975 GHz f =.985 GHz L = 5 cm A smaller structure gives reduced directivity while the back-radiation is increased, due to the reflections at the no-feeding end. f =.96 GHz f =.975 GHz f =.985 GHz 83 84 4
Conclusions Conclusions The history of metamaterials Metamaterial terminology Complementary metamaterial pairs Patch antennas with metamaterial loading Leaky wave antennas with metamaterial loading Conclusions Metamaterial complementary pairs are able to overcome the diffraction limit in the design of microwave components. Sub-wavelength cavities, waveguides, scatterers, and antennas may be obtained. Patch antennas and leaky wave antennas with sub-wavelength resonant dimensions have been presented in details. 85 86 43
Acknowledgements Prof. Lucio Vegni (University of Roma Tre) Dr. Andrea Alù (University of Roma Tre) Prof. Nader Engheta (University of Pennsylvania) References Alù, Bilotti, Engheta, Vegni, IEEE IMS 5, Long Beach, USA, June 5 Bilotti, Alù, st EU Ph.D. School on Metamaterials, San Sebastian, Spain, July 5 Alù, Bilotti, Engheta, Vegni, IEEE AP/URSI Symp., Washington, USA, July 5 Alù, Bilotti, Engheta, Vegni, ICEAA 5, Turin, Italy, September 5 Alù, Bilotti, Engheta, Vegni, ICECom 5, Dubrovnik, Croatia, October 5 87 88 44