Left-Handed (LH) Structures and Retrodirective Meta-Surface
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1 Left-Handed (LH Structures and Retrodirective Meta-Surface Christophe Caloz, Lei Liu, Ryan Miyamoto and Tatsuo Itoh Electrical Engineering Department University of California, Los Angeles
2 AGENDA I. LH transmission line approach with microstrip realization II. LH forward coupler III. An active retrodirective meta-surface
3 LH-TL as the Dual of the Conventional TL ( j C Z Z dz ω slope v > slope v < g ω p ( j L Y Y / dz ω ( C γ jβ Z Y j ω ( ω nonlinear β C high - pass + z prop. z prop. (energy (energy ϕ β { } from the [ ABCD]matri S ϕ { S } -β p v p v v p g ω + ω < > v fct( ω distortion g ( jω ( jω C Z c λg π p p e ϕ as ω f (MHz ϕ as ω β πω ω λ ω ( at! g
4 Determination of LH Material Parameters PW in an medium: LH-TL parameters: Z Z jωµ Y jωε ( jω Y ( jω Dispersive ε & µ: ( ω ωµ ω µ ( ω Dispersive n: Z Y jβ ( jωµ ( jωε Z Y j µ <! µ ω + j c ( ω µ rε r ωε ω ε ε <! ε ( ω n µ ε <! ( n c L C ω ω r r Entropy conditions: ωε W ω ( ( ωµ E + ω H > ( εµ ω ω ( ωµ > >
5 Lumped-Element Appro. of the LH Line Physical Line Infinitesimal model Lumped-el. Appro. Fictitious Line TL model : F m ( unit cell: C u (Anticipated artificial LH - TL : N cells physical length p known Cu,Lu,Ru,Gu C,,R,G defined C u p ( p N, etc. ω β diagram : γ β G ( S m dz line of length p : C p, L L p, tot tot Gtot G p, Rtot R ( R + jω ( G + jω ( ω Im γ ( ω { } R ( H m ( Ω m p C u ladder circuit : N ω β diagram : β G u p u p p L u R u N [ S] ( ω ϕ{ ( ω } p scattering matri u S ( N p, etc.
6 Lumped-Element Realization of a LH-TL Magnitude of approimat ion cutoff ( f λ ω!!! p p e c N peaks N frequency (GHz ( β ( β L ω S- parameters > lossless > unlimited BW λ ω p e ω-β diagram vs. N (obtained by phase unwrapping 64 nh m, 5.6 pf m, R, G, p m f c N f appro. ω c N L C u u p N f u < λ > > Phase of approimat ion cutoff ( f ω dependence β ω L ϕ as ω g ( π p f p S- parameters c ( frequency (GHz N min ( f, or ( π N ( π LuCu e.g. : L' 64 nh m, C' 5.6 nh m, p GHz, MHz, N ϕ asω > unlimited BW > moderate dispersion β ( m
7 Microstrip Design of a LH-TL ( Simple microstrip realization: C: interdigital capacitor L: shorted-stub inductor High-pass filter designed from synthesis of a -cell Chebyshev lowpass prototype via interdigital capacitor shorted-stub inductor unit cell Photograph of the microstrip prototype
8 Microstrip Design of a LH-TL ( Magnitude of S- parameters Phase of S- parameters LH range LH range frequency (GHz ( β ( β L ω f ma ω - β diagram LH range frequency (GHz Unwrapped phase of S LH range C L C L f f min cutoff β (/m frequency (GHz
9 Dual-Mode (RH/LH TL: Series RH-TL and LH-TL RH-TL low - pass : ω L LH-TL high - pass : β β ( ω L Magnitude of LH f c S- parameters f RH f c whereω v v D.M.-TL pass - band : β β + β p g ω ω ω ω ω ω ω ω, ω ( ω ω, ( ω ωω ( ω + ω ω ω ( ω ω ω ω β ω > ω : RH - range frequency (MHz ω β ω ω ω ω ω ωω ω < ω : LH - range + z prop. z prop. (energy (energy β
10 Microstrip LH Forward Coupler Conventional (RH forward coupler isolated coupled 4 3 input through coupling p e p λ ω g Requires long coupling length Requires very small gap What happens if coupled lines are LH? e.g. LH coupling p e p LH λ ω g Photograph of the microstrip LH forward coupler prototype isolated coupled 4 3 input through
11 Circuit Description of the LH Coupler C u Cu LE-circuit model Lu Cmu Lu C u Cu Lu C mu Lu C u Cu Lu Cmu Lu even-mode equivalent magnetic wall + + odd-mode equivalent electric wall + - C mu C mu / / ω L / ucu jωcu [ ABCD] Γ ue jωl ( S e e + T ( S e [ ABCD] Γ e uo Ae + Be / Z CeZ Ae + Be / Z + CeZ Ae + Be / Z + CeZ ω Lu (Cmu + C ω LuCu ( ω LuCmu / u u jωl Ao + Bo / Z CoZ Ao + Bo / Z + CoZ Ao + Bo / Z + CoZ De De + De ( S o o + T ( S o o u / jωcu Do Do + Do { S-parameters transmission matri for corresponding Γe, o and Τe, o 3 S Γe + Γo, S Te + To, S3 Te To, S4 [ ABCD] [ ] N TOT ; e, o ABCD u; e o N cells :, Γ e Γ o
12 S-Parameters (db Simulation/Measurement Results for the Coupler f c Magnitude, LE-ckt model appro. f min f 3 db S S S S3 S4 S Frequency (MHz f p 85mm ' C.33pF m ' L.59nH m N Cu.3 pf Lu 4.4nH C.9 pf mu f c appro. f min Phase, LE-ckt model S 3 S ( ω ( ω λ β π β ω g p p λ ω f Frequency (GHz e S-parameters (db f c Measured S and S 3 S Measurement S3 Measurement Frequency (GHz f 3dB f RT/Duroid 588 ε r., h.57mm N 7 5GHz Cu.6 pf 5GHz Lu 4.6nH ' C.33pF m ' L.59nH m Characteristics: shorter coupling length too lossy highly dispersive difficult to design LH Forward Coupler Conventional Coupler Conventional coupler S (mm... P (mm
13 Retrodirective Array: An Active Meta-Surface source Macroscopic Effect source Microscopic Mechanism: phase conjugation (RF E C f RF diff. f IF f RF θ i, θ r ( RF inc. E E ( RF i E Ci f LO f RF i th element meta-surface phased array-antenna Working principle incident : E i antenna - induced : 3 local oscillator : Vi ( IF j 4 miing : I e Ci 5 PC field : E ( RF Ci ( ( ( ( j ωt ϕ r i A r i e, whereϕ i i + i ( i k r ϕi r (RF j( ωt ϕ V A r i e i (LO ωt Ce j e 6 array re - radiated field : j ωt ( f f ( ωt ϕ j( ωt+ ϕ e LO ( ( j( ωt+ ϕ r i A r i e ( RF ( ( E C r E Ci r i i i i i i i RF : wave fronts (sameω & w.f.; opposite direction
14 Equivalent Surface Impedance Z s Surface Impedance Determination H i E i k r k i E r H r z θ y Surface Characteristics Z s Basic Equations jk jk z z jk Ey E e e + Γe e (incident E jk jkz z jk H e e Γe e η (incident Ey e Z s η sec θ H e z Z s (,θ (reflected jk jk jk (reflected jk ( jk jk z z z z cos + Γe Γe ( θ Z s (, θ; Γ η sec( θ cot[ k sin( θ ] anisotropy inhomogeneity ( k k sin( θ λ 3
15 Schematic of the Phase Conjugator (one element antenna IF out RF in (gates θ Modulated IF (6. GHz RF (5.99 GHz ϑ LO + π θ θ + π θ θ θ + π θ +π/ at RF +π at LO θ π θ π FET miers LO (drains ( GHz (+Modulation Characteristics: θ ϑ LO Active ckt Conversion Gain: brighter than metal θ Modulation possible (LO transmission of information RF / IF share one port compactness Self-phasing, omni-directional
16 A 4-Elements Retrodirective Array: Results Prototype Monostatic RCS Monostatic RCS (db rel Measured Theory Azimuth (deg. Bistatic RCS Bistatic RCS (db rel Source at broadside Measured Theory Bistatic RCS (db rel Source at -3 deg. Measured Theory Bistatic RCS (db rel Source at 45 deg. Measured Theory Scattering angle (deg. Source at broadside Scatter angle (deg. Source at Scatter angle (deg. Source at 45
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