How To Understand The Physics Of Metasurfing

Transcription

1 ASI, ROMA, 4 Novembre, 13 Acknowledgements A Toccafondi (Associate Professor) M. Albani (Assistant Professor) Modulated Metasurface Antennas S. Maci Dept. Information Engineering and Math Science, University of Siena, Via Roma 6, 31 Siena, Italy macis.dii.unisi.it Post Doc E. Martini A. Vallecchi M. Casaletti (now in UR1, Rennes) F. Caminita G. Carluccio C. Della Giovampaola (now UPenn) A Mainghi (with UNIFI) S. Skokic (host from UNIZAG) M. Bosiljevac (host from UNIZAG) M. Violetti PhD students G. Minatti (now in ESTEC) G. Sardi F. Pugelli M. Balasubramnian (now in Fraunhofer) M. Faeni V. Soio M. Mencagli Technician D. Rossi Metasurfing Summary Variable Metasurface j ( ρ) 1 BoundedWave Metasurfing Introduction and numerical issues Isotropic Metasurfaces Anisotropic Metasurfaces Transformation Optics for Metasurfaces ρ 1 k t ρ metasurface reactance (lossless) ρ 1 k t ρ addressing Surface or Guided waves Metasurfing Possible transition to LeakyWaves Unboundedwave Metasurfing Spiral LW antennas Anisotropic Metasurfaces and Polarisation control Circularly Polaried Isoflux Antenna Dual frequency Conclusions

2 UNIFORM Isotropic Reactance Propagation of SW and Guided modes TM Surface waves (SW) k x k (phase velocity less than speed of light). x 19 How to realie a variable metasurface? E E x j x f (GH) 3. = =4 =9 Rectangular patches with variable sies H y k d ( ) E jx ˆ H t s t k t k t k X S () 1 X L k k t k X S,k t Implicit formula 1 Circular patches with variable sies isotropic E t (k t,) Z S (k t,,) ẑ H t (k t,) Z S (k t,,) jx S (k t,,) anisotropic E t (k t,) Z s(k t,) ẑ H t (k t,) T* Z s(k t,) Z s (k t,) Inductive impedance support propagation of TM SW with ero cut off frequency 1Small sies of the elements in terms of the wavelength (pixellike approach) Gradual variation of a geometry (local periodicity) Reflectarray Vs Metasurfing antenna Reflectarrays Synthesis of the metasurface Local periodicity. The texture and the relevant reactance are locally indentified with those of a periodic structure that locally matches the geometry (smooth, gradual variation) Inhomogeneous Metasurfaces local periodicity Elements small in terms of a wavelegnths Resonant elements Use of periodic Green s Function. The local periodic problem can be analyed very easy by a periodic MoM. The number of unknown are those of a single cell.

3 Patch on a grounded slab (effect of variation of the capacitance) Modulated Surface Reactance (MSR) Evanescent SW mode capacitance X ( k, x, ) S t k Patches (capacitive below resonance) Ground plane k x. x 19 k 4. f (GH) = =4 =9 Almost independent of the wavenumber direction k d ( ) Modulated Surface Reactance (MSR) Implementation of the anysotropic impedance k X ( k, x, ) S t x k a ' a a a a H E k H E k a a

4 Anysotropic elements local periodicity Design of anisotropic b.c. f (GH). x = =4 3 = k d ( ) f (GH). x Eigenvaues k t = =4 = k d ( ) Z s E t Z s ẑ H t E t Z s J t jx jx jx jx Z s E t Z s ẑ H t E t Z s J t jx jx jx jx Z s E t Z s ẑ H t E t Z s J t jx jx jx jx

5 Multiscale analysis Multiscale problem Isoflux antenna for space (ESA Project) 8. GH Antenna diameter: 4 cm Period of impedance modulation: cm Patches average diameters: 4 mm Slots:,4 mm Intel Xeon 3.7GH, X64, 96 GB RAM Parallel code (8 threads) 1) Macroscale: Antenna dimension (1 Computational Models: ) Homogeneied Impedance Variation: 3) Patch scale: /1 3) Microscale (Slot widths and rwg basis function): /1 Use of sheet impedance MoM for macroscale Use of local periodic MoM for implementing the impedance For microscale: analytical functions or aggregation of RWG in MoM analysis (in addition to all acceleration techniques like adaptive Integral methods) Luneburg law for the refractive index Luneburg lens n R radial coordinate lens radius Substrate parameters: r = 1. d =.7 mm R = 7.6 mm 11. GH 1. GH 1. GH 13. GH 13. GH 14. GH

6 Bandwidth 11. GH 1. GH 1. GH 13. GH 13. GH 14. GH n ( ) [ ( ) ] eq ρ R 1/ Maxwell s fish-eye lens: simulation with ADF SCHWARZCHRISTOFFEL w f ( ) dw F, ; ; n ( ) [1 ( ) ] eq ρ R 1/

7 w f ( ) dw F, ; ; Applications Hplane Horn antenna Compact Meta-Horn Horn parameters: flare angle Waveguide height 1.8 mm Design frequency 13 GH Results obtained in a parallel plate waveguide (no transition to free space): 4 flare angle Conventional H-plane horn 1. GH 13 GH 13. GH (13 GH) vertical E field inside the horn Results from MarkoBosiljevac

8 Summary 1 BoundedWave Metasurfing Introduction and numerical issues Isotropic Metasurfaces Anisotropic Metasurfaces Transformation Optics for Metasurfaces Chessboard surfaces Leakywave effect X (, ) S x AVERAGE Unboundedwave Metasurfing Spiral LW antennas Anisotropic Metasurfaces and Polarisation control Circularly Polaried Isoflux Antenna Dual frequency Conclusions k n sw d n Forward/Backward Beam n=1 beam direction: sw d ksin sw sw 1 / L p 1. GH L 16 GH d h = 1. mm L = 177 mm (1(@ 17GH) p= 4.1 mm 16. GH Backward beam d sw sw d sin 1 Forward beam d sw 17 GH 17. GH

9 1. GH 16 GH h = 1. mm L = 177 mm (1(@ 17GH) p= 4.1 mm 16. GH 17 GH Corner reflector 17. GH Probe 1 Probe BACKWARD BROADSIDE FORWARD

10 Doppler radioguide Local interaction by D planewave d (1 M) Forward1 (17. GH) CP BROADSIDE (18.7 GH) BACKWARD 1 ( GH) (1 M) (,) 1 Msin d - X( s ) d Leaky Wave radiation Circular polariation at broadside d (1 M) (1 M) (,) 1 Msin d - d If we chose sw SW as the propagation constant of the TMSW on the average impedance The period of the modulation along each ray is almost equal to λ sw (SW wavelength in the unperturbed medium) 1 LW sw sw k sw sw 4 sw (,) 1 Msin L - Two rays separated by 9 intercept a spiral line (ρ,φ)=constant at distances from the origin that differ each other of λ sw /4. Any elemental sector separated by 9 gives rise to orthogonal quadraturephased components to provide the circular polariation

11 Printed patch metasurface antenna Local impedance variation: patch dimension are changed, being the period constant. Pixel-like approach: patch sies are very small w.r.t. the wavelength Thickness: 1.4 mm Mass:. Kg 1 cm (.7 λ) 1.6 mm 3.9 mm.1mm Maximum Gain meas. comparisons 1.1mm sw X 6% s m.48 f 17GH Max Gain,(dB) Frequency [GH]

12 Prototype Experimental Results Reducing cross-polar components Anisotropic Impedance Pattern Reducing cross-polar components

13 Complemetary structure (Slots) w p Slot Vs. Patches (8.4 GH, cm radius, 7 wavelength radius) UpDown link operations (Slots) (8.4/7.16 GH) 3 3 Slot Comp. type Lhc Tx 8.4GH 3 1 Phi= 1 1 Patch type Phi= Th t (d ) Thickness: 1. mm (Xband) Thickness: 1 m (Xband) Phi=

14 Phi=4 UpDown link operations (Slots) 8.4GH 3 Phi= 7.16 GH Rx Phi=4 1 1 y x Phi= Elliptic Spiral Surface Impedance Z jx m k x ' s 1 sin sw sin

15 Printed metasurface/elliptical strips Sector beam antenna for space application Aimuth-elevation mechanical steering Mechanical isoflux aimuthal scanning for higher gain The circular surface is considered as composed by elemental sectors. For each elemental sector, the impedance modulation is obtained from the conjugate-match of the source and target waves. Contributions from each elemental sector are combined to produce a peak of radiation toward the desired direction Sector beam metasurface antenna Numerical results Isoflux antenna Thickness: 1.7 mm Dielectric Constant: 9.8 (Arlon AR1) Metal thickness: 3 um Loss Tangent:.3 Diameter: 4 mm (7. 8.4GH) 7 cm 7.λ 161 patches Full-wave analysis: 3DAMxLAD ADF developed by IDS

16 Isoflux antenna design principle Circular polariation Anysotropic surface impedance Zs, j, ρ jx s 1M cos K M sin K φ printed metasurface dielectric ( r ) ground plane w p Feeding line e Roger 43C Thickness:.8 mm Dielectric Constant: 3.38 Metal thickness: 3 um Loss Tangent:.9 Panel Radius: 8x mm Antenna layer Feeding point Ground plane layer Feeding line layer

17 Experimental Results - S11-1 X: 8.6 Y: X: 8.8 Y: db - - X: 8. Y: -18. X: 8.31 Y: -4.6 X: 8.4 Y: X: 8. Y: X: 8.7 Y: [GH] The sie of the chamber is x x 4 m. It is fully lined with 18 absorbers (see. Fig.), and it is used between 7 MH and 4 GH. Experimental Results Conclusions 1 1 RHCP LHCP 9 8. GH EXP GH 6 SIM Deg Deg GH Deg GH Deg