Modulated metasurfaces antennas Design workflow issues

Modulated metasurfaces antennas Design workflow issues P. De Vita, M. Bercigli, M. Bandinelli Computational ElectroMagnetic Laboratory Ingegneria dei Sistemi, IDS s.p.a., Pisa, Italy all rights reserved 1

Rationale Rationale & Content The issues related to the design of antennas based on modulated metasurfacesare reviewed, and the currently applied workflow (developed by IDS, UNISI, UNIFI, POLITO and ESA) is described. In particular the attention is posed on the modelling tools and on the algorithms which are needed to support the designer. Further methodological developments to face more complex, tridimensional, conformal radiators are finally discussed. Content Formalization of the design problem (not focused on a particular class of metasurface based antennas) Design workflow relevant to a metasurface based leaky-wave antenna Next design challanges all rights reserved 2

Formalization of the design problem all rights reserved 3

The problem in brief The problem we are interest to is based on the following idea: Once defined the architecture of the radiating structure of interest (in terms of «geometry», «materials» and «excitation») it is possible to satisfy requirements in terms of radiating performance through the implementation of a proper punctual boundary condition on the whole or on part of the external surface of the structure. A possible view of interpreting such boundary condition is through the concept of Surface Impedance (*). The concept of modulated metasurfaces can be then applied to practically realize the required surface distribution. (*) Indeed, other different representations can be applied depending on the selected geometry of the radiating structure. This one has been demonstrated to be particularly convenient, also thanks to its generality. all rights reserved 4

Some examples. Similarities and differences Depending on the selected «architecture» and specially on the selected «excitation» different classes of radiating structures can be addressed: a) Direct radiating antennas b) Lenses c) Reflectors (a) (b) (c) Antenna port A. Grbic et al. Near-Field Plates: SubdiffractionFocusing with Patterned Surfaces all rights reserved 5

Some examples. Differences and similarities Each case in general involves different physical phenomena (leaky-wave, transmission, reflection...), which pose different problems to be managed at design procedure level, but anyway some main features are shared: A distribution (able to produce the desired radiation performance once the selected architecture is illuminated by the selected excitation) has to be preliminarily identified; Such must be practically implemented (e.g. through a modulated metasurface); The problem is sufficiently complicated to require accurate and computationally effective (the radiating structures are usually electrically large) modelling tools. all rights reserved 6

Design workflow relevant to a metasurfacebased leaky-wave antenna all rights reserved 7

Metasurface-based leaky wave antenna by surface reactance modulation Grounded dielectric slab Sinusoidal modulation of surface reactance (*) ( ρ ) = + cos( ρ ) X X mx K s s s K = 2π d TM 0 Surface wave Floquet Waves (FW) 2π kρn = κ + n, n Z d Leaky Wave Radiation by FW with n<0 (*) Oliner, A.; Hessel, A.;, "Guided waves on sinusoidally-modulated reactance surfaces, Antennas and Propagation, IRE Transactions on, vol.7, no.5, pp.201-208, December 1959. 8

Architectural decomposition of a leaky-wave antenna based on modulated metasurface The following basic elements compose this kind of antenna: A dielectric slabable to support a primary surface wave and an implementation of a modulated metasurface; An exciter(to generate the surface wave and, in some cases, also to provide a useful radiated field); An implementation of a modulated metasurface able to generate radiation in the form of leaky-wave. Dielectric slab Exciter Modulated metasurface implementation all rights reserved 9

Main logical electrical design steps A typical design procedure for this kind of radiating structures is composed of the following main steps: 1) Selection of the antenna architecture (geometry, materials, excitation type) and assessment of the requirements at pattern level; 2) Exciter design; 3) Synthesis of the distributionwhich, in the selected antenna architecture and when excited by the selected exciter, is able to provide the required pattern; 4) Selection of the metasurface technology synthesis of the initialmetasurface configurationable to implement 5) Numerical optimization of the metasurface configuration virtual prototyping No particular comments about pt. (1) and (2), which involve considerations and activities quite common for antenna designers (physical feasibility...). Indeed the typical steps for this kind of radiators are those mentioned at pt. (3)-(5). all rights reserved 10

Main logical electrical design steps (continue) (3) Synthesis of the distribution which, in the selected antenna architecture and when excited by the selected exciter, is able to provide the required pattern. Two procedures have been identified, namely: Holographic technique Numerical approach based on a Moment Method procedure The applicability/performance of each approach depends on the type of requirements at pattern level which are to be satisfied (shaping, complex values, power mask etc) (4) Synthesis of the initial metasurface configuration able to implement. In general it depends on the selected metasurface technology. In most cases it is based on the hypothesis of local periodicity. all rights reserved 11

Main logical electrical design steps (continue) (5) Numerical optimization of the metasurfaceconfiguration The initial metasurface configuration usually only roughly satisfy the requirements. It must be therefore optimized. This is as much true as the requirements are demanding (e.g. wide-band, shaped beam...). Given the complexity of the structures of interest this point poses strong requirements in terms of fast modelling capabilities (5) Virtual prototyping As already demonstrated on other antenna technologies, the idea is that accurate modelling methods can be applied in order to reduce the need of measurements only at the final verification step. Achievements towards this goal will obviously improve at the same the design capabilities all rights reserved 12

Metasurface elements parametric modelling (2) Design workflow Virtual prototyping (5) Pixels type (params) Surface geometry computation DB Five steps. Different tools. Final CAD model Full-wave validation SM-AIM, MR-MLFMA Initial layout synthesis (3) MOM-BOR Fast approx. modelling Metasurface initial layout Metasurface optimized layout Pattern Reqs. Fast full-wave modelling Numerical optimization Exciter design Selected antenna architecture synthesis layout synthesis (1) SM-AIM/SFX Global functions Metasurface antenna optimization (4) Input Design step Design data all rights reserved 13

Numerical tools in support to design In general the geometrical/physical architectures of this kind of radiators are quite complex. Further they usually are electrically large. Willing to reach optimal performance and to apply as much as possible the concept of virtual prototyping (to reduce cost/time of the design cycle, only performing measurements at a final verification step), suitable numerical tools are needed in support to design phase: Full-wave numerical models which are accurate, fast and reasonably lowdemanding in terms of computer memory; Optmization procedures (global and local search) Relevant efforts have been performed in collaboration with ESA, POLITO, UNIFI and UNISI in this sense: MoM-BOR (Body Of Revolution MoM) SM-AIM(Sparse Matrix Adaptive Integral Method) SM-AIM / SFX (SM-AIM / Synthetic Function expansion) MR-MLFMA(MultiResolution MultiLevel Fast Multipole Approach) ADF Antenna Design Framework all rights reserved 14

Project Management Data Logic (for professional users) Versioning Antenne a Metasuperfici Modulate PO/UTD Frjis PIM Ray Tracing diagnostic coupling Professional CAD Clean-up Multi format Workflow management G/T Plot on Earth Pattern integration P rad Huygens sources Mesh optimization Synthetic antenna models Pattern by formula CAD, Clean-up & meshing services Fast Prototyping tools ADF ADF Special functions for antenna engineers Tools dedicated to aperture synthesis Reaction Integral (Cmax) SWE Parametric synthesis Phase Centre 1D/2D Field/Power synthesis SWE Patterns Huygens sources Antenna e.m. models Import 3D general purpose modelling tools IDS Optimizer Dedicated modelling tools Array (from fast prototyping to optimization) 2.5D modelling tools (microstrips, EBG...) Horns modelling Full-wave methods Asymptotic methods Hybrid methods Global search Localsearch all rights reserved 15

Step 1: synthesis Holographic technique Source field (TM 0 Surface Wave) RequiredAntenna Pattern Projection on antenna surface Holographic Technique (Reaction Integral) Diffraction figure : all rights reserved 16

1 Vertical dipole Step 1: Exciter design 2 Sequentially rotated feeding system A B a b h h Study for a dual polarized antenna b a a all rights reserved 17

Step 2: Possible Metasurface Realizations Gradual smooth cell-by-cell variation of the geometrical parameters (local aperiodic elements). Constant basic cell of the texture. Sub-wavelength cell elements (pixel). To produce radiation by modulating the components of the main diagonal. Circular polarization by modulating the terms of the crossdiagonal with quadrature phase. ( K ) ( ) ( Kρ ) ηρρ = ηs + ηsmcos ρ η ρρ ηρ φ X = ζ ηρφ ηφρ ηsm'sin Kρ ηφ ρ η = = φφ η φφ = ηs ηsm cos Synthesis Functions all rights reserved 18

Step 2: Pixel Types parametric modelling Pixel type Full-wave cell model Periodic structure model Cell characteristic Cell behaviour mapping (numerical/ analytical) 19

Step 2: Pixel for Circular Polarization Screw-Head pixel: more suitable type in our application a/a primarily affects the co-diagonal terms ψ primarily affects the cross-diagonal terms Rotational Phase Excitation Ring Impedance Pattern ( K ) ( K ) ( K ) ηρρ = ηs + ηsmcos ρ η ρφ = ηφρ = ηsm'sin ρ η φφ = ηs ηsm cos ρ Linear Phase Excitation Spiral Impedance Pattern ( K ) ( K ) ( K ) ηρρ = ηs + ηsmcos ρ + φ η ρφ = ηφρ = ηsm'sin ρ + φ η φφ = ηs ηsm cos ρ + φ Minatti, G.; Maci, S.; De Vita, P.; Freni, A.; Sabbadini, M.; "A Circularly-Polarized Isoflux Antenna based on Anisotropic Metasurface", 20 Antennas and Propagation, IEEE Transactions on, vol.60, no.11, pp.4998,5009, Nov. 2012

Step 3: Initial antenna layout Antenne a Metasuperfici Modulate DB Printed Circuit Board (low-cost) Metalized Dielectric Substrate (low mass) MOM-BOR Antenna Design Framework (ADF) 3D Mesher 12061 array cells 774922 triangle elements 1.100.000 RWG Feeding Point 54cm 15λ all rights reserved 21

Step 4: Modelling for layout optimization Modelling Tool 3DAMxLAD@ADF SM-AIM / SFX Method Array Formed by Scaling and Rotating the Pixel Hybrid SM-AIM / SFX (Syntetic FunctioneXpansion) (1) Time = 7 min 1,1 millions basis functions RAM = 4 GB (dp) compatible to be used in an optimization loop ( 200 iterations/day) Intel XeonX5667 @ 3.07GHz, X64, 96 GB RAM Parallel code (8 threads) (1) IDS, UNIFI, POLITO, ESA all rights reserved 22

Accuracy(SMAIM.vs. SMAIM/SFX) (1) -40-45 -50-55 Far Field (db) -60-65 -70-75 -80-85 -90 Comp. Rhc SMAIM Comp. Lhc SMAIM Comp. Rhc HYBRID Comp. Lhc HYBRID -80-60 -40-20 0 20 40 60 80 Theta (degree) (1) SM-AIM has a high accuracy and can be used as reference all rights reserved 23

Step 5: Virtual prototyping Standard MoM not applicable Required modellingtool for multilayer structures Modelling Tool 3DAMxLAD@ADF Near Interactions by Integral SM-AIM Method Sparse Matrix - Adaptive Integral Method (1) Far Interactions by FFT2D Time = 2 h 40 min RAM = 18 GB (dp) Intel XeonX5667 @ 3.07GHz, X64, 96 GB RAM Parallel code (8 threads) (1) IDS, UNIFI, ESA 24

Some examples: X-Band Isoflux Demonstrator 12 Freq. 8.3 GHz RHCP exp LHCP exp LHCP sim RHCP sim 9 6 3 0-3 -6 Arlon AR1000 Thickness: 1.575 mm Dielectric Constant: 9.8 Metal thickness: 35 um Loss Tangent: 0.003 Panel Radius: 540 mm (7.5 λ@ 8.4GHz) -9-12 -15-18 -21-180 -150-120 -90-60 -30 0 30 60 90 120 150 180 Deg all rights reserved 25

Some examples: Sectorial Beam Antenna Mechanical/Thermal design/analysis ON GOING 27 cm 7.5λ @ 8.6GHz Optimization Required all rights reserved 26

Next design challenges all rights reserved 27

Next design challenges Next research area focuses on the application of metasurfaces on non-planar geometries. J. S. Colburn et al. D. Sievenpiper et al. D. J. Gregoire Q. I. Wu et al. Q. I. Wu et al. all rights reserved 28

Next design challenges The modelling methods based on 2.5 algorithms are no more applicable. More complex 3D algorithms are needed, which however must continue to satisfy the same important requirements: a) Mixed dielectric-metallic electrically large structures (tens of wavelength) b) Multi-scale problems (thin dielectric substrates; sub-wavelength shaped pixels; reactive coupling... in the frame of large structures) c) Fast computation, suitable to be used in the frame of optimization loops d) Accuracy compatible with virtual prototyping Further, methods to synthesize distribution on non-planar geometries are needed. all rights reserved 29

3D modelling The MLFMA(Multi-Level Fast Multipole Algorithm) code integrated in ADF (Antenna Design Framework has been recently updated with the PMCWHT Formulation (Poggio-Miller-etc) and IBC(Impedance Boundary Condition), in order to be able to manage mixed dielectric-metallic models. This code is able to satisfy pt.(a) (i.e. electrically very large structures). The basic algorithm has been further improved with MR(Multi-Resolution) algorithm(*) in order to also satisfy pt. (b)(i.e. able to effectively manage multiscale problems). MR-MLFMA has been proved to satisfy pt. (d). Reasearch activities are currently on going to also satisfy pt. (c), as done through the 2.5D methods SM- AIM/SFX. (*) POLITO all rights reserved 30

Synthesis of distribution on non-planar geometries A procedure is under investigation, which should allow, starting from pattern requirements, the synthesis of the distribution on selected parts of the antenna geometry.no matter the complexity of such geometry provided that a modelling tool like the MR-MLFMA based before mentioned is available. S o Required Antenna Pattern S A J e (or J m ) + = Antenna (geom., mat., excitation) on S o E o, H o J e (or J m ) Planar surface S o on which the objective pattern is projected E on SA+δ =F(J e ) (*) POLITO all rights reserved 31