Arbitrary Patterning Techniques for Anisotropic Surfaces, and Line Waves

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1 Arbitrary Patterning Techniques for Anisotropic Surfaces, and Line Waves Dan Sievenpiper, Jiyeon Lee, and Dia a Bisharat January 11,

2 Outline Arbitrary Anisotropic Surface Patterning Surface wave propagation and control Radiation and polarization control Scattering control Progress this year: Developed verification method for impedance tensor of complex cell patterns Demonstrated functions that are difficult or impossible with other methods Nearly completed method for generating starting function Line waves New kind of waveguide with field singularity Topological photonic insulator Reconfigurable THz or photonic circuits Progress this year: Conceived of entire concept and determined TPI properties Demonstrated in simulation and verified in experiments Developed concept of reconfigurable THz circuits in graphene 2

3 Example Applications of Anisotropic Impedance Surfaces Guiding and Scattering Anisotropic waveguides can be non-scattering for other directions Boundaries between regions can control wave propagation and scattering 3

4 What Problem Are We Trying to Solve? (Mathematical Approach to RF Snakeskin ) Problem Solution Anisotropic impedance surfaces provide significant advantages to propagation and scattering problems, but they are not easy to make into arbitrary patterns. Develop verifiable approach to generating arbitrary anisotropic surfaces that can perform valuable RF functions 4

5 Point Shifting and Voronoi Cell Generation Method f = 5x 20 Sin[.5 x + y ; 5 10Cos[0.5x + y, 20Cos[0.5x + y Starting function Gradient Point grid (529 points) Voronoi cell generation Unit cell pattern after Voronoi function is applied to the point grid Produces smoothly varying cells with various sizes and orientations Previously demonstrated planar lenses, beam shifting patterns 5

6 Examples of Range of Capabilities Varying Shape Varying Size Varying Direction Extreme and Arbitrary Anisotropy Can make cells that vary in size, shape, and orientation Enables functions that would be difficult to produce by other methods 6

7 How to Characterize the Impedance of Non-Symmetric Anisotropic Cells Z xx Z yx Z xy Z yy How to calculate impedance tensor? The unit cells created by point shifting method are highly asymmetric, and cannot be analyzed by eigenmode simulations Developing a technique to accurately estimate impedance tensor for arbitrary complex cell shapes 7

8 Moment of Inertia Method to Extract Equivalent Rectangular Cell θ Moment of Inertia I (Polygon) = Eigenvalue = 5.33, 0.33 Eigenvectors = (-0.707, 0.707), (-0.707, ) I x = I y = Moment of Inertia (Rectangle) b/2 b/2 b/2 b/2 h/2 h/2 h/2 h/2 y 2 dydx = bh3 12 = 5.33 x 2 dydx = b3 h 12 = 0.33 Rotation Matrix = Cos θ Sin θ θ = Eigenvectors angle Sin θ Cos θ h = 4 (Length) b = 1 (Width) Procedure of calculating an equivalent rectangle of the polygon 8

9 Examples of Unit Cells and Equivalent Rectangles, with Impedance Estimate Polygon cells appear to have same impedance as their moment of inertia extracted equivalent Method is most accurate when gaps are small compared to cell size. 9

10 Applying Impedance Extraction Method to Large Complex Pattern Move the cell to zero point to calculate inertia moment Z frequency Z yy Propagating length Impedance Transverse length Z equivalent rectangle = z xx 0 0 z yy Find an equivalent rectangle and get its impedance from the simulated impedance plot θ Z Polygon = R T Z er R = z xx z xy z yx z yy Applying Jacobian rotation on the Z equivalent rectangle 10

11 Impedance Boundary Simulation with Extracted Impedance Set (1) 5.3 GHz 7.5 GHz PEC patches Impedance Boundary patches 11

12 Impedance Boundary Simulation with Extracted Impedance Set (2) PEC patches Impedance Boundary patches Verifying extracted impedance of polygon cells with impedance boundary simulations Field plots are matched with the result of PEC pattern 12

13 90 Degree Curve Pattern Example Near field plot of the surface waves scanned over a mm area The 35mm wide flat wavefronts excited by the feed smoothly move from the bottom edge to the left side edge of the panel 13

14 Inverse Gradient Procedure Tensor matrix Starting function F = F(x, y) F = [ F x,y x, F(x,y) y ] ( F) = x 2 y x x y y x 2 0.5xy y x 0.5y 0.5x + 0.5y F = x 2 dx + x y 0. 25x xy dx dx + x 2 dx x x y -0. 5y dy y x dy + y 2 dy dy 0. 25y xy y x -0. 5x dx + y y dy Take integral of tensor matrix terms and sum up the results (Z xx + Z xy, Z yx + Z yy ) Terms with x and y sometimes have overlapping results, take only one of them 14

15 Inverse Gradient with Starting Function Example Starting function 3y 2 + xy + 50y + x y 2 + xy y x + 6y + 50 y x + 6y 1 Tensor matrix F = x 2 dx + y x xy dy + 3y 2 + xy x y dx dx + y 2 dy dy x 2 dx + y x x y 0 y dx + y 2 x 6y dy dy Constants or 1 st order terms are not restored 15

16 Inverse Gradient with Starting Function Example F = 1 + y x + 6y + 50 F = 3y 2 + xy + 50y + x + 44 F = 3y 2 + xy F = y x + 6y Patterns are same, constants and 1 st order terms in the starting function only affect the location of the pattern i.e. a static offset 16

17 Tensor Matrix in Point Shifting Method Starting function F = [ F x,y F(x,y) F = F(x, y), ] ( F) = x y Tensor matrix x 2 y x x y y 2 F = 0.5 ( x 2 + y 2 )2 F = [0.707 x 2 + y 2, x 2 + y 2 ( F) = Scale factor ( F) = Z x, y Z o = α tensor matrix Actual impedance of the cell Average impedance 17

18 Tensor function pattern ( F)= 0.06x y 2 F = 0.005x y 4 Y X 18

19 Inverse Gradient Example Planar Lungburg lens function = 1000 e 0.2(x2 +y 2 ) 0.9 Starting Function (previously a guess) Used to Generate Cell Patterns Impedance Tensor Representing Cell Patterns (Verified in Simulations and Experiments) e 0.2(x2 +y 2 ) 0.9 Method Produces Correct Starting Function 19

20 Dan Sievenpiper - UCSD, ,dsievenpiper@eng.ucsd.edu Inverse Gradient of Tensor Matrix Smooth Twist <Tensor matrix plot> Cos x/2 + 1 Cos x + 1 Cos x + 1 Cos y/2 + 1 Cos x y Sin x 2 Cos x + 1 Cos x + 1 Cos y/ Still Working on This Issue x + y y Cos x + 2 Sin y 2 x + y Sin x 2 Sin y 2 1 x 2 y2 + xy Cos x 2 +4 Cos y y Sin x 2 Starting function 20

21 Example from Northrop Grumman Smooth Transition Between Two Impedance Surfaces Received small grant from Northrop Grumman last year to design this pattern

22 Line Waves at Impedance Boundaries (A New Kind of Topological Photonic/RF Waveguide with a Field Singularity) Inductive Sheet Capacitive Sheet We can create a line wave at the boundary between two impedance sheets Analogous to surface waves (but one-dimensional instead of two-dimensional) Possibly the smallest waveguide that can be created Contains a field singularity at the center, where nonlinearities can be significant Photonic topological state, so orthogonal modes travel in opposite directions 22

23 Examples of Useful Structures Implemented with Line Waves Route Around Curves Magic T Ring Resonator Coupler Phase Shifter Graphene sheets on layered substrate Can build many of the same structures using line waves as in conventional waveguide, microstrip lines, or in micro-scale photonics applications Can make them electronically reconfigurable on graphene 23

24 Very Low Reflection Even From a Hard Discontinuity, Illustrating Topological State R=377 Field rotates in region above line z=16 z=16 S11 = -10db to -27dB Different propagating directions have opposite polarization Very low scattering from one direction to reverse direction Line waves appear to be EM equivalent to topological insulators Can potentially be used to couple into electronic edge states 24

25 Implementation on Capacitive and Inductive FSS Sheets Lattice of discrete metal plates form capacitive side (TE guiding) Inverse (wire grid) structure forms inductive side (TM guiding) Line wave exists at the interface between two frequency selective surfaces Singularity likely limited by the discrete nature of the grids 25

26 Broad Bandwidth Operation (Measured Data!) Inductive Capacitive Measured data shows that line waveguide operates over about 2 octaves Only limited by the metal pattern used to implement the surface impedance 26

27 Electronically Reconfigurable Topological THz States in Graphene Graphene has impedance that can be electronically tuned from inductive to capacitive depending on the applied voltage bias Greatest tunability in the THz range, where building complex circuits and devices is also difficult Can create reconfigurable waveguides by defining a pattern of voltages

28 Other Related Programs: Nonlinear and Active Metasurfaces (NSF) Add non-foster circuits (negative capacitors and inductors) to passive surface Make phase velocity (and index and impedance) constant over frequency Potential to reach UHF range with practical thickness and cell size 28

29 Other Related Programs: Nonlinear Surfaces for Counter-DEW (ONR) Adding nonlinear circuit elements creates new capabilities in absorbers Demonstrated nonlinear absorption, and waveform dependent absorption Working on nonlinear self-tuning surfaces for frequency agile threats 29

30 Metasurface Enhanced Photoemission (DARPA) Current is controlled by combination of electrical and optical input signals Current Density = 250A/cm 2 Surface Enhanced Raman Scattering (SERS) uses random cavities in rough metal surfaces to create large nonlinear effects by concentrating the optical field Our idea is to engineer the surface to create specific cavity resonances that will enhance the field of an incoming laser beam to perform useful functions 30

31 Theoretical Analysis Suggests Unexpected Levels of Field Enhancement Thermionic Emission Photovoltaic Effect Field Effect Photoemission Combined Field Effect And Photoemission Theory Theory explains photoemission levels only with extreme enhancement: 1800X Possibly due to field extending into the metal, and/or pondermotive forces 31