Configurations These slides will be casted into a poster form here - PowerPoint PPT Presentation

Metasurface Cloaks for Large Cylindrical Cluster Configurations These slides will be casted into a poster form – here is just an overview of results that I would like to show. There are probably too many results/figures – I would rather go for fewer, thus making the poster clear. Let me know of you opinion. 1 2 S. Arslanagi ć and A. B. Yakovlev 1 Department of Electrical Engineering Electromagnetic Systems Technical University of Denmark 2 Center for Applied Electromagnetic Systems Research (CAESR) Department of Electrical Engineering, University of Mississippi

Outline • Background & motivation • Configuration(s) & numerical model - HFSS • Reference configuration – analytical/numerical treatment – verification of models • Column configurations • Slab-like configurations • Ultimate goal – cloaking of electrically large slabs with meta-surface cloak impregantion • Summary and conclusions 2

Background & motivation Electromagnetic invisibility by metamaterials: • the coordinate transformation method • the scattering cancellation method with a plasmonic coating, • anomalous localized resonance method, • transmission line/waveguide technique • the scattering cancellation method by a metasurface (mantle) cloak Alex – in the motivation I will mention the work of Alu with plasmonic cloaking of a single column of cylinders, and another reference of Bilotti that was introduced in our paper upon its revision. Then I will say that we want to do not only column of cylinders, but even larger configurations with the aim of investigating meta-surface potentials for large structure cloaking/scattering supression. If you have anything to add, please do so  [1] 3

Configurations     j D w    0 ln csc Z s    2 2 c D Alex, this figure will change – the new one will have the figure to the right, the mesh-grid surface, and a sketch of a full HFSS model (which will explain that the source is of a finite radius, and that symmetry planes are used on the top & bottom, as well as that PMLs are used to model infinite space) 4

  1 , 0 n     n  2 , 0 Reference configuration n             ( 2 )  J ( k ) H ( k ) cos( n ( )) , y    n n s n s s s s I    ( 2 ) ρ ρ  0 ( | |) n H k e  0 s s            ( 2 ) ( ) ( ) cos( ( )) , J k H k n  n n s s n s s s   s   ( , ) 0 n s z x  1 BCs & orthogonality relations   k     , , , , , , k 0 0 0 0 c c c c   s 1 s 2 i | ( ) | E E E       z z z 1 1    1 [ 2 1 ] s s i s ( ) | | E Z H H H Fields:          z s    1 1 1        I      ˆ ( 2 ) j 0 j   e 1 ( | |) E z H k C M i 0 0 s n n n 4          ( 2 ) ( ) ( ) J k H k       1 n 0 n 0 1 n 0 s     I          ˆ n e 1 ' ( 2 ) ( ) cos( )   ( ) ( ) E z C J k n  jk Z J k H k  2 n 0 0 1 0 1 s n 1 n n 1 s n n s 4  0 n        ( 2 ) ( ) ( ) J k H k  1 1 1 0 0 1  n n  M n        ' ( 2 )'    ( ) ( ) ( )   jk Z J k J k jk Z H k  I 1 s n 1 1 1 n 1 1 0 s n 0 1     ˆ 0 ( 2 ) e ( ) cos( ) E z C H k n 2 2 0 s n n n 4  0 n   Reference configuration was also treated 1     H E in HFSS!  j i 5

Reference configuration Initial (analytical) results [cf. [1]]:    0 10 0   0   300 MHz 1 MHz c f     s 1 0 c    (  / 10 0 . 1 m) 1 0   z 48 . 9 Z s j y   (  / 16 0 . 0625 m) D 0    , , , k   (  / 200 0 . 005 m) w 0 0 0 0 x 0  0 . 0625 m D        304 MHz 10 /( 2 ) 0 . 99471839 m 49 . 6 HFSS model: D f Z s j 1 0  w 0 . 005 m Re( E z ) [V/m] – Analytical (with HFSS model data) Re( E z ) [V/m] - HFSS     0 . 2 m 0 . 2 m s s x [m] x [m] Cloaking observed! Cloaking observed! 6

Reference configuration Initial (analytical) results [cf., [1]]:    0 10 0   0   300 MHz 1 MHz c f     s 1 0 c    (  / 10 0 . 1 m) 1 0   z 48 . 9 Z s j y   (  / 16 0 . 0625 m) D 0    , , , k   (  / 200 0 . 005 m) w 0 0 0 0 x 0  0 . 0625 m D        304 MHz 10 /( 2 ) 0 . 99471839 m 49 . 6 HFSS model: D f Z s j 1 0  w 0 . 005 m   Re( E z ) [V/m] ; 0  Analytical vs. HFSS ; 0 . 2 m 304 MHz f s No cylinder Bare cylinder Cloaked cylinder x [m] x [m] x [m] Excellent correspondence between analytical and HFSS results – models are verified! 7 From now on, only HFSS results are shown!

Reference configuration 0  HFSS results – field overlay plots:   304 MHz f 0 . 2 m s Origin Free space No cloak Cloak Re( E z ) [V/m] 4 m x 4 m y Poynting vector [W/m 2 ] Alex, comment to you  4 m P radiated [W/m] XXX .XX P radiated [W/m] = XXX.XX P radiated [W/m] = XXX.XX Cloaking not just along the x -axis, but many observation points outside the cylinder! 8

Reference configuration Larger distance! 0    304 MHz f 0 . 5 m s Origin Free space No cloak Cloak Re( E z ) [V/m] 4 m x 4 m y Poynting vector [W/m 2 ] Re( E z ) [V/m] HFSS P radiated [W/m] = XXX.XX 4 m P radiated [W/m] = XXX.XX P radiated [W/m] = XXX.XX y [m] Cloaking not just along the y -axis, but many observation points outside the cylinder! 9

Column configurations I 0    304 MHz | E z | [V/m] f 0 . 2 m s 5 3 2 1 4 m x 4 m x 4 m y Scattering supression / cloaking in evidence when observing the absolute value of the field ! 10

Free space → Column configurations II 0    304 MHz Re( E z ) [V/m] f 0 . 2 m s 5 3 2 1 4 m x 4 m Line 1 x 4 m y Line 2 Line 3 Scattering supression / cloaking in evidence when osberving the real part of the field ! Near-field cuts will be shown along the ” white lines” for 2-, 3-, and 5-cylinder configurations: 11 Line 3: Diagonal Line 1: x =0, as a function of y . Line 2: y =0, as a function of x .

Re( E z ) [V/m] 0  Column configurations III   304 MHz f 0 . 2 m s 5-cylinders 3-cylinders 2-cylinders Line 1 Alex, comment to you  Line 2 Line 3 Scattering supression/cloaking in evidence in all cases – but slightly direction dependent! 12

Free space → Column configurations IV 0    304 MHz Re( E z ) [V/m] f 0 . 5 m s 5 3 2 1 4 m x 4 m x 4 m y Scattering supression / cloaking in evidence! Direction dependence confined mostly to the parts of the y<0 half-space, while y>0 works better now! PS : Near-field cuts can be done when I get back! Otherwise, I will keep just what is shown here! 13

Column configurations V 0    304 MHz | E z | [V/m] f 0 . 5 m s 5 3 2 1 4 m x 4 m x 4 m y Scattering supression / cloaking in evidence! 14

Free space → Slab-like configurations I 0    304 MHz Re( E z ) [V/m] f 0 . 2 m s 2 by 3 cylinders 3 by 3 cylinders 4 m Line 1 x Line 2 4 m x 4 m y Near-field cuts will be shown along the ” white lines” for both of these configurations. Line 1: x =0, as a function of y . Line 2: y =0, as a function of x . 15

Re( E z ) [V/m] 0  Slab-like configurations II   304 MHz f 0 . 2 m s 2 by 3 cylinders 3 by 3 cylinders Line 1 x =0 Alex, comment to you  Line 2 y =0 Slightly better resutls along x-axis than y-axis – but scattering supression still present! Note: the field between the cylinders (and not just around them all) in the ” cloaked 16 cylinders” case approached the ” no cylinders case” – this is quite remarkable!