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

SLIDE 1

• S. Arslanagić and A. B. Yakovlev

Department of Electrical Engineering Electromagnetic Systems Technical University of Denmark Center for Applied Electromagnetic Systems Research (CAESR) Department of Electrical Engineering, University of Mississippi

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 1 2

SLIDE 2

2

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

SLIDE 3

3

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]

SLIDE 4

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Configurations

       D w c D j Zs 2 csc ln 2   

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)

SLIDE 5

5

e

I

1



z

y

x ) , (

s s 



, , ,    k

c c c c

k    , , , ) cos( ) ( 4 ˆ

1 1 1 1

    n k J C I z E

n n n n e s



 

  

) cos( ) ( 4 ˆ

) 2 ( 2 2

    n k H C I z E

n n n n e s



 

 

E j H

i

       1

1 1

| ) ( |

2 1      

 

i z s z s z

E E E

] [

1 1 1

| | ) (

1 2 1            

  

s i s s s z

H H H Z E

          ) ( ) ( ) ( ) ( ) (

1 )' 2 ( 1 1 1 1 1 ' 1 1 ) 2 ( 1 1 1

         k H Z jk k J k J Z jk k H k J M

n s n n s n n n

n n n

M C  

 



1

                 ) ( ) ( ) ( ) (

) 2 ( 1 ' ) 2 ( 1 2 1 s n n s s n n n n n

k H k J Z jk k H k J      

|) | ( 4 ˆ

) 2 ( j s e j i

k H I z E         

BCs & orthogonality relations Fields:

Reference configuration

            

 

    ) 2 ( ) 2 ( ) 2 (

, )) ( cos( ) ( ) ( , )) ( cos( ) ( ) ( |) | (

n s s s n s s n n s n s s s n s n n s s

n k H k J n k H k J ρ ρ k H                

      , 2 , 1 n n

n

 Reference configuration was also treated in HFSS!

SLIDE 6

6

Reference configuration

  9 . 48 j Z s

1



z

y

x

s



, , ,    k

010

     

c c

Initial (analytical) results [cf. [1]]:

10 /

1

   MHz 300

0 

f MHz 1

0 

 16 /   D 200 /   w m) 1 . ( m) 0625 . ( m) 005 . (

HFSS model:

m 99471839 . ) 2 /( 10

1

    D m 0625 .  D m 005 .  w  f

304 MHz

  6 . 49 j Z s

Re(Ez) [V/m] - HFSS Re(Ez) [V/m] – Analytical (with HFSS model data)

x [m] x [m]

Cloaking observed! Cloaking observed!

m 2 . 

s

 m 2 . 

s



SLIDE 7

7

Initial (analytical) results [cf., [1]]: Re(Ez) [V/m] ; No cylinder Bare cylinder Cloaked cylinder Analytical vs. HFSS ;

m 2 . 

s

 MHz 304

0 

f

Excellent correspondence between analytical and HFSS results – models are verified! From now on, only HFSS results are shown!

x [m] x [m] x [m]

Reference configuration

1



z

y

x

s



, , ,    k

010

     

c c

10 /

1

   MHz 300

0 

f MHz 1

0 

 16 /   D 200 /   w m) 1 . ( m) 0625 . ( m) 005 . (

HFSS model:

m 99471839 . ) 2 /( 10

1

    D m 0625 .  D m 005 .  w  f

304 MHz

  6 . 49 j Z s   9 . 48 j Zs

SLIDE 8

8

m 2 . 

s



MHz 304

0 

f

Poynting vector [W/m2]

HFSS results – field overlay plots:

Cloaking not just along the x-axis, but many observation points outside the cylinder!

m 4 x y m 4

Origin

Pradiated [W/m] XXX.XX Pradiated [W/m] = XXX.XX Pradiated [W/m] = XXX.XX

Re(Ez) [V/m]

m 4

Free space No cloak Cloak

Reference configuration

Alex, comment to you 

SLIDE 9

9

m 5 . 

s



MHz 304

0 

f m 4 m 4

Origin Re(Ez) [V/m] Free space No cloak Cloak

Larger distance!

Reference configuration

y [m]

Re(Ez) [V/m] HFSS

Poynting vector [W/m2]

m 4

Pradiated [W/m] = XXX.XX Pradiated [W/m] = XXX.XX Pradiated [W/m] = XXX.XX

Cloaking not just along the y-axis, but many observation points outside the cylinder!

x y

SLIDE 10

10

Column configurations I

|Ez| [V/m] 5 3 2 1

m 2 . 

s



MHz 304

0 

f m 4 m 4 m 4 x x y

Scattering supression / cloaking in evidence when observing the absolute value of the field!

SLIDE 11

11

m 4

Re(Ez) [V/m]

m 4 m 4

m 2 . 

s



MHz 304

0 

f

Free space →

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: 5 3 2 1

x y x

Line 1: x=0, as a function of y. Line 2: y=0, as a function of x. Line 3: Diagonal Line 1 Line 2 Line 3

Column configurations II

SLIDE 12

12

Re(Ez) [V/m]

m 2 . 

s



MHz 304

0 

f

5-cylinders 3-cylinders 2-cylinders Line 1 Line 2 Line 3 Scattering supression/cloaking in evidence in all cases – but slightly direction dependent!

Column configurations III

Alex, comment to you 

SLIDE 13

13

m 5 . 

s



MHz 304

0 

f m 4 m 4 m 4

Free space →

Re(Ez) [V/m] 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! 5 3 2 1

x x y

Column configurations IV

SLIDE 14

14

|Ez| [V/m] 5 3 2 1

m 5 . 

s



MHz 304

0 

f m 4 m 4 m 4 x x y

Scattering supression / cloaking in evidence!

Column configurations V

SLIDE 15

15

m 4 x

Re(Ez) [V/m]

m 2 . 

s



MHz 304

0 

f m 4 m 4 x y

2 by 3 cylinders 3 by 3 cylinders

Free space →

Slab-like configurations I

Line 1 Line 2 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.

SLIDE 16

16

Slab-like configurations II

Re(Ez) [V/m]

m 2 . 

s



MHz 304

0 

f

2 by 3 cylinders 3 by 3 cylinders Line 1

x=0

Line 2

y=0

Alex, comment to you  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 cylinders” case approached the ”no cylinders case” – this is quite remarkable!

SLIDE 17

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Electrically large structures – Metasurface cloak impregnation

Illustrating the concept and final purpose – ongoing and future work! Results obtained for 28-cylinder case! Collection of electrically small (ES) dielectric cylinders Equiavalent electrically large (EL) dielectric slab Model an EL slab by collection of tiny ES cylinders. Equiavalence must first be established! If the collection of cylinders can be cloaked by meta-surfaces on each of them, then the EL slab should be cloaked by retaining the meta-surface cloaks as shown in the figure. Meta-surface

SLIDE 18

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Summary and conclusions

• This will come when I get back – I worked too much now to make sound and clear conclusions 

SLIDE 19

19

Additional results I – Configuration I

m 2 . 

s



MHz 304

0 

f

Analytical results (HFSS results on p. 8)

• I have them, but they are not needed, I suppose. Note, I did not make any normalization when

comapring HFSS results with Matlab, they fitted right on the spot from the very beginning.

• If you look at colour plots they will differ because the colorbars are simply using different span of

colors to represent same field values (and I say this even when dynamic ranges in HFSS and Matlab are identical!). This is why I would not show the analytical color figures – the verification done in terms of cuts should be sufficient for the present purposes.

SLIDE 20

20

Additional results II – Configuration I

m 5 . 

s



MHz 304

0 

f

Analytical results (HFSS results on p. 9)

• I have them, but they are not needed, I suppose. Note, I did not make any normalization when

comapring HFSS results with Matlab, they fitted right on the spot from the very beginning.

• If you look at colour plots they will differ because the colorbars are simply using different span of

colors to represent same field values (and I say this even when dynamic ranges in HFSS and Matlab are identical!). This is why I would not show the analytical color figures – the verification done in terms of cuts should be sufficient for the present purposes.