Super Imaging With a Plasmonic Metamaterial:Super Imaging With a Plasmonic Metamaterial: Role of Aperture ShapeRole of Aperture Shape

Shiyi Xiao, Qiong He, Xueqing Huang, Lei Zhou*

Physics Department, Fudan University, Shanghai, 200433, China

I. Motivations:

Holy metallic plates with different aperture-shape were recently suggested to realize subwavelength imaging.

[1]S. Xiao, et al., Metamaterials (2011) doi:10.1016/j.metmat.2011.03.005

PROBLEMS !

• The role played by the aperture shape is not elucidated.

• Structure is anisotropic.

II. Theoretical Analysis of the Aperture Shape’s Role

( cos sin )0 0

2

2TE 2 TM 2

20

( , , ) 8

( ) cos ( )sin

ik x y

yz

z

i P eE x y d

k

kT k T k k dk d

k

Suppose a source: 0( , ) ( ) i tJ r t yP r e

The E-field of image plane is found explicitly as:

TE ( )T kPTM ( )T kPand are the transfer functions

TE, TM ( ) 1T k P

Fig. 1 super imaging

the image plane is identical to

the source plane

02 2 2

0 0

4( )

z

z

iq hTE TMTE TM hole

xiq hTE TM TE TM

hole hole

Y Y eT k

Y Y Y Y e

,,

, ,

For HMP:

20 0hole zY q S /Here,

2 20 1 /z h cq k

is the admittance

Wave vector

0S a d / is the overlapping integral.

(Structure is deep sub-wavelength)

c When , (cut off mode)0z cq ( )

, 20( ) 1/ / 4 2 / 1 ( )TE TM

x zT k S h i O q

0 1S TE, TM ( ) 1T k P

I

II c d

III. Numerical verification To Identify the Conditions

Fig.3 (a) High Trans. freq. and (b) the phase changes for square-aperture HMPs with different a/d.

(Fixing cut off Freq.)

Only a/d→0

1. High Trans. occurs at the cut off Freq.

2. Phase change is zero

V. Conclusions:In short, we found two analytical conditions for such systems to work as super lenses. We employed FDTD simulations to study the imaging functionalities of two types of super lenses, and found that the aperture shape plays a crucial role in achieving the super imaging effect.

Fig.4 E-field image patterns of square-aperture HMPs with different values of a/d: (a) a/d =0.9,(b) a/d =0.5,(c) a/d =0.3 and (d) a/d =0.1.

IV. Isotropic Fractal-like HMP Super-lens

Fig.8. FDTD calculated E-field pattern on the image plane of a 5-mm thick fractal-aperture HMP,

J. Jung , et al., Phys. Rev. B 79,153407 (2009).

X. Huang, et al., Opt. Express 18, 10377 (2010).

Fig.2 square aperture with different thickness

Two analytical conditions:

Eq. (1)

0S

High Trans. Freq.

=0.9

Unfixed

TE, TM ( ) 1T k P

Smaller S0

Better Cut-off mode

BetterImage

Fig.6 square aperture with different thickness

0S

High Trans. Freq.

=0.2

Fixed

The Better ImageThe Better Image

GOODResolution

Fig. 7. Amplitude (squares) and phase (dashed line) of the transfer functions

TE, TM ( ) 1T k P

Fig. 5 S0 of the fractal aperture