Yadong Xu & Huanyang Chen

Soochow University

15 Jan 2016

Loss problem

J. B. Pendry, Negative Refraction Makes a

Perfect Lens, Phys. Rev. Lett. 85, 3966 (2000).

D. R. Smith and D.

Schurig, Phys. Rev. Lett.

90, 077405 (2003).

1 0.001i

Conjugate metamaterials

0E i H

0H i E

' iE e E

' iH e H

( )' ie ( )' ie

2 ' 'n

1 ' ie ' ie

' ' 1

D. Dragoman, Optics Communications 284, 2095-2098 (2011). Y. Xu et al, arXiv:1510.08638

1

tan1 2

i

TE i

er i

e

22

sec1 2

ii

TE i

et e

e

cot1 2'1

i

TE i

er

e i

2csc2 2'

1

i

i

TE i

ee

te i

'z zk k 'z zk k

,TE TEr t

1

tan1 2

i

TE i

er i

e

22

sec1 2

ii

TE i

et e

e

cot1 2'1

i

TE i

er

e i

2csc2 2'

1

i

i

TE i

ee

te i

'z zk k 'z zk k

2

TEr i

1TEt i

2

'TEr i

' 1TEt i

2 2

22

1 1

1 1tan cot

2 21 1

i i

TE i iii

i i

e er

e ei e ie

e e

2 2

2 2 22 2 2

(1 ) (1 )

(1 ) (1 )sin cos

2 2

i i ii

TE i i ii

e e et e

e e ee

2

2 2 22 2 2

cos2 (1 ) 2

(1 ) (1 )cos sin

2 2

i

i i

p i i ii

ee e

ae e e

e

( )22 2

2

2 2 22 2 2

sin2 (1 ) 2

(1 ) (1 )cos sin

2 2

ii

i i i

n i i ii

e ee e e

ae e e

e

2 2

22

1 ( 1)

1 1tan cot

2 21 1

i i

TM i iii

i i

e i er

e eee

e e

2 2

2 2 22 2 2

(1 ) (1 )

(1 ) (1 )sin cos

2 2

i i ii

TM i i ii

e e et e

e e ee

2

2 2 22 2 2

cos2 (1 ) 2'

(1 ) (1 )cos sin

2 2

i

i i

p i i ii

ee e

ae e e

e

222

2 2 22 2 2

sin2 (1 ) 2'

(1 ) (1 )cos sin

2 2

ii

i i i

n i i ii

i e ee e e

ae e e

e

2 2 2

cos2

| cos sin |2 2

pi

A

e

2 2 2

sin2

| cos sin |2 2

ni

A

e

zk d 0, 1, 0p nA A

, 0, 1p nA A

1 1, ,

2 2 2p nA A

( )2 2

exp

exp2 cos sin2 2

s pT

d

( )2 2

exp( )

cos sin exp(2 )2 2

zs p

z

ik dT

ik d

zk i

1

tan1 2

i

TE i

er i

e

22

sec1 2

ii

TE i

et e

e

cot1 2'1

i

TE i

er

e i

2csc2 2'

1

i

i

TE i

ee

te i

'z zk k 'z zk k

2

TEr i

1TEt i

2

'TEr i

' 1TEt i

2sin

cos 2

0 sindk其中

2sin

cos

2

0 sin dk，

arcsinc

i i共轭材料：

FP

resonance

Surface

states

Transmission

Transmission

0 20 40 60 80

0.1

0 20 40 60 80

0.1

0 20 40 60 80

0.1

exp(i )

exp( i )

A

A

(a)

(b)

(c)

0.5, 0.5A

0.5, 0.55A

0.5, 0.45A

0.5, 0.65A

0 20 40 60 80

0.1

0.5, 0.35A

0 20 40 60 80

0.1

Yanyan Cao, Yangyang Fu, Yadong Xu,

and Huanyang Chen, unpublished.

Odd modes

Even modes

Surface modes

* 0.5u i

1

FP Resonance Diagram

m=2

m=1

m=3

Eigen states Diagram

Odd modes

Even modes

Surface modes

FP Resonance

Diagram

Eigen states

Diagram

m=2

m=1

m=3

* ,0 1u ni n

1, 2d

Transmission

Transmission

Odd modes

Even modes

Surface modes

FP Resonance Diagram

m=2

m=1

m=3

Eigen states Diagram

Eigen states Diagram

FP Resonance Diagram

Odd modes

Even modes

Surface modes

m=2

m=1

m=3

Conclusions Transformation optics makes it possible to design

conjugate metamaterials.

Perfect lens is the limiting case, tiny deviations will produce imperfections in the imaging functionality.

Purely imaginary metamaterials support perfect conversions from propagating waves to evanescent waves, lasing modes, and FP resonances, if the incident momentum is matched.

Acknowledgements Yadong, Jianhua

Yangyang, Yanyan, Xulin

Funding from NSFC

Ministry of Education

Thanks you!