Something About Optical Blackhole

Something About Something About Optical Blackhole Optical Blackhole

Li Li (Li Li ( 李力李力 ))Dept. Phys., Fudan Univ.Dept. Phys., Fudan [email protected]@gmail.com

091229 ED 10min presentation091229 ED 10min presentation

Appl. Phys. Lett. 95, 041106(2009)

Outline

• Introduction• Begin with Maxwell Equation• Mathematica• Comsol

0

0

E(r,t) E (r)

H(r,t) H (r)i te

��

��

00

0

E (r)

H (r)ik ns rik re e

e eh h

��

��

0

0 0

2 2 2k s s ns

( )S r ns r

real scalar function of position

0

1

0

1

D

BE

c t

B

DH

c t

��

��

��

��

0

0 0 0

0

0 0 0

0

0

0

0

E

E ik H

H

H ik E

��

��

��

��

0

0

E(r,t) E (r)

H(r,t) H (r)i te

��

��

00

0

E (r)

H (r)ik See

h

��

��

0

0

0

0

1( ln )

1

1( ln )

1

e S e eik

S e h eik

h S h hik

S h e hik

0

0

0

0

e S

S e h

h S

S h e

Short Wave Limit 0k

2 2( )S n

n

2 2( )S n

n

0

0

0

0

e S

S e h

h S

S h e

SS

n

��

S Ss

n S

drn Sds

d drn n

ds ds

Uniform Medium ： n=const.2

20

d r

ds

Straight Line

0 2 2 2

r

R

dc

n c

( )n n r

Appl. Phys. Lett. 95, 041106(2009).nd const Bigger n!

Outline


.n const

0 2 2 2

r

R

dc

n c

11

nr

0 2 2 2

r

R

dc

n c

0 2 2 2

r

R

dc

n c

11

2nr

0 2 2 2

r

R

dc

n c

1rn

1

1.73 ,3

Rn

r

1/ 2

,10

Rn k

r

Outline


1n

r1n

•There are solutions of Maxwell equation in short wavelength to describe geometrical optics.

•With designed refractive index(mainly ε), we can control the path of light such as blackhole.

Prof. Zhifang LinProf. Zhifang LinWeihua WangWeihua WangLianxi ChengLianxi Cheng

林志方教授林志方教授王伟华王伟华程恋茜程恋茜

Derivation of the eikonal equation

21[( ) ( ) ] 0e S S e S e

=02 2( )S n n

0

0

0

0

e S

S e h

h S

S h e

Differential Equation of Optical Path

drn Sds

d dr

nds ds

2

2

( )

1( )

1[( ) ]

21

2

dS

ds

drS

ds

S Sn

Sn

nnn

d drn n

ds ds

22

( )sin

( )

r

drr

d

sin .nr const

2 2 2dr rn r c

d c 0 2 2 2

r

R

dc

n c

d dr dr ns ns r ns

ds ds ds

0s ns

r n

r dnn

r dr

( )n n r

0r dn

rr dr

.r ns const

sin .nr const

.nd const

1d sK v

ds

��

Curvature Vector Unit Normal Line Vector

d drn n

ds ds

dn

nK n sds

��

( )dn

K nK K n sds

��

1lnK v n

��

•Incident wave•Decay range•Symmetry

1

4

Rn

r 2

Rn

r

Something About Optical Blackhole

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