TMM Applied for Shell Scattering

Weijia Wang

Dec.14.2010

Outline

Model

Spherical coordinates:Epsilon=-0.5 Check Epsilon=-0.5

Quasi Static Approximation

Cylindrical Coordinates

Model

A single shell with E

psilon

a static electric field

a plane wave

r

2R

=

Spherical Coordinate

TMM2

( ) cosll l

dc r

r

3301

21

2 1 1(1 )(1 ) (1 2 )(1 ) 0

9 2 9r rr r

RRT

0.5r

3302

3302

2 1 2 12 2 (1 ) (1 )(1 ) (1 )3 2 33 2 3

1 1 21 (1 ) (1 )(1 ) (1 2 )3 33 3

rr

r l rl

llr r

r r

R cc R

dd RR

1

0

tTr

21

22

Tr

T

Drude Model+Mie Theory

2

2( ) 1 pr

ww

w

296nm e= -0.13

254nm e= -0.53

20nm:24nm

Quasi Static Approximation

2R

=

10nm:12nm Epsilon=-0.5

Quasi Static ApproximationR （ nm ） Wavelength (nm)

12 370 4.91

24 880 5.84

36 1460 6.45

48 2080 6.90

60 2750 7.29

72 3460 7.65

84 4190 7.94

96 4950 8.21

108 5740 8.46

120 6540 8.67

180 10860 9.60

240 15560 10.32

600 48910 12.97

1200 116340 15.43

2 R

~20

2R

=

Cylindrical Coordinates

5000Hz ， R 0.2 m: 0.4mEpsilon=-2

Cylindrical Coordinates

TMM

( ) cosll l

dc r

r

3 321 1 0

1 1( ) (2 )r r

r r

T R R

Summary

Shell Epsilon=-0.5

Quasi Static Approximation

Nanoscale: ~ 20

Thanks!