复旦大学：《电动力学》课程教学资源（学生课堂报告）转移矩阵研究球壳散射

TMM Applied for 2 Shell Scattering Weijia Wang Dec.14.2010

TMM Applied for Shell Scattering Weijia Wang Dec.14.2010

Outline Model Spherical coordinates: Epsilon=-05 Check Epsilon=-05 Quasi Static Approximation Cylindrical Coordinates

Outline ◼Model ◼Spherical coordinates:Epsilon=-0.5 ◼Check Epsilon=-0.5 ◼Quasi Static Approximation ◼Cylindrical Coordinates

Model A single shell with Epsilon a static electric field R a plane wave 2丌

Model ◼ A single shell with Epsilon ◼ a static electric field ◼ a plane wave r  2 R   =

Spherical Coordinate TMM p,=(cr+ur 2) cos 8 =(1+) (1-s,)2(1+) 323R 2 3(1 R (1-E,)(1+2E,) (1+ 3 T 22 2R 1、,R (1-6,)1+x)+ (1+26,)(1--)=0 28 0.5

Spherical Coordinate ◼TMM 2 ( ) cos l l l d c r r   = + 3 3 1 0 21 2 1 1 (1 )(1 ) (1 2 )(1 ) 0 9 2 9 r r r r R R T     = − + + + − = 0.5 r  = − 3 3 2 0 3 3 2 0 2 2 2 1 2 1 (1 ) (1 ) (1 ) (1 ) 3 2 3 3 2 3 1 1 1 2 (1 ) (1 2 ) (1 ) (1 ) 3 3 3 3 r r r l r l l l r r r r c R R c d R R d            + − + −        =                 − +   − +    1 0 t T r         =     21 22 T r T = −

Drude Model+Mie Theory 20nm:24n 0.6 Epsilon 296nme=-0.13 10000 04 0.2 1000 0.0 -0.2 254nme=-0.53 100 -04 -0.6 -0.8 -1.0 1.2 886,()≈1 0.1 200 250 300 400 Wavelength(nm)

Drude Model+Mie Theory 2 2 ( ) 1 p r w w w   − 296nm e= -0.13 254nm e= -0.53 20nm:24nm

Quasi Static Approximation 10nm: 12nm Epsilon=-05 100000 234567891 10000 R 1000 2丌 200 400 800 1000 Wavelength(nm)

Quasi Static Approximation 2 R   = 10nm:12nm Epsilon=-0.5

Quasi Static Approximation R(nm Wavelength(nm) 2 R 12 370 4.91 24 880 5.84 36 1460 6.45 48 2080 690 60 2750 7.29 72 3460 7.65 R 84 4190 7.94 2丌 6 4950 8.21 ~20 108 5740 8.46 120 6540 8.67 180 10860 9.60 240 15560 10.32 600 48910 1297 1200 116340 15.43

Quasi Static Approximation R（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 2 R   =

ylindrical Coordinates 3)=-2 Surface: Total energy dansity, tine average [/m] Arrow: Electric field Streamline: Electric field Max:1.302e12 5000Hz,R0.2m: 0.4m Epsilon=2 -2-1.8-1.6-1.4-1.2-1-0.8-0.6-0.4-0.200.20.40.60.81 Min:=2.312e-12

Cylindrical Coordinates 5000Hz，R 0.2 m: 0.4m Epsilon=-2

ylindrical Coordinates TMM 9,=(C,r+-)cos 0 T,=P3/。1 )+R(2

Cylindrical Coordinates ◼TMM ( ) cos l l l d c r r   = + 3 3 21 1 0 1 1 ( ) (2 ) r r r r T R R     = − + − −

Summary Shell Epsilon=-05 Quasi Static Approximation Nanoscale:- 20

Summary ◼Shell Epsilon=-0.5 ◼Quasi Static Approximation Nanoscale: ~ 20