プラズモンの基礎 - home.sato-gallery.com

1 ( ) (JST) CONTENTS 1. 2. 3. 4. 1. 1 ~aurora/ p=(ne/ 0m)1/2 p n e m 0 n m m* 0 ( )

2 P p , =0 =0 p <0 p 2. Drude-Lorentz P E u s + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + E *

3 M*d2u/dt2 (m*/ )du/dt qE (1) E u e-i t P=-Nqu D= 0 rE= 0E+P r=1-Nq2/{m* 0 2(1+i/ )}=1- p2/{ ( +i/ )} (2) p=(Nq2/m* 0) 1/2 Drude (3) r= r+i r r 1- p2/( 2+1/ 2) r" p2/ ( 2+1/ 2) Drude 1 0 - + p=2eV / = (3) R r a r a 100% 11 rrR 111111111222 aaaiaiaaRrr (eV) p p=2eV / =0 ( (eV) p=2eV / = p ( r ) Drude 2 Ag r Fermi EF EF Cu EF 2eV 3d 4s4p E>EF EF Cu Ag 3 Au EF Lorentz u m* 0 m*d2u/dt2+(m*/ 0)du/dt+m* 02u=qE (4) 0 Lorentz E u e-i t u Nb P=Nbqu r=1- b2/( 2+i / 0- 02) (5))

4 B2=Nbq2/m* 0 r'=1- b2( 2- 02)/{( 2- 02)2+( / 0)2} (6) r"= b2( / )/{( 2- 02)2+( / 0)2} Lorentz Lorentz (6) 3 r" r' 3d r 3. 0= 0= 0= 4 (3) (6) r' 1 r' 0 p 0 2 Ag 4 ( p=2eV, / = , 0= , 0= ) Drude-Lorentz 4 (eV) p=2eV, / = , 0= , 0= Drude Lorentz (2) 1 r' 0 p' p ( p2/ 1/ 2)1/2 (7) Ag p= p= (1) div D=0 (8) D( ,k)= ( )E( ,k) = ( )E0e-i( t-k r) i ( )k E=0 (9)

5 K E=0 k E ( )=0 ( L)=0 L 1 -P/ 0 P=Nqu m*d2u/dt2 Nqu/ 0 qE (10) ( m* 2+Nq/ 0)u0=qE0 (11) E0=0 =(Nq/m* 0)1/2 p 0 = P ( P)=0 (7) p' EELS 3. 1/10 SPR md2u/dt2=qE (12) P=Nqu P d2P/dt2=(Nq2/m)E= p2 0E P e-i t - 2P- p2 0E =0 (13) E, H e-i t+iKz rotH= D/ t =-i ( 0E+P) rotE=- B/ t =i 0H (14) (14) H - 2P+(c2K2- 2) 0E=0 (15) (13) (14) P E p2-( 2-c2K2) =0 (17) ={ p 2+c2K2}1/2 (18) (16) 002222022 Kcp < p (17) c2K2<0 (18) K = cK (19)

6 5 = cK + E 6 1 1 2 2 ,2 k1, k2 k1x2+k1z2=k12=k2 1 (20) k2x 2+k2z2=k22= k2 2 (21) 6 1 2 k k=2 / = /c k1x= k2x=k// (20) (21) k//2+k1z2= k2 1 k//2+k2z2=k2 2 2 k1z2- k2z2= k2( 1- 2) (22) k//2={k2( 1+ 2)-( k1z2+ k2z2)}/2 (23) k// divD=0 k//E1x+k1zE1z=0 (24) k//E2x+k2zE2z=0 (25) k1z k2z 2k1z= 1k2z (26) k1z2= k2 1 2/( 1 + 2) (27) k2z2= k2 2 2/( 1 + 2) (28) (23) (27) (28) k//2=k2 1 2/( 1 + 2) (29) z Ez k1z2<0 k2z2<0 1 + 2<0 k1z k2z k// 1 2<0, 1 + 2<0 (30) Au Ag < p (30) (SPP) 1 1 = 1 +i 1 (31) 1 1 2 2 SPP k// k//= k// +i k// SPP SPP (29) | 1 | | 1 | k// k// k// k{ 1 2/( 1 + 2)}1/2 (32) k// k 1 -1/2 1 21/2 ( 1 + 2)-1/2/2 (33) (32) SPP =2 /k// = {( 1 + 2)/ 1 2}1/2 (32)

7 1 1 =1- p2/ 2, 2 2=1 k// 2= k2{ 1 2/( 1 + 2)}=( /c)2(1- p2/ 2)/(2- p2/ 2) k// 0 k//c k// p/21/2 7 7 8 SPP SPP < p/21/2 1 2<0 1 + 2=2- p2/ 2<0 SPP =ck// SPP 8 SPP 9(a) n =ck///n 9(b) Otto / / / SPP Kretschmann / / / SPP SPP SPP (a) (b) 9 and : Optical Properties of Oxides Films Dispersed with Nanometric Particles In UV-VIS and Photoluminescence Spectroscopy for Nanomaterials Characterization , ed.

8 , Springer-Verlag GmbH (2012) E0 P =n P n P E E0 E1 E1 E0 . E=E0+E1 (34) (i=x, y, z) E1i E1i=NiiPi/ 0 (35) Pi(i=x, y, z) Nii 3 Nx+Ny+Nz=1 (36) (a) (b) (c) P E P= 0E (38) E E0 E=E0+E1=E0-NP/ 0 (39) E P={ 0/(1+ N)} E0 (40) ( ( )+2) ( ) ( ) ( )= ( )-1 (40) P=( ( )-1) 0/(1+N( ( )-1) ) (41) V p P V p=( ( )-1) 0V/(1+N( ( )-1) ) (42) a N=1/3 V=4 a3/3 p=4 a3 {( ( )-1) 0/ ( ( )+2)} E0 (43) ( ( )+2) (43) ( ) ( )

9 2 Drude N (N p)1/2 (44) N p/(1+2 ) 1/2 (45) Gustav Mie Maxwell Mie (EMA) EMA , Maxwell-Garnet(M-G) Bruggeman i f e 1-f eff Maxwell-Garnet Maxwell-Garnet 1 +2= +2 fi = 1+2 2 2 2+ + 1 Bruggeman Bruggeman 1 1 1+2 + 2 2 2+2 =0 1 2 1 2 Au