「光の散乱」テキスト 物理工学専攻 H20 後期 光計 …

1 H20 1 ( ) ( ) (Spontaneous light scattering ) (Stimulated light scattering ) (Nonlinear light absorption) ( ) (Scalar light scattering ) (Tensor light scattering ) ( ) H20 2 (a) incident beamfrequency 0scattering mediumscatteredlight (b) 0 Stokesanti-Stokes IntensityRamanRamanRayleighRayleigh-wing Brillouin Spontaneous Light scattering Spontaneous Light scattering Stimulated Light scattering (a) (b) (b)

2 (Raman scattering ) (Brillouin scattering ) (Rayleigh scattering ) (Rayleigh-Wing scattering ) (Stokes) (Anti-Stokes) 5x10-12 sec/cm H20 3 (cm-1) (cm-1) (sec) (cm/MW) 1000 5 10-12 5 x 10-3 5 x 10-3 10-9 510-2 0 5 x 10-4 10-8 10-4 0 5 10-12 10-3 (i) Optical phonon (ii) Acoustic phonon (iii) (iv) 10-12 ( ) dV1 =0 /(2sin ) dV2 dV1 0 =0 =0 (coherent forward scattering )

3 H20 4 /2 /(2sin )dV2dV1transmitted beamscatteredbeamincidentplanewave ( =0) dV1 dV2 ikikik +=0 ( ) 0 ik ik ik ik(t) )(tikikik + = ( ) (scalar light scattering ) ik(t) (tensor light scattering ) ik(t) 0)(= tiii ik(t) )()()(aiksiktik + = ( ) ik(s) ik(t) (symmetric) ik(s) = ki(s) ik(a) ik(t) (anti-symmetric) H20 5 ik(a) ki(a) , ik(s), ik(a) (polarized scattering ) ik(t) (depolarized scattering ) ( scattering coefficient)R I0 V Is L I0 V L Is 20 LRVIIs= ( )

4 R dA dP=Is dA d =dA/L2 dP /d =Is L2 RVIddP0= ( ) ( ) ( ) R =90 R=2x10-8 cm-1 R=1x10-6 cm-1 scatteringangle, scattering volume, Vdistance, LI0 IsdA H20 6 I0 P P I0 0IP = ( ) (Total scattering cross section) I0 I0 1 d dP/d 0 = ddIddP 0 ( ) d /d P dddP)/( ( ) ( ) = ddd 4 ( ) V ( ) ( ) =ddVR ( ) H20 7 R=0 )/)(/( =ddVR ( ) N ( ) (collective effects) )exp(~0+ =ti EE ( ) 200)2/(EncI = 1 p~ )exp()(~0+ =ti Ep ( ) ( ) ( )

5 ( ) I0 polarizationdirectioninduced dipoleof scattererr ( ) L far field 232202422322sin)(sin4~LcEnLcpnIs => <= ( ) H20 8 r ( ) ( ) dP/d =Is L2 ( ) d /d = (dP/d )/ 0=Is L2/ 0 ( ) 4224sin)(cdd = ( ) 200)2/(EncI = d /d ( ) sin2 d /d sin2 2444)(38 cddd= = ( ) ( ) ( ) = 90 ( ) 2424cos)(cddp= ( ) p p 90 s 424)(cdds = ( ) ( ) ( ) )cos1()(221424 += cdddunpolarize ( ) ( ) )()( N= 2 H20 9 1 ime2/)(2202 = ( ) 0 ( ) 22222042224)

6 (38 + =mce ( ) 2 Frequency, 000 Cross section ( ) ( ) 0404222for,38 << =mce ( ) 022020222for,)(38 + =mce ( ) 0222for38 >> =mce ( ) ( ) 0 << 0 H20 10 ( ) 0 ( ) 0 >> 0 re=e2/mc2 (Thomson scattering ) ( ) 1 a 3112a + = ( ) 1 ( ) ( ) 211644238 + = ac ( ) 4 I0V V Is V V V Clausius-Mossotti Classical Electrodynamics by J.)

7 D. Jackson, 3rd Ed 159 1 H20 11 V V V V Iv molVII2' = ( ) V Imol 1 Iv 2 V V V V V molI2 222 = V VVIImolV =2 ( ) V/V V V IV 2 IV 2 N V 'NV= ( ) = = 222 ( ) ( ) H20 12 molmolVINVII == ( ) 1 NV= ( ) R ( ) NV= = =ddNddVR ( ) ( ) 2244sin)(cNR= ( ) )(21)(41)(41)()1( NNn+ +=+== ( ) Nn 21)

8 ( = ( ) )()()1( N= ( ) 22244sin41 NncR = ( ) 2 n R N Loschmidt s number, 0 C 1 N0= x 1019 cm-3 ( ) H20 13 V V V V =1+4 = /4 V' 00~4~~EEP = = ( ) 0~4~~EPp = =VV ( ) > <=2~)4/(SSncIE ( ) ( ) 4222224016sin'cLVIIS > <= ( ) p~ > <=200~)4/(E ncI ( ) V ( ) V/V TTT + = ( ) 2 > < >= <222 ( ) T T e H20 14 20222 > <>= <e ( ) 0 e 0 = =e ( ) ( ) 202/ > <)