第二章SPP的基本概念及物理2.1Surfaceplasmonpolariton(SPP)dielectric constant, plasmon frequency,dispersionrelation,evanescentfieldpropagationlength,SPP waveguides2.2Surfaceplasmonresonance(SPR)andMietheoryMietheory,extinction,absortion,scatteringSPR of metallic nanospheres and nanoshells古英2012年3月ygu@pku.edu.cn
1 第二章 SPP的基本概念及物理 2.1 Surface plasmon polariton (SPP) dielectric constant, plasmon frequency, dispersion relation, evanescent field propagation length, SPP waveguides 2.2 Surface plasmon resonance (SPR) and Mie theory Mie theory, extinction,absortion, scattering SPR of metallic nanospheres and nanoshells 古英 ygu@pku.edu.cn 2012年3月
2.1.1 PreparationA.Dielectricconstantε(α)Frequency dependent, Drude free electrons modelPlasma: a medium with equal contribution of positive andnegative charges,of which at least onechargetype is mobileE=Eeiot后，其振幅分量在金属表面上加上电场dx-eE电子受力（x<<）mdielectricdt?E00000由于电子随EMfield以の振荡，metal可令xxeiot则x=eE/ mo?-°mx =-eEP=-ex=-e'E/mo那么dipolemomentofoneelectron2Introductiontosolidstatephysics,Chapter1o,CharlesKittel,SeventhEdition
2 2.1.1 Preparation Introduction to solid state physics, Chapter 10, Charles Kittel, Seventh Edition. A. Dielectric constant ε(ω) Frequency dependent, Drude free electrons model Plasma: a medium with equal contribution of positive and negative charges, of which at least one charge type is mobile E metal dielectric 加上电场 i t E Ee ω = 后，其振幅分量在金属表面上 电子受力（ x l << 自 ） 2 2 d x m eE dt = − 由于电子随EM field 以 ω 振荡， 可令 i t x xe ω = 则 2 2 − =− = ω ω mx eE x eE m/ 2 2 1 那么 dipole moment of one electron P ex e E m =− =− / ω
P(の) = nP =-ne?E / mo若电子密度是n，则目的是求Drudemodeloffreeelectronm(0)24元neD(o)E(の)+ 4元P()8m()2E(o)E()mo随变化，(の)可正可负8m(の)=0 时的の1.5叫做plasmafrequency4元ne?0Lm主要和电子密度n相关03Introductiontosolidstatephysics,Chapter1o,CharlesKittel,SeventhEdition
3 Introduction to solid state physics, Chapter 10, Charles Kittel, Seventh Edition. 若电子密度是n，则 2 2 1 P nP ne E m ( ) ω ω = = − / 目的是求 ( ) ε ωm 2 2 () () 4 () 4 ( ) 1 () () m D E P ne EE m ω ω πω π ε ω ωω ω + = = = − Drude model of free electron 随ω变化，ε ωm ( )可正可负 ε ωm () 0 = 时的ω 叫做 plasma frequency 2 2 4 p ne m π ω = ωp 主要和电子密度n 相关
B.金属中的色散关系，の～k的关系8m(0) = Em (00)由Drudemodel可知e考虑到电子不是free，而做的一个修正考虑到损耗写成:8m(の)=m(0)[1-+ioy0a?DD= m(@)Ec??E代入传播方程将Ot?ik.z+iot1E=ELik.z又知道传播因子是e得到 ()[の~-のckIntroductiontosolidstatephysics,Chapter1o,CharlesKittel,SeventhEdition
4 Introduction to solid state physics, Chapter 10, Charles Kittel, Seventh Edition. 由Drude model 可知 0 ( ) z m ik z i t D E E Ee ω ε ω + = = B. 金属中的色散关系， ω～k的关系 2 2 ( ) ( )[1 ] p m m ω εω ε ω = ∞− 考虑到电子不是free，而做的一个修正 将 代入传播方程 2 2 2 2 D c E t ∂ = ∇ ∂ 得到 22 2 ( )[ ] p z ε ωω ∞ −= ck 又知道传播因子是 z ik z e 考虑到损耗写成： 2 2 ( ) ( )[1 ] p m m i ω εω ε ω ωγ = ∞− +
当K，是实数时，光传过去了0>0p=>8m>0，等离子体频率以上WWRegion ofpropagationRegion ofattenuation当k，是复数时，传不过去0<0。=>8m<0，等离子体频率以下5Introductiontosolidstatephysics,Chapter1o,CharlesKittel,SeventhEdition
5 Introduction to solid state physics, Chapter 10, Charles Kittel, Seventh Edition. 当kz是实数时，光传过去了， ω>ωp => εm>0，等离子体频率以上 当kz是复数时，传不过去， ω<ωp => εm<0，等离子体频率以下