模式的概念戈弦调尔e.弹性模式弹城名程十体54zP4+mod元元元元中电磁模式hR0美电回你（友播同）axeelteguaaVWImodes.对金属来说，通常有美电i地天之x个南名6（）n的印信，nnitinz对于我南海麦蓝来说西米会居1pn.con.70Re(ca)yomeds对国cnE214夜女%2
14 模式 弹性模式 电磁模式 对金属来说，通常有 模式的概念
Differencebetweensurfaceplasmon(SP)and surfaceplasmon polaritons(SPP)"a trapped surface mode which has electromagnetic fieldsdecaying into both media but which, tied to the oscillatorysurface charge density, propagates along the interface"R.J.Sambles 1991E（0)'we are dealing with a resonant excitation of a coupledstate between the plasma oscillations and the photons, i.e.,the plasmon surface polariton'W.Knoll199115
15 Difference between surface plasmon (SP) and surface plasmon polaritons (SPP)
1.1特鲁德模型(Drude model)t (α)A.Dielectric constantFrequencydependent,DrudefreeelectronsmodelPlasma: a medium with equal contribution of positive andnegativecharges,of whichatleastonechargetypeismobileE=Eeiot后，其振幅分量在金属表面上加上电场uqx电子受力（x<<）-eEmdielectricdt?E00000由于电子随EMfield以の振荡，metal可令 x=xeiotx=eE/mo?则 -の'mx=-eEP =-ex=-e'E/mo那么dipolemoment of one electron16Introductiontosolidstatephysics,Chapter1o,CharlesKittel,SeventhEdition
16 1.1 特鲁德模型 （Drude model） Introduction to solid state physics, Chapter 10, Charles Kittel, Seventh Edition. A. Dielectric constant () 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 = ur ur 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 = − r ur 由于电子随EM field 以 振荡， 可令 i t x xe = r 则 2 2 − = − = mx eE x eE m/ 2 2 1 那么 dipole moment of one electron P ex e E m = − = − /
J P(の)=nP =-ne’E/ mの若电子密度是n，则Drude model of freeelectron目的是求8m()4元neD(の)E()+ 4元P()8m(の)2E(0)E(の)mo随变化，Sm(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0.17Introductiontosolidstatephysics,Chapter1,CharlesKittel,SeventhEdition
17 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 ( ) / = = − 目的是求 ( ) m 2 2 ( ) ( ) 4 ( ) 4 ( ) 1 ( ) ( ) m D E P ne E E m + = = = − Drude model of free electron 随变化， m ( ) 可正可负 m ( ) 0 = 时的 叫做 plasma frequency 2 2 4 p ne m = p 主要和电子密度n 相关
B.金属中的色散关系8m(0)= 8.由Drudemodel可知0考虑到电子不是free，「而做的一个修正8m(0) = 8m(00)[1考虑到损耗写成? +iya?DD = εm(o)Ec?√?E代入传播方程将Ot?ik,z+iotE=Hoe无损耗时，得到ik..()[α? -,]= ck,又知道传播因子是Introductiontosolidstatephysics,Chapter1o,CharlesKittel,SeventhEdition.18
18 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 E e + = = B.金属中的色散关系 2 2 ( ) ( )[1 ] p m m = − 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 = 无损耗时，得到 2 2 2 2 ( )[ ] p z − = c k 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 = − +