纳米光子学-第二讲资料下载.pdf

1、Format?Ask questions any time.Direct questions Big comments on the nanocourse are most welcome!3What Happened in the Previous Lecture?Maxwells Equationsf=D0=B=BEt=+DHJtCurl Equations lead to22200022tt=+EPE0=PEWave EquationLinear,Homogeneous,and Isotropic Media（under certain conditions）（）（）22222,tntc

2、=E rE rtIn real life:Response of matter（P）is not instantaneous（）（）（）0,tdt x ttt+=P rE rSolutions:EM waves（）（）,Re,exp2z tzi zzi t=+EE0k n=02k n=whereandPhase propagationabsorption（）=（）nn=（）=（）nn=Bold face letters are vectors!4Today:Microscopic Origin -Response of MatterOrigin frequency dependence of

3、in real materialsLorentz model（harmonic oscillator model）Real and imaginary part of are linkedKramers-KronigInsulators（Lattice absorption,color centers）Semiconductors（Energy bands,Urbach tail,excitons）Metals（AC conductivity,Plasma oscillations,interband transitions）But first.When should I work with,

4、or n?They all seem to describe the optical properties of materials!5n and nvs and vs and All pairs（n and n,and,and）describe the same physicsFor some problems one set is preferable for others anothern and n used when discussing wave propagation（）（）,Re,exp2z tzi zzi t=+EE0k n=02k n=whereandPhase propa

5、gationabsorption and and used when discussing microscopic origin of optical effectsAs we will see todayInter relationships（）（）22rnn=2 rn n=（）（）222rrrn+=（）（）222rrrn+=Example:n and rn=From and rrnini+=+6Behavior of bound electrons in an electromagnetic field Charges in a material are treated as harmon

6、ic oscillators Optical properties of insulators are determined by bound electrons,elE LocalDampingSpringm=+aFFF（）22expLddmmCei tdtdt+=rrrE（）0expi t=pp Guess a solution of the form:22000LmimCe+=pppEe（）0;expdii tdt=pp The electric dipole moment of this system is:e=pr（）222expLddmmCei tdtdt+=pppE（）2202;

7、expdi tdt=ppSolve for p0（EL）Linear Dielectric Response of MatterLorentz model（one oscillator）Nucleuse-,me=pr+C,rLE7Atomic PolarizabilityDetermination of atomic polarizability22000LmimCe+=pppE Last slide:202201Lemi=pE22000LCeimm+=pppE（Divide by m）Define as 02（turns out to be the resonance）Atomic pola

8、rizability（in SI units）Resonance frequency（）2022001ELpemi=0 Define atomic polarizability:Damping term8Characteristics of the Atomic Polarizability（）（）2022001expELpeAimi =0 Atomic polarizability:（）21/222222001eAm=+Amplitude Response of matter（P）is not instantaneous Phase lag of with E:1220tan=Amplitu

9、dePhase lag0018090smaller smaller-dependent response9Relation Atomic Polarizability（）and :2 casesCase 1:Rarified media（.gasses）（）0jjL=pE Dipole moment of one atom,j:Polarization vector:001jjLjLjjNVV=PpEEsum over all atoms（）222001jemi=（）202201LLNemi=PEEE-field photon（）222001Nemi=Microscopic origin su

10、sceptibility:Plasma frequency defined as:220pNem=（）2220pi=DensityOccurs in Maxwells equation.10Remember:and n follow directly from Relation of to :222011pi=+=+Frequency dependence（）（）（）222022222011p=+=+（）（）2222220p =+222011piii+=+=+0（）2201p+10=220p=p11Propagation of EM-waves:Need n and n0（）2201p+1（）

11、nnn1n=0Relation between n and n=（）（）22rnn=2 rn n=0:High nlow vph=c/nn=1 vph=c1222201kkkN emi=Resonances occur due to motion of the atoms（low）and electrons（high）Where Nkis the density of the electrons/atoms with a resonance at kRealistic atoms have many resonances Realistic Rarefied Media=2k0nn213Log

12、（）MoleculerotationAtomicvibration Electron excitation n 1 indicates presencehigh oscillatorsExample of a realistic dependence of n and n13Back to Relation Atomic Polarizability（）and :Case 2:SolidsField without matter Local field:SolidE-field?pi Atom“feels”field from:1）Incident light beam 2）Induced d

13、ipolar field from other atoms,piLocal fieldInduced dipolar field from all the other atoms0LI=+EEE14Electric Susceptibility of a SolidLocal fieldField without matter All the other atoms Local field:Local fieldInduced dipolar field Example:For cubic symmetry:03I=PE（Solid state Phys.Books,e.g.Kittel,As

14、hcroft.）0LI=+EEE003L=+PEEPolarization of a solid00000033jjLjjjjjjjjjjNNNN=+=+PPPEEE0113jjjjjjNPEN=（Similar relations can be derived for any solid）00113jjjjjjNN=PEjp Solid consists of atom type j at a concentration Nj150113jjjjjjNPEN=Clausius-Mossotti RelationPolarization of a solid Susceptibility:Limit of low atomic concentration:jjjN By definition:Clausius-Mossotti1=+01123jjjN=+IIIIII Rearranging I gives Conclusion:Dielectric properties of solids related to atomic polarizability This is very general!.or weak polarizability:pretty good for gasses and glasses