凝聚态光物理学2.ppt

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1、Classical propagation 2.1 Propagation of light in a dense optical medium 2.2 The dipole oscillator model 2.3 Dispersion 3.4 Optical anisotropy:birefringence2Chapter 2 Classical propagationModel:Light:electromagnetic waveAtom and molecule:classical dipole oscillator n(),()Two propagation parameters:n

2、,2.1 Propagation of light in a dense optical medium Three types of oscillators:1.bound electron(atomic)oscillator 2.vibrational oscillator;3.free electron oscillators 2.1.1 Atomic oscillators2.1 Propagation of light in a dense optical medium 2.1.1 Atomic oscillators If =0,resonant absorption (Beers

3、law)h =E2-E1 re-radiated photon luminesce radiationless transition If 0,non-resonant,transparent The oscillators follow the driving wave,but with a phase lag.The phase lag accumulates through the medium and retards the propagation of the wave front,leading to smaller velocity than in free space(v=c/

4、n).-the origin of n2.1.2 Vibrational oscillatorsClassical model of a polar molecule(an ionic optical medium)Infrared spectral regionIn a crystalline solid form the condensation of polarmolecules,these oscillations are associated with lattice vibrations(phonons).2.1.3 Free electron oscillators Free e

5、lectrons,Ks=0,0=0 Drude-Lorentz model 2.2 The dipole oscillator model 2.2.1 The Lorentz oscillatorLight wave will drive oscillations at its own Frequency:Solution;The gives:With:The macroscopic polarization of medium P:The electric displacement D:2.2 The dipole oscillator model 2.2.1 The Lorentz osc

6、illator low frequency limit:high frequency:Thus Close to resonance:Frequency dependence of the real and imaginary Parts of the complex dielectric constant of a dipole At frequencies close to resonance.Also shown is The real and imaginary part of the refractive indexCalculated from the dielectric con

7、stant.1.吸收峰位于o,半宽=;2.1的极值位于 o ，1出现负值;3.折射率在o 区间出现反常色散。2.2 The dipole oscillator model 2.2.2 Multiple resonance Take account of all the transitions in the mediumSchematic diagram of the frequency dependence of the refractive index and absorption of a hypothetical solid from the infrared to the x-ray

8、spectral region.The solid is assummed to have three resonant frequencies with width of each absorption line has been set to 10%of the centre frequency by appropriate choice of the js.Assign a phenomenological oscillator strength fj to each transition:For each atom.2.2 The dipole oscillator model 2.2

9、.3 Comparison with experimental data(a)Refractive index and(b)extinction co-Efficient of fused silica(SiO2)glass from theInfrared to the x-ray spectral region.1.n except near the peaks of the absorption;2.The transmission range of optical materials is determined by the electronic absorption in UV an

10、d the vibrational absorption in IR;3.IR absorption is caused by the vibrational quanta in SiO2 molecules themselves(1.4 1013 Hz (21m)and 3.3 1013 Hz(9.1 m);4.UV absorption is caused by interband electronic transition(band gap of about 10 eV),threshold at 2 1013 Hz(150 nm)(108 m-1);5.UV absorption de

11、parture from Lorentz model;6.n actually increases with frequency in trans-parency region,the dispersion originates from wings of two absorption peaks of UV and IR;7.The phase velocity of light is greater than c in region where n falls below unity;8.Group velocity:2.2.4 Local field correction 2.2 The

12、 dipole oscillator model Clausius-Mossotti relationshipThe actually atomic dipoles respond not only to the external field,but also to the field generated by all the other dipoles Model used to calculate the local field bythe Lorentz correction.A imaginary sphericalsurface drawn around a particular a

13、tom divides the medium into nearby dipoles and distant dipoles.The field at the centre of the sphere due to the nearby dipoles is sunned exactly,while the field due to the distant dipoles is calculated by treating the material outside the sphere as a uniformly polarized dielectric.2.2.5 The Kramers-

14、Kronig relationships2.2 The dipole oscillator model The discussion of the dipole oscillator shows that the refractive index and the absorption coefficient are not independent parameters but are related to each other.If we invoke the law of causality(that an effect may not precede its cause)and apply

15、 complex number analysis,we can derive general relationships between the real and imaginary parts of the refractive index as follows:Where P indicates that the principal part of the integral should be taken.The K-K relationships allow to calculate n and,and vice versa.2.2 Dispersion Refractive index

16、 of SiO2 glass in the IR,visible And UV regions Normal dispersion:the refractive index increases with frequency;Anomalous dispersion:the contrary occurs.This dispersion mainly originates from the interband absorption in the UV and the vibrational absorption in IR2.2 Dispersion Pulse broadeningDisper

17、sion causes the very short pulse to broadenin time as it propagates through the medium.group velocity dispersion(GVD)The Lorentz model indicates that GVD is positive below an absorption line and negative above it.There is a region of zero GVD around 1.3 m in silica.So short pulses can be transmitted

18、 down the silica fibre with negligible temporal broadening at this wavelength.The relationship of the P and E 2.2 Optical anisotropy:birefringence Cubic:11 22 33,isotropic;Tetragonal,hexagonal or trigonal:11 22 33,uniaxial;Orthorhombic,monoclinic or triclinic:11 22 33,biaxial.2.2 Optical anisotropy:

19、birefringence Double refractive in a natural calcite crystal,an un-polarized incident light ray is split into two spatially separated orthogonally polarized rays.2.2 Optical anisotropy:birefringence Electric field vector of ray propagating in a uniaxial crystal with is its optic axis along the z dir

20、ection.The ray makes an angle of with respect to the optic axis.The polarization can be resolved into:(a)a component along the x-axis and(b)a component at an angle of 90o-to the optic axis.(a)Is o-ray and(b)is the e-ray.Exercises:l1.The full width at half maximum of the strongest hyperfine component

21、 of the sodium D2 line at 589.0 nm is 100 MHz.A beam of light passes through a gas of sodium with an atom density of 11017 m-3.Calculate:(i)The peak absorption coefficient due to this absorption line.(ii)The frequency at which the resonant contribution to the refractive index is at a maximum.(iii)Th

22、e peak value of the resonant contribution to the refractive index.(i);1.7*103m-1;ii)50 MHz below the line center;iii)3.95*10-5)l2.A damped oscillator with mass,natural frequency 0,and damping constant is being driven by a force of amplitude F0 and frequency.The equation of motion for the displacement x of the oscillator is:What is the phase of x relative to the phase of the driving force?(-tan-1/(02-2)l3.Show that the absorption coefficient of a Lorentz oscilator at the line centre does not depend on the value of 0.