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1、Classical propagation 2.1 Propagation of light in a dense optical medium2.2 The dipole oscillator model 2.3 Dispersion3.4 Optical anisotropy: birefringence2Chapter 2 Classical propagationModel: Light: electromagnetic wave Atom and molecule: classical dipole oscillatorn(), ()Two propagation parameter
2、s:n, 2.1 Propagation of light in a dense optical mediumThree types of oscillators:1. bound electron (atomic) oscillator2. vibrational oscillator;3. free electron oscillators2.1.1 Atomic oscillators2.1 Propagation of light in a dense optical medium2.1.1 Atomic oscillatorsIf = 0, resonant absorption (
3、Beers 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 andretards the propagation of the wave front, leading to smaller velocity thanin free
4、 space (v =c / 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 polar molecules, these oscillations are associated with lattice vibrations (phonons). 2.1.3 Free elect
5、ron oscillatorsFree electrons, Ks = 0, 0 = 0Drude-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
6、model 2.2.1 The Lorentz oscillatorlow 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 index Calcul
7、ated from the dielectric constant.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 sol
8、id from the infrared to the x-ray 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 ato
9、m.2.2 The dipole oscillator model 2.2.3 Comparison with experimental data(a) Refractive index and (b) extinction co- Efficient of fused silica (SiO2) glass from the (a) Infrared to the x-ray spectral region. 1. n except near the peaks of the absorption;2. The transmission range of optical materials
10、is determined by the electronic absorption in UVand the vibrational absorption in IR;3. IR absorption is caused by the vibrational quantain SiO2 molecules themselves(1.4 1013 Hz (21m) and 3.3 1013 Hz(9.1 m);4. UV absorption is caused by interband electronictransition(band gap of about 10 eV), thresh
11、old at2 1013 Hz(150 nm)( 108 m-1);5. UV absorption departure 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 inregion where n falls below un
12、ity; 8. Group velocity:2.2.4 Local field correction 2.2 The 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 by the Lorentz correc
13、tion. A imaginary spherical surface drawn around a particular atom 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
14、the sphere as a uniformly polarized dielectric.2.2.5 The Kramers-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 l
15、aw of causality (that an effect may not precede its cause) and apply 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 a
16、llow to calculate n and , and vice versa.2.2 Dispersion Refractive index of SiO2 glass in the IR, visible And UV regions Normal dispersion : the refractive index increaseswith frequency; Anomalous dispersion: the contrary occurs. This dispersion mainly originates from the interband absorption in the UV and the vibrational
