光学OPTICS教学课件：第二章光的传播

1、光 学,OPTICS,第二章 光的传播,第二章 光的传播,第一节 散射、反射和折射 第二节 Snell定律和Fresnel公式 第三节 全反射 第四节 金属的光学性质,Phenomenon Transmission, Reflection and Refraction Blue sky A far-off mountain doesnt look reddish Rainbow Index of refraction Snells Law Fresnel Equations Approach Rayleigh Scattering Fermats Principle Electromagnet

2、ic Theory (Maxwells Eqs. + Model of atomic emitter,第二章 光的传播,Elastic Scattering,Each molecule behaves as a little oscillator whose electron cloud can be driven into a ground-state vibration by an incoming photon, and then initiates the re-emisson of light immediately,Secondary waves,第一节 散射、反射和折射,Prim

3、ary waves + Secondary waves,Primary waves,Rayleigh Scattering,Scattering involving particle small than a wavelength ( /15) has been called Rayleigh scattering. Eos Eoi Eos 1/r, r is the distance from the scattering sources Ios V, V is volume of the scattering sources,Ios 1/4,第一节 散射、反射和折射,Scattering

4、the associated wavelets arrive at P nearly in-phase. Principle of Reversibility A ray going from P to S will trace the same route as one from S to P,第二节 Snell定律和Fresnel公式,Fermat and mirages,第二节 Snell定律和Fresnel公式,Electromagnetic Approach,Boundary conditions: The tangential components of E-field must

5、be continuous on the interface. The tangential components of H-field must be continuous on the interface,第二节 Snell定律和Fresnel公式,Electromagnetic Approach,第二节 Snell定律和Fresnel公式,Electromagnetic Approach,第二节 Snell定律和Fresnel公式,The Fresnel Equations,Case 1: E plane-of-incidence,Linear, isotropic, homogeneo

6、us media,第二节 Snell定律和Fresnel公式,The Fresnel Equations,Case 1: E plane-of-incidence,Linear, isotropic, homogeneous media,第二节 Snell定律和Fresnel公式,Case 2: E / plane-of-incidence,第二节 Snell定律和Fresnel公式,The Fresnel Equations,Linear, isotropic, homogeneous media,第二节 Snell定律和Fresnel公式,The Fresnel Equations,Lin

7、ear, isotropic, homogeneous media,Case 2: E / plane-of-incidence,Another Form of Fresnel Equations,第二节 Snell定律和Fresnel公式,External Reflection (nt ni,第二节 Snell定律和Fresnel公式,nt (1.5) ni (1,At normal incidence, i = 0,for all i,Polarization (Brewsters) angle: i + t = /2 r/ = 0,External Reflection (nt ni,A

8、t glancing incidence,第二节 Snell定律和Fresnel公式,Internal Reflection (nt ni,第二节 Snell定律和Fresnel公式,nt (1) ni (1.5,Internal Reflection (nt ni,At normal incidence, i = 0,for all i,Polarization angle: i + t = /2 r/ = 0 Critical angle: t = /2,At glancing incidence,第二节 Snell定律和Fresnel公式,Phase Shifts,External re

9、flection,Internal reflection,第二节 Snell定律和Fresnel公式,E0r,E0r,E0r,E0r,Example 1: A laser beam is incident on the interface between air and some dielectric of index n. For small values of i, show that t = i / n. Use this and the above equation to establish that at near-normal incidence -ri0 = (n-1) / (n

10、+1,第二节 Snell定律和Fresnel公式,Example 2: Use the above equation and the power series expansion of the sine function to establish that at near-normal incidence we can obtain a better approximation than that in the previous example, namely,第二节 Snell定律和Fresnel公式,Example 3: Show that the polarization angles

11、for external and internal reflection at a given interface are complementary, that is, p + p = 90o,第二节 Snell定律和Fresnel公式,Reflectance & Transmittance,第二节 Snell定律和Fresnel公式,Conservation of Energy,At normal incidence,第二节 Snell定律和Fresnel公式,How to increase reflectance (or transmittance),第二节 Snell定律和Fresne

12、l公式,第二节 Snell定律和Fresnel公式,1,Total Internal Reflection,In case of internal reflection, and t = 90o sini = sinc = nti,critical angle,For i c, all the incoming energy is reflected back into the incident medium. This is called total internal reflection,第三节 全反射,Scattering Aspect of Total Internal Reflect

13、ion,第三节 全反射,A,A,D,Application of Total Internal Reflection optical fibers,第三节 全反射,The refractive constant of air is slightly larger than 1 and depends slightly on temperature, pressure and moisture. These effects are not considered here,Parameters used in simulations,第三节 全反射,The Evanescent Wave,第三节

14、全反射,Frustrated Total Internal Reflection & Beam Splitter,第三节 全反射,Optical Properties of Metals,第四节 金属的光学性质,Penetration Depth,Penetration depth,31015Hz) 0.6nm (31013Hz) 6nm,第四节 金属的光学性质,Optical Properties of Metals,第四节 金属的光学性质,Reflectance & Complex Refractive Index of Metals,第四节 金属的光学性质,Reflectance & C

15、omplex Refractive Index of Metals,第四节 金属的光学性质,( ) nI R,e.g. Au, Cu,The Stokes Treatment,E0rt,E0tt + E0rr = E0 E0rt + E0tr = 0,t(1) t(2) = 1 - r2(1) r(2) = -r(1,1 and 2 are pairs of angles that are related by Snells Law,第四节 金属的光学性质,E0r,E0rr,E0t,E0tr,E0tt,Huygens Principle (wavefront & geometry) Fermats Principle (least time & least OPL) Maxwells Equations,Reflection Snells Law,Case 1: E plane-of-incidence,Case 2: E / plane-of-incidence,Summary,Remark on Huygens Principle,Summary,Remark on group velocity,Remarks: (linear homogeneous isotropic dielectrics