Chapter I Ray Optics

# Chapter I Ray Optics

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## Chapter I Ray Optics

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1. Chapter IRay Optics

2. Comments 高中内容 强调光的直线传播 关注光场的强度 对偏振等其它信息不关注，或暗含

3. Why first Ray Optics? • Short Wavelength of EM wave • From Spatial Confinement • Big xsmallkx • Influence too small

4. Comments • 在所有维度上的特征尺寸远大于波长 • 光束宽度 • 平面波 • 不涉及到波的干涉和衍射 • 即使涉及到干涉和衍射，也无法观测 • 被背景掩盖掉

5. 1.1 POSTULATES OF RAyOPTICS

6. a set of postulates (provided without proof) • Why these postulates? • From Maxwell’ Equations • From Quantum Theory

7. 为什么？

8. 注意 (1.1-2)最短路径原理，在其它物理学科中也经常见到，譬如量子力学的路径积分原理 • 动物的群体运动里也有，http://blog.sciencenet.cn/blog-64458-362786.html • 典型的包括大量全同个体的波动行为 Classically, Fermat's principle can be considered as a mathematical consequence of Huygens' principle. Indeed, of all secondary waves (along all possible paths) the waves with the extrema (stationary) paths contribute most due to constructive interference.

9. Supposing that light waves propagate from A to B by all possible routes ABj, The various optical paths ABj will vary by amounts greatly in excess of one wavelength, and so the waves arriving at B will have a large range of phases and will tend to interfere destructively. • But if there is a shortest route AB0, and the optical path varies smoothly through it, then a considerable number of neighboring routes close to AB0 will have optical paths differing from AB0 by second-order amounts only and will therefore interfere constructively. Waves along and close to this shortest route will thus dominate and AB0 will be the route along which the light is seen to travel.

10. Fermat's principle is the main principle of quantum electrodynamics where it states that any particle propagates over all available paths and the interference of its wavefunction over all those paths gives the correct probability of detection of this particle. Thus the extremal (shortest, longest or stationary) paths contribute into this interference most as they can not be completely canceled out. In the classic mechanics of waves, Fermat's principle follows from the extremum principle of mechanics (see variational principle).

11. Propagation in a Homogeneous Medium

12. Why? • 直线传播？ • Ray Optics只涉及光场强度 • 各向同性材料的对称性 • 光束直线传播 • 光束的扩散？ 中心依然直线传播

13. 非直线传播的模式？ • Airy Beams(from Wiki) • A cross section of an Airy beam would reveal an area of principal intensity, with a series of adjacent, less luminous areas trailing off to infinity • As the beam propagates, it does not diffract, i.e., does not spread out. The Airy beam also has the characteristic of freely accelerating. As it propagates, it bends so as to form a parabolic arc. • 不属于Ray Optics范畴

14. Reflection from a Mirror

15. Reflection and Refraction at the Boundary Between Two Media

16. 1.2 SIMPLE OPTICAL COMPONENTS

17. 高中内容 自学

18. Total Internal Reflection

19. Not So Simple 在发射过程中可能产生位移， 与靠近界面的波的泄漏有关 Otto Kretschmann Evanescent Wave

20. GH shift

21. 1.4MATRIX OPTICS

22. Chapter 2 WAVE OPTICS

23. 需要记住的参数

24. 390760 nm, 100 THz10000 THz

25. Why this wavelength? ………..SUN!

26. About THz…… • 频率在0.1THz到10THz(0.33THz)范围的电磁波，波长大概在0.03到3mm范围，介于微波与红外之间。 • 涉及太赫兹波段的研究结果和数据非常少，主要是受到有效太赫兹产生源和灵敏探测器的限制，因此这一波段也被称为THz间隙。 • 优点 • 方便进行时间分辩的研究，能够有效地抑制远红外噪声 • 许多生物大分子的振动和转动能级、半导体材料、超导材料等的声子振动能级落在THz 波段范围 • 光子的能量低，不容易破坏被检测物质 • 许多的非金属非极性材料对THz 射线的吸收较小，使得探测材料内部信息成为可能。

27. 2.1 POSTULATES OF WAVE OPTICS

28. 可以从Maxwell’s equations推导出 但对其中电场和磁场分量的耦合，做暗含处理！

30. Comments • 时空反衍对称性 • Time-Spatial Inversion Symmetry • x-x, t-t, 形式不变 • 由一个平面内的电磁场分布，可以得到其它处的场分布 • Reciprocal

31. Non- Reciprocal ? Magneto-Optical Nonlinear Optics Polarization Manipulation Optical Diode / Isolator Science_333_729 (2011) and the comments

32. 2.2 MONOCHROMATIC WAVES

33. Plane Wave

34. The Spherical Wave

35. Comments • About i and j • Different preferences for Optics Society and Engineering Society • i = j

36. Comments kz―t=k(z ― ct) • exp(-jk.r) or exp(jk.r) ? • Depend on the choice of current j or energy flux S • Outward S

37. Paraxial Waves

38. The Paraxial Helmholtz Equation

39. Importance of this Assumption 紧聚焦/超分辨成像时，不能使用旁轴近似，必须考虑纵向场的存在 • 方便求解 • Nonlinear Optics • Limitation? • Tightly focused beams • Emergence of longitudinal EM fields

40. 2.4 SIMPLE OPTICAL COMPONENTS