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Chapter 07&08 & 09 & 10

Chapter 07&08 & 09 & 10. PHOTONIC-CRYSTAL OPTICS. 下几页列出重 要的概 念，需掌握. WaVE Transfer Matrix. Scattering Matrix. Airy's formulas. Fabry -Perot Etalon. Bragg Grating. Bloch Modes. Chapter 8. Comments…why?. Comments…integration circuits. 在小空间里控制光场的传播 ， 用 于信息交换及应用！.

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Chapter 07&08 & 09 & 10

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  1. Chapter 07&08 & 09 & 10

  2. PHOTONIC-CRYSTAL OPTICS • 下几页列出重要的概念，需掌握

  3. WaVETransfer Matrix

  4. Scattering Matrix

  5. Airy's formulas

  6. Fabry-Perot Etalon

  7. Bragg Grating

  8. Bloch Modes

  9. Chapter 8

  10. Comments…why?...

  11. Comments…integration circuits 在小空间里控制光场的传播，用于信息交换及应用！

  12. Photonic Crystals Metamaterials 尺寸更小，亚波长，<200nm • From a similar consideration

  13. Planar-Mirror Waveguides

  14. Firstly, from ray optics… • Reflection by mirrors • Correct in microwave frequency

  15. Why?... At microwave • Perfect electric conductor (PEC) • ε = ― • n= j • |r|=1 • Phase change: 0 or π （半波损） • 0: 边界场强极大 • π: 边界场强为零

  16. Periodicity  Discrete modes

  17. Propagation Constants

  18. Dispersion Relation 截止频率f0。f <f0 (波长大时)模式消失，无法传播。在截止频率处，群速度为零，即慢光效应。

  19. Group Velocity c.cosθ c 一种特殊的光学延迟线 θπ/2, 越慢

  20. Field Distributions 正交归一本征模式

  21. Multimode Fields

  22. Comments • m=1,2,3… • How about m=0? • Infinite field amplitude, not allowed • Cutoff size: d>dc=/2 But coaxial PEC waveguide supports m=0 TEM mode, which in non-cutoff!

  23. PLANAR DIELECTRIC WAVEGUIDES

  24. Comparing to Section 1 No longer PEC boundary conditions • With field outside the core • With non-zero/pi reflection phase Now Electromagnetic optics

  25. Phase condition

  26. Field Distributions … with EM boundary conditions!

  27. Dispersion Relation

  28. Dispersion…

  29. Group Velocity Goos-Hänchenshift 当相位为常数时,v=c.cosθ

  30. Goos-Hänchen shift • Usually… positive and very small, <0.05λ • Could be negative and with large value in left-handed metamaterials • Backward energy flux • Strong dispersion in LHM

  31. GH shift can make a cavity nature_450_397

  32. Two-Dimensional Waveguides

  33. Boundary Conditions

  34. Applications

  35. Optical Coupling in waveguides

  36. Input Couplers 尽可能大的交叠积分

  37. End-Fire configuration

  38. Prism & Grating Side Couplers To match the wavevectorm…

  39. Fibers 圆柱对称二维光波导，选择性阅读

  40. Vortex modes & Higher-OAM modes

  41. Resonator • From waveguide • Spatial confinement of EM waves • select specific frequencies from a signal • To generate stronger EM field intensity • For applications that need strong EM field • Laser • Quantum Physics • ……

  42. Examples

  43. Planar-Mirror Resonators

  44. Resonator Modes Interference … standing wave …

  45. Similar to 1D waveguides … Smaller d  larger vf (uncertainty principle)

  46. As Traveling waves Multiple interference…

  47. Traveling-Wave Resonator 驻波的缺点：场强分布不均匀，例如E~cos(kz)。 Traveling wave? 场强均匀分布，优点: 例如可以充分利用增益介质等。

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