Chapter 07&08 & 09 & 10 1

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！

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

PLANAR-MIRROR WAVEGUIDES

Firstly, from ray optics…  Reflection by mirrors  Correct in microwave frequency

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

Periodicity  Discrete modes

Propagation Constants

Dispersion Relation 截止频率 f 0 。 f < f 0 ( 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。

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

Field Distributions 正交归一本征模式

Multimode Fields

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

PLANAR DIELECTRIC WAVEGUIDES

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

Phase condition

Field Distributions … with EM boundary conditions!

Dispersion Relation

Dispersion…

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

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

GH shift can make a cavity nature_450_397

TWO-DIMENSIONAL WAVEGUIDES

Boundary Conditions

Applications

OPTICAL COUPLING IN WAVEGUIDES

Input Couplers 尽可能大的交叠积分

End-Fire configuration

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

FIBERS 圆柱对称二维光波导，选择性阅读

Vortex modes & Higher-OAM modes

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  ……

Examples

PLANAR-MIRROR RESONATORS

Resonator Modes Interference … standing wave …

Similar to 1D waveguides … Smaller d  larger  v f (uncertainty principle)

As Traveling waves Multiple interference…

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。

Fabry-Perot resonator

Method I

Methods II  E1 ： E0 透射 +E3 反射； E3 ： E1 反射；  E2 ： E1 透射； E4 ： E3 透射 E0E1 E2 E3 E4 Much simple Transfer Matrix Method exp(―jkd) 不要忘了相位项 exp(―jkd) ！

r 不能为 1 Resonance  strong dispersion  smaller group velocity 多次反射减缓光的速度

Quality Factor Q Q 越大，共振越强，群速度越小： 空间上对光脉冲的挤压，增强能量密度

Off-Axis Resonator Modes A special design for optical delay purpose … because a longer optical path…

SPHERICAL-MIRROR RESONATORS

Ray Confinement

Resonator stability diagram

Two-Dimensional Rectangular Resonators

Circular Resonators and Whispering-Gallery Modes

Three-Dimensional Rectangular Cavity Resonators

MICRORESONATORS  Microresonators are resonators in which one or more of the spatial dimensions assumes the size of a few wavelengths of light or smaller.

Applications  To confine other elementary excitations  Electrons, Polaritons, ions…  To enhance the interaction of photons with excitations  To enhance the quantum phenomena of excitations  Especially when the size is comparable with the wavelength  Optical Integration circuits

月 19 日 Science

Comment  Size of resonator  Usually a minimum of λ/2  Smaller size d?  From 2dk=2mπ, k=n2π/ λ, one can use a medium with larger n value  To λ/2n

Other possibility?  Metamaterial with negative n L  n L d L +n R d R =mλ/2  Solution of m=0 is possible  d L =―n R d R /n L  两个厚度成正比关系，可以缩 放  腔的厚度可以做的尽可能的小

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Homework 07  EXERCISE  解释什么是 Omnidirectional Reflection 。 我们日常生活中用的镜子是不是 Omnidirectional Reflection ？ 为什么？

Homework 08  解释方程 每一项的物理意义。  Problems 8.2-6

Homework 10  EXERCISE  Problem