1

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！

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 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。

/c c d

Group Velocity

c

c.cosθ

一种特殊的光学延迟线 θπ/2, 越慢

Field Distributi

ons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>dc=/2 /c c d

But coaxial PEC waveguide supports m=0 TEM mode, which in non-cutoff!

PLANAR DIELECTRIC WAVEGUIDES

Comparing to Section 1No 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 ……

e of d r

Examples

PLANAR-MIRROR RESONATORS

Resonator Modes

Interference … standing wave …

Similar to 1D waveguides …

Smaller d larger vf (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

E0 E1 E2

E3E4 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

201210 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 nL

nLdL+nRdR=mλ/2 Solution of m=0 is possible

dL=―nRdR/nL

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

END

Homework 07 EXERCISE 7.1-1

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 8.2-25 每一项的物理意义。 Problems 8.2-6

Homework 10 EXERCISE 10.1-1

Problem 10.1-7