Chapter 6
POLARIZATION OPTICS
1
From EM optics…
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Vectorial nature
2-dimensional freedom in the E & H components

Even 3-dimensional freedom in optical beams
Examples
 Maxwell’s equations
 Boundary conditions
 Conservation laws on momentum k and
energy flux S
6.1 POLARIZATION OF LIGHT
Consider a Plane wave…
2维的自由度
About Eq. (6.1-3): express any field by the eigen-states of the whole system
Plane EM waves are the eigen-states of isotropic media
Polarization Ellipse
Linearly Polarized Light
ψ= 0 or π
同相或反相
Circularly Polarized Light
ψ= 土π/2 and ax=ay
沿着光束入射的方向看去，即往-z方向观测
 眼睛作为一个探测器
根据左右手特性，确定Right or Left
Poincaré (庞加莱) Sphere
Stokes Parameters
3个独立变量
S0: 强度，S3: 偏振态
 线偏：0，圆偏：1
Berry / Geometric phase
偏振操作可以导致Berry
/Geometric phase
 Adiabatic evaluation
 A close loop in the Poincaré
Sphere
回归到出始态时，受到一个附
加的相位变化，即Berry
Phase
 的大小为环路对应的固体角
的一半
在量子体系中有类似的效应，最初Berry提出这
套理论也是针对量子体系中量子态的绝热变换
PRL 57, 937 (1986)
左右旋相位差（Berry Phase）线偏振的偏振态旋转
Nature Photonics 2, 748 (2008)
Similar for EM modes…
仅针对2维空间
Coordinate Transformation
Jones matrix
Normal Modes
Eigen-functions or Eigen-states
Others
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谁更基本？线偏振 or 圆偏振
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圆偏振：Spin Angular Momentum=ħ，其它偏振？线性叠
加！
类比于量子态的eigen-，各向同性（真空）材料里，圆偏
振更基本
Optical Activity也有同样结论
 Polarization of an EM
Beam with z component？
 尚未定义
 3个变量，32=9个
张量元
6.2 REFLECTION AND REFRACTION
Electric-magnetic
duality
 EH, H-E
 ɛμ, μ-
Internal reflection (n1> n2).
TM Polarization
Applications
Power Reflectance and
Transmittance
r
S z ~  E  H  .z
*
c
2
2
:

E


H
cos


n
: cn cos E 2
6.3 OPTICS OF ANISOTROPIC
MEDIA
Positional and orientational order in
different types of materials
各向同性需要高的对称性：无序 & 立方晶格
Permittivity Tensor
From symmetry…
Index Ellipsoid
Propagation Along a Principal Axis
Along an Arbitrary Direction
先向normal modes（eigne-states or eigenfunctions）空间投影, 然后再叠加！
Propagation in an Arbitrary
Direction
Directions
Directions
normal surface or the k
surface
S的方向为群速度方向
k为相速度方向
物理中：能流方向垂直于等能面
Double Refraction
动量的守恒
能流方向的守恒
Refraction of Rays
如何解释动量守恒？
 平面波？
 对于光束(beam)，为平面波的叠加，
可以观测到！
 可实验观测的是能流（群速度）…
6.4 OPTICAL ACTIVITY AND
FARADAY EFFECT
Normal Modes of the Optically
Active Medium
厄密矩阵正交的本征态两个
本征态为1-2平面内的圆偏振光
Magneto-Optics: The Faraday Effect
可用于制备光隔离器 (optical isolator
or optical diode)
6.5 OPTICS OF LIQUID CRYSTALS
END
Homework
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EXERCISE 6.1-1
EXERCISE 6.1-4
Prove equations (6.2-8) and (6.2-9)
Prove equation (6.4-7)