第06 章

```Chapter 6
POLARIZATION OPTICS
1
From EM optics…


Vectorial nature
2-dimensional freedom in the E &amp; 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

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
Poincar&eacute; (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

/Geometric phase
 A close loop in the Poincar&eacute;
Sphere

Phase
 的大小为环路对应的固体角
的一半

PRL 57, 937 (1986)

Nature Photonics 2, 748 (2008)
Similar for EM modes…

Coordinate Transformation
Jones matrix
Normal Modes
Eigen-functions or Eigen-states
Others






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

6.2 REFLECTION AND REFRACTION
Electric-magnetic
duality
 EH, H-E
 ɛμ, μ-
Internal reflection (n1&gt; 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

Permittivity Tensor
From symmetry…
Index Ellipsoid
Propagation Along a Principal Axis
Along an Arbitrary Direction

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

Double Refraction

Refraction of Rays

 平面波？
 对于光束(beam)，为平面波的叠加，

 可实验观测的是能流（群速度）…
6.4 OPTICAL ACTIVITY AND
Normal Modes of the Optically
Active Medium

or optical diode)
6.5 OPTICS OF LIQUID CRYSTALS
END
Homework




EXERCISE 6.1-1
EXERCISE 6.1-4
Prove equations (6.2-8) and (6.2-9)
Prove equation (6.4-7)
```