The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θp Brewster’s Law relates the polarizing angle to the index of refraction for the material



The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontally The vertical part of the vector simultaneously causes them to vibrate vertically Horizontally and vertically polarized waves are emitted
Birefringence
The molecular "spring constant" can be different for different directions.
Birefringence
The x- and ypolarizations can see different refractive index curves.
Birefringence can separate the two polarizations into separate beams
o-ray
no ne
e-ray
Due to Snell's Law, light of different polarizations will bend by different amounts at an interface.
Wire grid polarizer in the visible
Using semiconductor fabrication techniques, a wire-grid polarizer was recently developed for the visible.
The spacing is less than 1 micron.
Calcite
Calcite is one of the most birefringent materials known.
Birefringence
如：白纸上涂一黑点，将 方解石放在纸上，可观察到两 个黑点，旋转方解石，一个黑 点不动，另一个黑点旋转。
这种一束入射自然光进 入各向异性的晶体（如方解石 晶体）后变成两束折射光的现 象称为双折射现象。 双折射的两条光线都为线偏光，且在晶体内的传 播速度不同。
sin i n21 const sin r sin i const sin r
e光 o光
Optical axis of crystals
In uniaxial crystals, the refractive indices, and hence the velocities of the o and e waves become equal along a unique direction called optical axis.
- biaxial
IF n0 n1ORn0 n2
Huygen‟s Principle in Crystal
Surfaces parallel and perpendicular to the optic axis
(a) (b)
........................ . . . . . . . .. . . . . . .. . .. . . . . . .. . . . . . . . . . . . . . . . .. . . . .. . . . .
Light in anisotropic media
—— crystal optics, birefringence
(下册第七章)
Different Polarization
y
E-field variation over time (and space)
a
x
E-field variation over time (and space)
y
x
E-field variation over time (and space)
y
kz-wt = 90°
kz-wt = 0°
x
Polarization by Selective Absorption

The most common technique for polarizing light Uses a material that transmits waves whose electric field vectors in the plane parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular to that direction
• K // optical axis, no=ne. o and e beam are collinear. • K optical axis |no-ne | and therefore the deviation between o and e beams reach maximum.
A
101.5
78.5
B
Doubly refracting crystals may be classified as uniaxial or biaxial.
Principle plane
晶体内任一光线和光轴所决定的平面称为此光线的主平面 。 • o 光、e 光都有各自的主平面 光轴
e光
71
• o光的振动方向与它的主平面垂直

n

sinq p cosq p
tanq p
θp may also be called Brewster’s Angle
Polarization by Scattering

When light is incident on a system of particles, such as a gas, the electrons in the medium can absorb and reradiate part of the light
Selective Absorption

E. Land found a material that polarizes light through selective absorption
He
called the material polaroid
The
oriented molecules readily absorb light whose electric field vector is parallel to their lengths and transmit light whose electric field vector is perpendicular to their lengths
Polarization by Selective Absorption

The principle of polarization: A transverse wave is linearly polarized when its vibrations always occur along one direction. (a) The rope passes a slit parallel to the vibrations, but (b) does not pass through a slit that is perpendicular to the vibrations.
Io
is the intensity of the polarized wave incident on the analyzer is known as Malus’ Law and applies to any two polarizing materials whose transmission axes are at an angle of θ to each other
(c) (a) and (b) are parallel to the optic axis while (c) is perpendicular.
IF n0 n1ORn0 n2
Therefore: If ne > no, material is said to be positive uniaxial. (e.g. quartz, no=1.543, ne=1.552) If ne< no, material is said to be negative uniaxial. (e.g. calcite, ne = 1.49, no = 1.66 at 600nm) The principal refractive indices are both measured perpendicular to the optic axis. Direction of the lesser index is called the fast axis because the speed of light is faster in that direction.
Wire Grid Polarizer
Input light contains both polarizations