Polarization
Table of Contents
1. Introduction to Light & Unpolarized Light
2. Linear (Plane) Polarization
3. Circular Polarization
4. Malus' Law
5. Degree of Polarization
6. Polarization by Re
ection
7. Brewster's Law
8. Double Refraction in Calcite Crystal
9. Ordinary and Extraordinary Rays
10. Birefringence
, Polarization Wave Optics
1. Introduction to Light
The speed of light is given by:
c=
E0
B0
= 3 × 108 m/s (1.1)
where E is the amplitude of the electric
eld and B is the amplitude of the magnetic
eld. Since E ≫ B , the optical properties of light depend primarily on the
0 0
electric
eld.
0 0
1.1 Unpolarized Light
Light waves in which the vibrations of the electric
eld vector are distributed in all possi-
ble directions perpendicular to the propagation direction are called unpolarized
light. In natural (unpolarized) light, the electric
eld oscillates randomly in every trans-
verse direction.
2. Linear (Plane) Polarization
If we oscillate one end of a string up and down, a transverse wave is generated. When
the string executes sinusoidal oscillations in a straight line, the wave is known as a linearly
polarized wave (also called a plane polarized wave), as the string is always con
ned
to the x-z plane.
The displacement for a linearly polarized wave (vibrating in the x-z plane) is:
x(z, t) = a cos(kz − ωt + ϕ) (2.1)
y(z, t) = 0 (2.2)
The string can also be made to vibrate in the y-z plane, giving:
x(z, t) = 0 (2.3)
y(z, t) = a cos(kz − ωt + ϕ) (2.4)
The string can be made to vibrate in any plane containing the z-axis, producing a
superposition of these two modes.
3. Circular Polarization
If we rotate one end of the string on the circumference of a circle, each point of the string
will move in a circular path. Such a wave is known as a circularly polarized wave.
The corresponding displacement equations are:
1
Table of Contents
1. Introduction to Light & Unpolarized Light
2. Linear (Plane) Polarization
3. Circular Polarization
4. Malus' Law
5. Degree of Polarization
6. Polarization by Re
ection
7. Brewster's Law
8. Double Refraction in Calcite Crystal
9. Ordinary and Extraordinary Rays
10. Birefringence
, Polarization Wave Optics
1. Introduction to Light
The speed of light is given by:
c=
E0
B0
= 3 × 108 m/s (1.1)
where E is the amplitude of the electric
eld and B is the amplitude of the magnetic
eld. Since E ≫ B , the optical properties of light depend primarily on the
0 0
electric
eld.
0 0
1.1 Unpolarized Light
Light waves in which the vibrations of the electric
eld vector are distributed in all possi-
ble directions perpendicular to the propagation direction are called unpolarized
light. In natural (unpolarized) light, the electric
eld oscillates randomly in every trans-
verse direction.
2. Linear (Plane) Polarization
If we oscillate one end of a string up and down, a transverse wave is generated. When
the string executes sinusoidal oscillations in a straight line, the wave is known as a linearly
polarized wave (also called a plane polarized wave), as the string is always con
ned
to the x-z plane.
The displacement for a linearly polarized wave (vibrating in the x-z plane) is:
x(z, t) = a cos(kz − ωt + ϕ) (2.1)
y(z, t) = 0 (2.2)
The string can also be made to vibrate in the y-z plane, giving:
x(z, t) = 0 (2.3)
y(z, t) = a cos(kz − ωt + ϕ) (2.4)
The string can be made to vibrate in any plane containing the z-axis, producing a
superposition of these two modes.
3. Circular Polarization
If we rotate one end of the string on the circumference of a circle, each point of the string
will move in a circular path. Such a wave is known as a circularly polarized wave.
The corresponding displacement equations are:
1
