1. Polarization

2. WHY POLARIZATION? After the study of interference and diffraction we
know that light behaves as wave. So light is a form
of wave motion. But a question still remains that
What type of wave is this?
Longitudinal?
Transverse?

3. Light is an electromagnetic wave and transverse in nature.
Natural light or ordinary light is unpolarized in nature.
Means vibrations take place symmetrically
in all directions in the plane perpendicular to the direction of propagation of light.
Direction of
propagation
Ordinary light

4. Polarized
light
Electric field only going up and down –
say it is linearly or plane polarized.
The process of transforming unpolarized light into polarized light is known as polarization.

5.     Representation of Plane polarized light
Plane polarized light with
Vibration perpendicular to the
Plane of paper
Plane polarized light with
vibrations parallel to the plane
of paper

6. X Z Y Mathematical representation of Plane polarized light
Suppose light is propagating in z-direction .
Mathematically a plane polarized light can be
represented as: X Z Y

7. Production of polarized light
By Reflection: Brewster’s Law
By Refraction: Malus Law
By selective absorption: Dichroic material
By double refraction:
-Nicol Prism
- Wave plates

8. Polarization by reflection: Brewster’s Law
In 1881 Brewster on the basis of his experimental observations discovered that when unpolarized light is incident at polarizing angle on the dielectric medium the reflected light is completely plane polarized. The polarizing angle is different for different reflecting surfaces.
According to him the tangent of polarizing angle (θp) is equal to the refractive index of the medium that is n1 n2

9. Use of Polaroid

10. Law of Malus Where I - is intensity of transmitted light.
I0 - is intensity of incident light.
θ - is angle between plane of incident light and direction of polarizer.
Unpolarized light have E field vibration in all directions.
Therefore I = I0 <cos2> = I0/2

11. Two consecutive polarizers.

12. Quest: 22.10 (page-22.38) Optics 4th ed by Ajoy Ghatak
Consider two crossed Polaroids placed in the path of an unpolarized beam of intensity I0. If we place a third Polaroid in between the two then, in general, some light will be transmitted through . Explain this phenomenon.
Assuming the pass axis of the third polaroid to be 450 to the pass axis of either of the polaroids, calculate the intensity of the transmitted beam. Assume that all the polaroids are perfect Ans: I0/8
Quest: An unpolarized light passes through a vertically placed polarizer having horizontal polarization axis. Subsequently it passes through a polarizer with its pass axis at 90o with respect to vertical and two polarizers having their polarization axes at an angle 30o and 60o with vertical respectively.
What will be the intensity of the emergent light? Ans : (3/32)I0

13. Polarization by multiple reflection

14. Polarization by Absorption: Dichroic materials
A number of crystalline materials absorb more light in one incident plane than another, so that light progressing through the material become more and more polarized as they proceed. This anisotropy in absorption is called dichroism. There are several naturally occurring dichroic materials, and the commercial material polaroid also polarizes by selective absorption.
Tourmaline crystal
is a dichroic material

15. Wire grid polarizer
It essentially consists of a large number of thin copper wires placed parallel to each other. When an unpolarized electromagnetic wave is incident on it then the component of the electric vector along the length of the wire is absorbed. This is due to the fact that the electric field does work on the electrons inside the thin wires and the energy associated with the electric field is lost in the joule heating of the wires. On the other hand the component of the electric field vector along the other axis passes through without disturbances. So the emergent wave is linearly polarized with the electric vector along x axis.

16. The system to be effective for the y component to be perfectly absorbed the spacing between the wires should be less than wavelength of light used. So it is difficult to fabricate the wire grid polarizer for visible light. To avoid this situation long chain polymer molecule may be used which contain atoms like iodine which provide high conductivity along the length of the chain.

17. These long chain molecules are aligned so that they are almost parallel to each other. Because of high conductivity of iodine the electric field parallel to the molecules gets absorbed. A sheet containing such long chain polymer molecules is known as Polaroid. When light beam incident on such Polaroid the molecules absorb the component of the electric field which is parallel to the direction of the alignment because of the high conductivity provided by the iodine atoms the component perpendicular to it passes through. So it is similar to the wire grid polarizer. Since the spacing between two adjacent long chain molecules is small compared to the optical wavelength the Polaroid is usually very effective in producing polarized light.

18. Wire Grid Polarizer
Input light contains both polarizations
The light can excite electrons to move along the wires, which then
emit light that cancels the input light. This cannot happen perpen-
dicular to the wires. Such polarizers work best in the IR.
Polaroid sheet polarizers use the same idea, but with long polymers.

19. 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.

20. DOUBLE REFRACTION

21. when unpolarized light passes through a uniaxial crystal it splits up into two refracted rays.
(Extraordinary)
E-ray 
1020 
O-ray 
(ordinary)     i re ro  
Principal section
780
Here re > ro
Hence o > e
Optic axis

22. Nicol prism
Calcite
no =
ne =
Canada
balsam
n = 1.55

23. Nicol Prism: Act as Polaroid
Principle: the principle is to remove one of the two
refracted beams in case of doubly refracting calcite crystal By total internal reflection.
canada balsam
Here O-ray will have total internal reflection because no > n(balsam).
TIR of O-ray

24. uses It can be used as polarizer and analyser too. polarizer analyser    
intensity’
maximum 

25. Use of Polaroid

26. Use of Polaroid
Without polarizer
With polarizer

27. Use of Polaroid
Without polarizer
With polarizer

28. Huygen’s explanation of double refraction in uniaxial crystal
More material on Double refraction
Huygen’s explanation of double refraction in uniaxial crystal
One ray obeys the laws of refraction, known as ordinary ray (o- ray).
Other ray does not obey the snell’s law for which sin i /sin r does not remain constant, known as extraordinary ray (e-ray).
Along optic axis velocities of the two rays are same.
Both rays travel along the same path but with different velocities in a direction perpendicular to the optic axis.
difference between the refractive indices for O ray and E ray is known as birefringence =(o-e)
Substance which exhibits different properties in different direction called anisotropic substance.

29. In negative uniaxial crystals the sphere lies inside the ellipsoid, while in positive uniaxial the ellipsoid lies inside the sphere.
In calcite the velocity of O ray is less than velocity of E ray vo < ve so o > e and ro < re
In quartz the velocity of O ray is greater than velocity of E ray vo > ve so o < e and ro > re

30. Different cases
Optic axis in the plane of incidence and inclined to the refracting surface
Optic axis parallel to the refracting surface and in the plane of incidence
Optic axis perpendicular to the refracting surface but lying in the plane of incidence
Optic axis parallel to the refracting surface but perpendicular to the plane of incidence

31. Optic axis parallel to the refracting surface and in the plane of incidence:
E (Fast)
O (Slow)
 : angle of inclination of the plane of vibration of the incident PPL to the optic axis.

32. Superposition of two plane polarized disturbancesy x z

33. 2) When  = (2n+1)/2 1) When  = 0 or n
Superposition of two plane polarized disturbances
1) When  = 0 or n
PLANE POLARIZED.
2) When  = (2n+1)/2
SO THE LIGHT IS ELLIPTICALLY POLARIZED.
3) When  =(2n+1) /2 and Eoy=Eox
SO THE LIGHT IS CIRCULARLY POLARIZED.

34. Optic axis parallel to the refracting surface and in the plane of incidence:
E (Fast)
O (Slow)
: angle of inclination of the plane of vibration of the incident PPL

35. A plane polarized light is incident on a double refracting plate of width d. As soon as the PP light enters the plate, it can be resolved into two components, one parallel (e ray) and other perpendicular to the optic axis(o ray). For e ray the refractive index is (ne )and o ray it is (no)

36. Retarders
This is a class of optical devices which introduce a phase difference between e- and o-rays. These are in the form of plates of doubly refracting crystal cut in such a way that optic axis is parallel to the refracting surfaces.
Optic axis θ
Plane polarized
Ed= optical path length of o-ray d
Od = optical path length of o-ray
(E ~ O)d = = path difference between e- and o-rays

37. y
Optic axis θ x
θ = angle made by vibration of plane polarized ray with the optic axis d z
X=0
From the figure, y- and z-components of the vibration would be
(e ray)
(o ray)
Where k = /c represents free space propagation constant.
At x = 0 we have,

38. Inside the crystal the two components can be written as:
Therefore at the emerging surface of the crystal, components would be
Thus phase difference at the emerging surface would be,
or path difference between o- and e-ray at the refracting surface would be

39. Quarter wave plate
If doubly refracting crystal is having thickness d such that path difference between E-ray and O-ray is /4 i.e. or
The crystal is known as Quarter Wave Plate (QWP).
Thus the plane polarized light with vibrations making angle θ with the optic axis incident normally on the refracting face of the quarter wave splits into e-wave and o-wave. After transmission through the crystal they have a phase difference /2 and resultant of these two vibration will be elliptically polarized wave or a circularly polarized wave if θ = 450.
Optical Path difference
= (2n+1)λ/4
n = 0,1,2,…
Phase difference
= (2n+1)π/2
For n = 0, 2, 4,….. Emergent light will be LCP and n = 1, 3, 5,… RCP

40. Half wave plate
If doubly refracting crystal is having thickness d such that path difference between E-ray and O-ray is /2 i.e.
Optical Path difference
= (2n+1)λ/2
n = 0,1,2,…
Phase difference
= (2n+1)π
The crystal is known as Half Wave Plate (HWP).
Thus the plane polarized light with vibrations making angle θ with the optic axis incident normally on the refracting face of the half wave splits into e-wave and o-wave. After transmission through the crystal they have a phase difference  and resultant of these two vibration will be plane polarized wave.

41. RECAP 1. or The emergent ray will be linearly polarized light. 2.
The emergent ray will be circularly polarized if θ is 450 otherwise elliptically polarized light.

42. Quarter wave plate (QWP)
For n = 0, 2, 4,….. Emergent light will be LCP and for n = 1, 3, 5,… RCP
Use: QWP Convert plane polarized (PP) to circular polarized (CP) or elliptically polarized (EP) light and vice verse.
Note: Birefringence is (E ~ O)

43. Half wave plate (HWP)
This is a plate of double refracting crystal having thickness t such that path difference between E-ray and O-ray is /2.
(E ~ O)t = /2
or (2n+1)λ/2
n=0,1,…
Phase difference:  =π
Use: HWP Convert Right circular polarized (RCP) or right elliptically polarized (REP) light to LCP or LEP and vice verse.
Linearly polarized light entering a wave plate can be resolved into two waves, parallel (shown as green) and perpendicular (blue) to the optical axis of the wave plate. In the plate, the parallel wave propagates slightly slower than the perpendicular one. At the far side of the plate, the parallel wave is exactly half of a wavelength delayed relative to the perpendicular wave, and the resulting combination (red) is orthogonally polarized compared to its entrance state.
Note: Birefringence is (E ~ O)
Similarly λ (Full wave Plate) , λ/6 plate or λ/8 plate etc

44. PRODUCTION OF POLARIZED LIGHT
1. Plane polarized light:
Un-polarized light
Plane polarized light
2. Circularly polarized light:
Un-polarized light
Plane polarized light
Vibration makes 450 angle with optic axis.

45. 3. Elliptically polarized light:
QWP
Elliptically polarized
Un-polarized light
Plane polarized light
Vibration makes angle other than 450 with optic axis.

46. ANALYSIS OF POLARIZED LIGHT
1. Plane polarized light:
Variation of intensity from a maximum to zero

47. 2. Circularly polarized light:
No variation in intensity.
- It may be a unpolarized or
- It may be a circularly polarized light
If variation in intensity is like plane polarized light original light is circularly polarized.
QWP
Otherwise, original light is un-polarized.

48. 3. Elliptically polarized light:
- It may be a partially polarized or
Variation of intensity from a maximum to minimum  0
- It may be an elliptically polarized light
If variation in intensity is like plane polarized light original light is elliptically polarized.
QWP
Otherwise, original light is un-polarized.

49. Scheme of analysis of a given beam of light
Incident on a rotating nicol prism
Variation in intensity with minimum non zero
Coclusion: Given light is either elliptically polarized or partially polarized
Variation in intensity with minimum zero
Coclusion: Given light is plane polarized
No Variation in intensity
Coclusion: Given light is either circularly polarized or unpolarized.
Incident on a QWP with optic axis || to the pass axis of the analyzing nicol at the position of maximum intensity and then examined by rotating nicol prism
Incident on a QWP in any position and then examined by rotating nicol prism
Variation in intensity with minimum zero
Coclusion: elliptically polarized
Variation in intensity with minimum non zero
Coclusion: partially polarized
Variation in intensity with minimum zero
Coclusion: circularly polarized
No Variation in intensity
Coclusion: unpolarized.

50. Optical activity
Phenomenon of rotation of the plane of vibration is called rotatory polarization and this property of the crystal (substance) is called optical activity or optical rotation and substances which show this property are called optically active substances.
When a beam of plane polarized light propagates through certain substances or crystals, the plane of polarization of the emergent beam rotated through a certain angle.
This phenomenon is called rotatory polarization and this property of the crystal and other substances is called optical activity or optical rotation and substances which show this property are called optically active substances

51. There are two types of optically active substances:
Righthanded or dextro-rotatory:-
Sodium chlorate, cane sugar.
Left handed or leavo rotatory:-
Fruit sugar, turpentine.
The property of rotation of plane of vibration is not only possessed by quartz, but also by all organic compounds whose molecules are asymmetric like sodium chlorate, sugar crystal and solutions like turpentine, sugar solution, quinine sulphate solutions etc.
Note: Quartz is an optically active substance.
Calcite does not produce any rotation.

52. Biot’s law for optical rotation
Applications:
1. To find the percentage of optically active material present in the solution.
2. The amount of sugar present in blood of a diabetic patient determined by measuring the angle of rotation of the plane of polarization.

53. Quartz is an optically active material
Quartz is an optically active material. First time experimentally observed by Arago in 1811. =0
Observation: In the absence of Quartz, I=0.
In the presence of quartz, I is not zero.
Conclusion: Plane polarized light is rotated because of quartz
Note: In quartz, when optic axis is perpendicular to refracting face then only we can observe the rotation of PP light other -wise it will act just as a wave plate which produce phase difference in e-ray and o-ray.

54. Fresnel’s theory of optical rotation
Fresnel’s theory of optical rotation by an optically active substance is based on the fact that any plane polarized light may be considered as resultant of two circularly polarized vibrations rotating in opposite direction with the same velocity or frequency.

55. Fresnel’s theory of optical rotation
In an optically inactive substance these two circular components travel with the same speed along the optic axis. Hence at emergence they give rise to a plane polarized light without any rotation of the plane of polarization.

56. Fresnel’s theory of optical rotation
In an optically active crystal, like quartz , two circular components travel with different speeds so that relative phase difference is developed between them.
If vR>vL the substance is dextro-rotatory
And if vR< vL the substance is leavo-rotatory

57. Fresnel’s theory of optical rotation
This explanation was based on the following assumptions:
A plane polarized light falling on an optically active medium along its optic axis splits up into two circularly polarized vibrations of equal amplitudes and rotating in opposite directions –one clockwise and other anticlockwise.
In an optically inactive substance these two circular components travel with the same speed along the optic axis. Hence at emergence they give rise to a plane polarized light without any rotation of the plane of polarization.
In an optically active crystal, like quartz , two circular components travel with different speeds so that relative phase difference is developed between them.
In dextro-rotatory substance vR>vL and in leavo rotatory substance vL>vR..
On emergence from an optically active substance the two circular vibrations recombine to give plane polarized light whose plane of vibration has been rotated w.r.t that of incident light through a certain angle depends on the phase diff between the two vibrations.

58. “Fresnel Theory of Rotation” (optic axes perpendicular to refracting face) Plane polarized means resultant of R and L.
Note: We can prove it mathematically.

59. For optically active substances   

60. Specific rotation
The specific rotation of an optically active substance at a given temperature for a given wavelength of light is defined as the rotation (in degrees) produced by the path of one decimeter length in a substance of unit density (concentration)
The unit of specific rotation is deg.(decimeter)-1(gm/cc)-1

61. Polarimeters
A device designed for accurate measurement of angle of rotation of plane of vibration of a plane polarized light by an optically active medium is said to be a polarimeter.
Two Types:
Laurent's Half shade polarimeter
Bi-quartz polarimeter

62. Bi-quartz Device 
Right handed Quartz
Left handed Quartz

63. Bi-quartz Device
Transmission axis of analyzer
Transmission axis of analyzer
White light source is used.
Two semicircular quartz plates (Right and Left handed) with Optic axis perpendicular to crystal surface (rotation effect only).
Device is designed for yellow color.
YY’ is tint of passes
If Analyzer axes is perpendicular to YY’ then yellow color will be disappeared and we can get resultant of Red and Blue colour (Reddish violet color) as min intensity.
Transmission axis of analyzer
Biquartz is much more sensitive and accurate then Half shade polarimeter. But having major drawback for color blind person.