Transcript 3. Polarization 2016..

Polarization
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?
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
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.
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
Mathematical representation of Plane polarized light
Suppose light is propagating in z-direction .
Mathematically a plane polarized light can be
represented as:
E x  z , t   i E0 x coskz  t 
or
E y  z , t   j E0 y coskz  t 
X
Z
Y
Production of polarized light
1.
2.
3.
4.
By Reflection: Brewster’s Law
By Refraction: Malus Law
By selective absorption: Dichroic material
By double refraction:
-Nicol Prism
- Wave plates
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   tan 
p
n 
2
 p  tan 1 
n 

 1
Show that  2   p 
tan  p 
n1
sin  p
cos  p


2
n2

n1
and snell ' s law
n1 sin  p  n2 sin  2
n2
therefore
cos  p  sin  2  cos (90   2 )
 p  2 

2
Use of Polaroid
Law of Malus
I  I 0 cos 2 
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
• Two consecutive polarizers.
Quest: 22.10 (page-22.38) Optics 4th ed by Ajoy Ghatak
(a) 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.
(b) 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
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
DOUBLE REFRACTION
• when unpolarized light passes through a uniaxial crystal it
splits up into two refracted rays.
(Extraordinary)
E-ray

1020


re 
i
Here re > ro
Hence o > e
780



 O-ray

(ordinary)
ro
Principal section
Optic axis
Nicol prism
Calcite
no = 1.6584
ne = 1.4864
Canada
balsam
n = 1.55
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
uses
It can be used as polarizer and analyser too.
polarizer
 



analyser
intensity’
maximum
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 (oray).
•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.
In negative uniaxial crystals the sphere lies inside the ellipsoid, while in
positive uniaxial the ellipsoid lies inside the sphere.
In quartz the velocity of O ray
is greater than velocity of E
ray.
vo > ve so o <
e and ro > re
In calcite the velocity of O ray
is less than velocity of E ray.
vo < ve so o > e and ro
< re
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
Optic axis parallel to the refracting surface and in the plane
of incidence:
E (Fast) E y  E cos 

E  E0 sin(kz  t )
Ex  E sin 
O (Slow)
Ray entered
Ex ( z , t )  E0 x sin(kz  t )
E y ( z, t )  E0 y sin(kz  t )
Emergent Ray (with the phase difference  )
Ex ( z , t )  E0 x sin(kz  t )
E y ( z, t )  E0 y sin(kz  t   )
Optic axis
 : angle of inclination of
the plane of vibration of
the incident PPL to the
optic axis.
SUPERPOSITION OF TWO PLANE POLARIZED DISTURBANCES
Consider two linearly polarized waves propagating along z-axis with their
E-field vectors oscillating along two perpendicular directions.
Ex ( z , t )  E0 x sin(kz  t )...(1)
 : the phase difference introduced
E y ( z , t )  E0 y sin(kz  t   )...(2)
with in the crystal between the two
From equation 1 and  2 
orthogonal components of the incident ray.
Ex ( z , t )
 sin(kz  t )...(3) and
E0 x
E y ( z, t )
 sin(kz  t   )...(4)
E0 y
E y (z, t)
E 0y
E y (z, t)
E 0y

Ey
E 0y
y
x
 sin(kz  t)cos   cos(kz  t)sin 
E x (z, t)
E x 2 (z, t)

cos   sin  1 
E 0x
E 0x 2

2
Ex
E
cos   sin  1  x 2
E 0x
E 0x
z
Squaring both sides

Ey2
E 0y 2
Ex 2
Ex Ey
2


2
cos


sin

2
E 0x
E0x E0y
This is the equation of the ellipse.
SUPERPOSITION OF TWO PLANE POLARIZED DISTURBANCES
Squaring both sides

Ey2
E 0y 2
Ex 2
Ex Ey


2
cos   sin 2 
2
E 0x
E0x E0y
This is the equation of the ellipse.
1) When  = 0 or n
Ey
Ex


Eoy Eox
PLANE POLARIZED.
2) When  = (2n+1)/2
E2y E2x
 2 1
2
E oy E ox
SO THE LIGHT IS ELLIPTICALLY POLARIZED.
3) When  =(2n+1) /2 and Eoy=Eox
SO THE LIGHT IS CIRCULARLY POLARIZED.
Quarter wave plate (QWP)
This is a plate of double refracting crystal having thickness 'd'
such that path difference between E-ray
and O-ray is  /4
( E  o )d   / 4 or (4n  1) / 4
(2n  1) / 4
where n=0,1,2,3,...
Phase difference   (2n  1) / 2
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)
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.
Note: Birefringence is (E ~ O)
Similarly λ (Full wave Plate) , λ/6 plate or λ/8 plate etc
PRODUCTION OF POLARIZED LIGHT
1. Plane polarized light:
Un-polarized light
Plane
light
polarized
2. Circularly polarized light:
Un-polarized light
Plane
light
polarized
Vibration makes 450
angle with optic
axis.
3. Elliptically polarized
light:
Un-polarized light
QWP
Elliptically
polarized
Plane polarized light
Vibration makes angle other
than 450 with optic axis.
ANALYSIS OF POLARIZED LIGHT
1. Plane polarized light:
Variation of intensity from
a maximum to zero
2. Circularly polarized
light:
No variation in - It may be a
intensity.
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.
3. Elliptically polarized light:
Variation of intensity - It may be a partially
from a maximum to polarized or
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.
Scheme of analysis of a given beam of light
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
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
Variation in intensity with
minimum zero
Coclusion: elliptically
polarized
Variation in intensity
with minimum non zero
Coclusion:
partially
polarized
No Variation in intensity
Coclusion: Given light is either
circularly
polarized
or
unpolarized.
Incident on a QWP in any position and
then examined by rotating nicol prism
Variation in intensity
with minimum zero
Coclusion: circularly
polarized
No
Variation
intensity
Coclusion:
unpolarized.
in
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.
There are two types of optically active substances:
• Righthanded or dextro-rotatory:Sodium chlorate, cane sugar.
• Left handed or leavo rotatory:Fruit sugar, turpentine.
Note: Quartz is an optically active substance.
Calcite does not produce any rotation.
Biot’s law for optical rotation
 
 : angle of rotation of the plane of vibration for any given wavelength.
: length of the optically active medium traversed.
 In case of solution or vapours
  C, C: concentration of the solution or vapour
 The total rotation produced by a number of optically active substances is equal
to the algebric sum of the individual rotations.
  1   2  3  ....  i
i
The anticlockwise rotations are taken +ve ;
while the clockwise rotations are taken -ve.
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.
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.
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.
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.
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
Fresnel’s theory of optical rotation
This explanation was based on the following assumptions:
1. 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.
2. 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.
3. In an optically active crystal, like quartz , two circular components travel
with different speeds so that relative phase difference is developed between
them.
4. In dextro-rotatory substance vR>vL and in leavo rotatory substance vL>vR..
5. 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.
“Fresnel Theory of Rotation”
(optic axes perpendicular to refracting face)
Plane polarized means resultant of R and L.
Note: We can prove it mathematically.
For optically active substances
R : the refractive index of the clockwise vibration
L : the refractive index of anticlockwise vibration
‘d’ : the thickness of the quartz plate,
thus the path difference between the two components
   L

R  d
Corresponding phase difference will be
2

d  L  R 

Angle of rotation of plane of vibration will be
 
c
c 


    L R  d or

d
2 
  vL vR 
In case of left handed optically substances vL  vR
In case of right handed optically active crystals vR  vL
 cd  1 1 
L 
  
  vR vL 
 cd  1 1 
R 
  
  vL vR 
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)
10
 
or   
(If is in cm)
C
C
The unit of specific rotation is deg.(decimeter)-1(gm/cc)-1
T

T
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
Bi-quartz Device
 
    L  R  t
2 
Left handed Quartz
Right handed Quartz
Bi-quartz Device
Transmission
axis of analyzer
Transmission
axis of analyzer
Transmission
axis of analyzer
Biquartz is much more sensitive and accurate then Half shade
polarimeter. But having major drawback for color blind person.