Software and Systems Engineering Standards: Verification and Validation of Sy...
PHYA3-POLARIZATION.ppt. For 1st year B.E. students
1. Prof. J. K. Goswamy
UIET, Panjab University
Chandigarh.
POLARIZATION OF LIGHT
2. It is phenomenon of restricting
electric vector vibrations of light along a plane
which may or may not rotate about the direction of propagation.
Polarization: Basic Concept
3. Plane Wave
It is an infinitely long light wave with a wide wave-front.
Electric and magnetic fields oscillations are mutually
perpendicular and also perpendicular to the direction of
propagation.
Light waves propagate in air with the electric and magnetic field
vectors vibrating with same phase and frequency.
Light wave propagating in the x direction is expressed as:
The electric vector amplitude is 378 times larger than that of the
magnetic vector.
ẑ
t)
-
kx
cos(
B
)
t
x,
(
B
;
ŷ
t)
-
kx
cos(
E
)
t
x,
(
E 0z
z
0y
y
4. Unpolarized (Ordinary) Light
A plane (or ordinary or unpolarized) light wave can be approximated as
constituted by electric field vector oscillating in all possible directions in a
plane perpendicular to the direction of propagation of light.
5. The ordinary light wave is
characterized by its oscillating
electric vector which has
symmetric distribution in the plane
perpendicular to the direction of
propagation. This is unpolarized (or
ordinary or natural) light.
The electric vector vibrations in the
ordinary light can be resolved into
two orthogonal components which
oscillate with same frequency but
can be characterized by different
amplitudes and phase.
6. The shape traced out by vibrating electric vector, as the plane
wave propagates, defines the State of Polarization (SOP) of light.
7. Polarization: Mechanical Analogue
• The light vibrations have been
restricted in vertical direction on
passing through the polarizer 1.
This phenomenon of restricting
light vibrations along a specific
direction is called Polarization.
• The plane of light oscillations is the
plane of vibration. The other plane,
perpendicular to it and devoid of
light oscillations is the plane of
polarization.
9. Superposition of Polarized Waves
Let’s consider two polarized light waves having their light
vector oscillations mutually perpendicular to each other and
propagating along x-direction. These are represented
mathematically as:
These two waves are propagating with a phase difference of θ.
The resultant superposed wave is to be analyzed.
ẑ
)
t
-
kx
cos(
E
)
t
x,
(
E
ŷ
t)
-
kx
cos(
E
)
t
x,
(
E
0z
z
0y
y
10. Both the light waves have electric field oscillations in YZ plane.
We wish to study their time variation in this plane (say x=0),
which will define relation between instantaneous
displacements of two waves and their relative phase.
:
,
1
sin
cos
sin
sin
cos
cos
cos
1
sin
;
cos
;
cos
2
2
get
we
equation
above
the
solving
and
Squaring
E
E
E
E
E
E
t
t
E
E
t
E
E
t
E
E
t
E
E
t
oy
y
oy
y
oz
z
oz
z
oy
y
oz
z
oy
y
2
2
2
sin
cos
2
oy
y
oz
z
oz
z
oy
y
E
E
E
E
E
E
E
E
11. States of Polarization
The equation describing different states of polarization is:
Depending upon relative phase difference between two
superposing waves, we have different SOP as:
,...
2
,
1
,
0
2
)
1
2
(
2
)
1
2
(
n
Polarized
Circularly
E
E
n
Polarized
ly
Elliptical
E
E
n
Polarized
Linearly
n
oz
oy
oz
oy
2
2
2
sin
cos
2
oz
z
oy
y
oz
z
oy
y
E
E
E
E
E
E
E
E
12. The Linearly polarized light is
represented as:
This state of polarization results in
light vector oscillations along a line.
Symmetric distribution of oscillating
electric vector about the direction
of propagation no longer exists.
0z
0y
z
y
E
E
E
E
Linear Polarization
13. Elliptical Polarization
• The elliptic polarized light is mathematically represented as:
• This state of polarization can be viewed as resulting due to superposition of
two linearly polarized waves propagating in same direction with their light
oscillations in mutually perpendicular directions and having relative phase
difference of 90o.
• When the two light oscillations do not have the
same amplitude
and/or
phase difference slightly different from 90o
the resultant electric vector traces out an ellipse in the plane of
vibration which is referred to as the polarization ellipse.
1
E
E
E
E
2
0z
z
2
0y
y
14. REP: Right Elliptic Polarization
(CW rotation of electric vector
while approaching observer)
LEP: Left Elliptic Polarization
(ACW rotation of electric vector
while approaching observer)
Sense in Elliptical Polarization
An ellipse is represented by
relative size of minor/major axes
and orientation in space. The
sense of rotation is CW or ACW.
15. Circular Polarization
If two linearly polarized light waves with
phase difference = 900 and E0z = E0y
superpose, then circularly polarized wave
results:
During propagation of such waves, the
oscillating electric vector rotates at uniform
angular velocity.
Similar to elliptic polarization, we define
right and left circular polarization
1
E
E
E
E
2
0y
y
2
0z
z
18. Polarization by Dichorism
Technique of selective absorption of electric vector vibrations in one
of the two orthogonal directions forms the basis of Dichorism.
19. Wire-Grid Polarizer
Grid is an array of parallel thin
conducting wires with their spacing
comparable to the wavelength of light.
Electric field oscillations parallel to
wires gets attenuated due to current
induced by them in wires. Energy of
this component appears as heat.
Electric field oscillations parallel to
wires get transmitted as polarized
output from the wire grid.
Applicable for polarization of
IR and longer wavelengths.
Wire grids paved the way for
atomic and molecular grids.
20. Dichorism
• Certain crystals strongly
absorb the incident light
oscillations along one
direction (absorption axis
of crystal).
• They easily transmit the
light oscillations in other
direction which is
perpendicular (optic axis
of crystal) to it.
Tourmaline, Quartz
21. J-sheet (Grid of Crystallites)
These were fabricated by E.H. Land in 1928.
Herapathite (Quinine Iodosulphate) crystal was grinded into
millions of needle shaped submicroscopic crystallites.
They were aligned as long parallel crystallite’s chains by using
external electric and magnetic fields.
The Herapathite crystallites can also be aligned by extruding its
viscous colloidal solution (in nitrocellulose) through a very long
and narrow slit.
This polaroid has optic axis perpendicular to the length of chain.
The component of electric vibrations parallel to chain are absorbed
while those perpendicular to the chain get transmitted.
Gives hazy appearance due to scattering of light by numerous crystallites.
22. H-sheet (Grid of Polymer Chain)
A sheet of polyvinyl alcohol is gently heated and stretched in a given
direction resulting in alignment of its hydrocarbon molecules along
long molecular chains.
It is then dipped in ink solution (rich in iodine), which impregnates
the plastic. The iodine molecules get attached along length of long
polymeric chain of hydrocarbon molecules, while forming effective
polymeric chains of their own. The free electrons of iodine move
along the chain thereby emulating a long conducting wire.
The electric field component of light parallel to chain gets absorbed
while the perpendicular component is easily transmitted.
In H-sheets, the hazy appearance is significantly reduced as scattering is
caused by molecules rather than the submicroscopic crystals.
H-sheets are effective polarizers over the entire visible spectrum.
23. K-Polaroids are made by stretching polyvinylene sheet by
slight heating in the presence of dehydrating agent (such
as HCl). Such polaroids are resistant to humidity and heat.
HK Polaroids: A combination of ingredients of H and K
sheet form HK-sheets which are very good polarizers for
light in the near infra-red region.
Other Polaroids: Dichoric sheet linear polarizers are also
available, which are effective in the UV region of
electromagnetic spectrum.
24. Polarization by Reflection
Transparent surfaces selectively reflect one component of electric vector
vibrations at a particular angle of incidence, which is polarized in nature.
25. Polarization By Reflection
The reflection coefficient for light, which has electric
field oscillations in the plane of incidence, reduces
to zero at some angle between 0° and 90°(often
called polarizing or Brewster angle).
The light reflected at that angle is linearly polarized
with its electric field vector oscillations
perpendicular to the plane of incidence and parallel
to the plane of the reflecting surface.
At other angles, the reflected light has admixture of
both the components of polarization.
The transmitted or refracted light remains partially
polarized at all angles of incidence of unpolarized
light.
26. Brewster
Angle
Angle of Incidence
Reflected
Intensity
Reflected
Intensity
Brewster Angle
The reflection coefficients
are different for waves
parallel and perpendicular
to the plane of incidence.
When light is incident at
the Brewster angle, the
reflected light is linearly
polarized because
reflection coefficient for
parallel component is zero.
Reflected intensity for
waves having electric
field oscillations
parallel and
perpendicular to the
plane of incidence.
27. Brewster’s Law
From Fresnel's equations, it can be determined that the
parallel reflection coefficient is zero, when the incident
and transmitted angles sum up to 90°. The use of Snell's
law gives an expression for the Brewster angle.
28. Polarization by Stack of Plates
on
Polarizati
of
Degree
n
n
m
m
I
I
I
I
P
2
2
1
2
S-polarized
P-polarized
Unpolarize
d
30. Polarization by Scattering
The light scattered by scatterers (air molecules or
suspended particles) produce linearly polarized
light, when observed in the plane perpendicular to
direction of propagation of the incident light.
When light is incident on an atom or a molecule, its
electronic cloud oscillates under the influence of
electric vector vibrations. The atom or molecule
behaves like a oscillating dipole which radiates EM
energy like an antenna in all directions other than
its line of oscillation.
If the charges in a molecule are oscillating along the
y-axis, it will not radiate along the y-axis. Therefore,
at 90° away from the beam direction, the scattered
light will always be linearly polarized.
32. What is Double Refraction ?
Double refraction is the splitting of
a ray of light into two rays, when
passing through anisotropic
materials such as Calcite, Quartz.
This phenomenon was first
reported by Erasmus Bartholinus in
1669.
Both the rays of light are plane
polarized with their planes of
polarization being mutually
perpendicular.
33. All transparent crystals, except those in cubic form, are double refracting. However in
most cases, the separation of two images is usually not large enough to be observable.
Property O-Ray E-Ray
Snell’s Law Obeys Snell’s law Doesn’t obey Snell’s law
E-Field Vibrations Electric field vibrations are
perpendicular to optic axis
Electric field vibrations are
along the optic axis.
Refractive Index Material exhibits different refractive index for two waves.
This property is called birefringence.
Shape of wave front Propagates with same
speed in all directions and
wave front is spherical in
shape.
Speed dependent on
direction in crystal w.r.t optic
axis and hence wave front
is spheroidal in shape.
34. Physics of Birefringence
• When light propagates through a transparent
substance, the electrons of the constituent atoms
are driven by the oscillating electric field.
• These electrons, vibrating under the influence of
external electric field, behave like oscillating dipoles,
which radiate electromagnetic energy in all
directions except along their line of oscillation.
• The emitted secondary wavelets superpose to form
the refracted wave-front.
35. • The speed of the refracted light and hence the
index of refraction of the medium is determined
by the frequency of oscillating electric field and
natural frequency of the atomic vibrations.
• Since there is anisotropy in forces binding the
atoms in the molecule as well as electrons in the
constituent atoms, this results in directional
dependence of refractive index of the medium.
36. Birefringence: Uniaxial Crystals
The optic axis is the direction in the birefringent crystal along which
E-ray and O-ray propagate with the same speed.
If the material has single optic axis, it is uniaxial or birefringent in
nature. Such a material is characterized by different refractive indices
for ordinary and extraordinary polarizations.
The birefringent crystal is
Positive If O-ray propagates faster than E-ray.
Negative If O-ray propagates slower than E-ray.
Non-cubic transparent crystals having hexagonal or tetragonal unit
cells are usually uniaxial in nature.
38. Nicol Prism: Construction
It was first type of polarizing prism
invented by William Nicol in 1828.
It consists of a calcite crystal of
length thrice its width. The faces of
this crystal have natural angles of 71o
and 109o.
Crystal faces are cut and polished to
have angles of 68° & 112o.
The crystal is split diagonally and
resulting diagonal plane surfaces of
two halves are polished.
Two polished halves are rejoined by
a layer of canada balsam, which is a
glue with opaque grey color.
71o
A
A’
B
D
C’
C
E-ray
O-ray
68o
An optical device to produce and
analyse plane polarized light.
39. Nicol Prism: Polarizing Action
Unpolarized light enters one end of the crystal and is split
into two polarized (o- and e-rays) rays by birefringence.
The ordinary ray propagating through the calcite (no = 1.658)
suffers total internal reflection at the balsam layer (being a
rarer medium with refractive index n = 1.526). This ray is
absorbed by blackened surface forming the sides of prism.
The extraordinary ray propagates through calcite crystal (ne =
1.486) and suffers refraction at the balsam layer interface,
and leaves the prism as plane polarized light.
E-ray is derived out as a polarized beam.
41. Law of Malus’
Amplitude of light transmitted by polarizer:
Intensity = Const .(Amplitude)2
Crossed
Polarizers
42. Optical Activity
The rotation of the plane of polarization of a polarized light
is optical activity and is a special type of birefringence.
43. • The rotation of the orientation of plane of linearly polarized light was
first observed in 1811 in quartz by Dominique Arago.
• Biot observed the similar effect in organic liquids and gases.
• Herschel discovered that different crystal forms of quartz rotated the
plane of linear polarization in opposite directions.
• Louis Pasteur recrystallized sodium ammonium tartarate and noticed:
Two types of crystals which could be separated physically.
Both types were optically active and rotated the plane light in opposite directions.
These molecules exist in two form (i.e left – and right- handed).
Together the mixture is optically inactive and referred to as Racemic.
Historical Developments
44. Optical Activity
When a substance rotates the plane of plane polarized light, it
is optically active and the phenomenon is referred to as
optical activity.
Dextrorotatory (+ or d) rotates the plane of polarized light in
clockwise direction, when viewed by an observer for light
propagating towards him.
Levorotatory (- or l) rotates the plane of polarized light in
counter-clockwise direction, when viewed by an observer for
light propagating towards him.
45.
46. Fresenel Theory of Optical Activity
Optical activity is a special type of
birefringence.
A linear polarized light can be expressed as
an equal combination of right-hand (RHC)
and left-hand circularly (LHC) polarized light
waves.
The relative phase 2θ between the two
circular polarizations sets the direction of
the linear polarization to θ.
LHC
i
RHC E
e
E
E
2
47. In an optically active material, the two circularly
polarized waves experience different refractive
indices. The difference in the refractive indices
quantifies the strength of the optical activity and is a
characteristic of a material.
After traveling through length L of material, the two
polarizations will have a relative phase of
Consequently, the final plane of polarization is rotated
through +Δθ (anticlockwise) or -Δθ (clockwise)
resulting in dextro- or leavo-type materials.
LHC
RHC n
n
n
n
L
2
2
48. Electro-Optic Effects
Optical phenomena observed in certain materials
under the influence of electric and magnetic fields.
• Faraday effect
• Cotton Mouton Effect
• Kerr effect
• Pockel effect
50. For a magnetic field of strength 106A/m and length of
material 1cm, the angle of rotation is 1o- 2o.
Some of the common applications of Faraday effect are:
The radio waves used in satellite communication suffer
rotation of plane of polarization from vertical to
horizontal alignment when they pass through
ionosphere under the influence of earth magnetic field.
Many microwave devices such as modulators, isolators,
couplers, decoupling and matching devices are based
on Faraday effect.
51. Cotton Mouton Effect
This phenomenon is related to induction of
optical birefringence behavior in a uniaxial
crystal under the action of an external
magnetic field.
The magnitude of induced birefringence is
usually very small.
54. Analysis of Light
It is the procedure to unambiguously assign
the state of polarization to a given light wave.
55. Retarders
• Retarders cause the delay in the phase of one state of
polarization with respect to the other.
• It results in phase difference between the two
components of polarization which may (or may not) alter
the state of polarization on superposition to yield the
emergent wave.
• Most retarders are birefringent materials (quartz, mica,
polymers etc) having different indices of refraction
dependent on the state of polarization of the light.
56. Physics of Retarders
• As the unpolarized light enters a retarder medium, it
splits into e- and o-rays owing to its double refractive
nature.
• The two component waves propagate with different
speed in the same medium.
• Two SOP have mutually orthogonal E-field vibrations.
e
o
e
o
e
e
o
o
v
v
n
n
n
c
v
n
c
v
;
57. • If two waves travel a distance d through the retarder
medium, then their path and phase difference, on
emerging out from the medium, will be:
)
(
4
4
1
)
(
2
2
1
)
(
1
2
2
2
)
(
QWP
x
HWP
x
FWP
x
If
x
x
d
n
n
x e
o
58. Half-Wave Plate (HWP)
It leads to retardation by
half wave or phase of 180o
for one state of polarization.
The half wave polarizer can
flip the state of linear polarization .
alter sense of circular polarization.
59. Quarter-Wave Plate (QWP)
Causes retardation by quarter wave
or phase delay of 90o for one of the
state of polarizations.
The quarter wave plate can convert :
SOP from linear to elliptical.
SOP of linear polarized light, when incident
at 45o w.r.t retarder’s axis, to circular
polarization.
60. Circular Polarizers
•It converts unpolarized
light to circularly polarized.
• It is fabricated by gluing a
linear polarizer to a
quarter-wave plate with
their optic axes at 450 w.r.t
each other.
61. Babinet Compensator
It is a crystal plate of variable thickness
along which the phase difference
between e-ray and o-ray can be varied
continuously.
It consists of two wedge shaped prisms
of quartz cut at a very small angle.
The optic axis is parallel to refracting
edge in one section while it is
perpendicular in the other section.
63. The arrangement acts as a plate of varying
thickness for two rays. At increasing distance from
the center, the path difference increases uniformly
and required path difference can be obtained at
any given position.
For a ray passing through the center, the path
difference is zero and incident vibrations are
transmitted as such.
On each side of the central point, one ray will be
ahead or behind the other because of difference in
their path lengths.
64. Working of Babinet Compensator
The Babinet compensator is used in
studying state of polarization of light.
The optical thickness of the plate can be
varied by working a micrometer screw,
which causes relative displacement
between two wedges. This helps in
obtaining desired path difference at any
particular position.
On either side of line of zero optical path
difference, the path retardation is λ/2 at a
distance L and λ at 2L. The light emerging
from these points is plane polarized while it
is elliptically polarized for other points.
65. For studying the SOP of light, the Babinet compensator is
placed between polarizer and analyzer. The light
emerging from analyzer is viewed and SOP can be
ascertained as:
If the light emerging from the center of compensator
is extinguished by rotating the analyzer then dark
fringes are seen in the field of view and light is
plane polarized in nature.
If the light incident on the compensator is elliptically
polarized, the fringes will shift by an amount
depending upon the ratio of major and minor axes
of ellipse.
66. Determination of State of Polarization
Linear polarizer is introduced in the path of polarized light and rotated
about axis coinciding with direction of propagation of light.
There is ambiguity in deciding the state of polarization in situations 2 and 3.
S. No. Observation Inference
1. Complete extinction of light intensity
at two orientations of polaroid.
Linearly polarized beam
2. No variation in beam intensity. Unpolarized
Circularly polarized
Unpolarized + Circularly polarized
3. Intensity variation but not complete
extinction.
Elliptically polarized
Unpolarized + Linearly polarized
Unpolarized + Elliptically polarized
67. Situation 2: Quarter Wave Plate is introduced before the polaroid.
Observation Inference
Light Intensity does not vary as
polaroid is rotated about optic axis.
Unpolarized Beam.
Light intensity suffers complete
extinction at two orientations of
rotating polaroid.
Circularly polarized Light as quarter
wave plate converts it to orthogonally
linearly polarized light beams.
Light intensity varies with rotation of
polaroid about optic axis but does not
suffer complete extinction.
Mixture of unpolarised and circularly
polarized light.
68. Situation 3: When the quarter wave plate is introduced with its
optic axis parallel to transmission axis of crystal.
Observation Inference
Light Intensity suffers complete extinction of intensity
for two orientations of rotating polaroid.
Elliptically Polarized Beam
Light intensity does not suffer complete extinction at
two orientations of rotating polaroid but position of
maximum intensities are same as before.
Mixture of linearly polarized
and unpolarised light.
Light intensity does not suffer complete extinction at
two orientations of rotating polaroid but position of
maximum intensities are different.
Mixture of unpolarised and
elliptically polarized light.
70. Polarizing Filters
Polarizing filters exclude all light not
vibrating in the preferred direction or
transmission axis of the filter.
Light reflected by shiny transparent
material is partly or fully polarized, except
when the light is normal to the surface.
Polarizing sunglasses, by orienting their
polarizing material vertically and
selectively, exclude the polarized portion of
light reflected by the horizontal surface.
71. Polarizing microscopes are equipped with polarizing
filters both below and above the stage of
microscope. The lower filter (polarizer) is rotatable
while the upper filter (analyzer) is non-rotatable but
removable.
Light of certain polarization passes through a sample
by the two polarizer arrangement and used to study
optical properties of rocks or minerals.
Polarizing Microscopes
72. Art
Visual artists work using birefringent materials to
create colorful and changing images.
The artist create images by using hundreds of small
pieces of cellophane and other birefringent films
and further laminate them between plane polarizing
filters.
73. Applications-Crossed Polarizers
Cross polarizers are used to detect materials
that rotate the plane of polarized light such as:
• Biological materials
• Materials under mechanical stress.
Inspection of skin under cross-polarization enhances
the sub-surface features such as vascular details,
pigmentation and infiltrates.
Surface topography of the skin is better visualized
with parallel polarization.
74. Visual Effects of Polarization
Polarization Photography
Without Polarizer With Polarizer
Polarization by scattering is observed as light passes through atmosphere.
The scattered light produces the brightness and color in clear sky.
This partial polarization of scattered light can be used to darken the sky in
photographs, increasing the contrast.
76. Biology
Many animals like octopus, squid, cuttlefish, insects
and bees use a component of the polarized light for:
navigational purposes.
orienting their communicative dances.
Chemistry
Polarization is principally of importance in chemistry
due to optical activity exhibited by chiral molecules.
77. Astronomy
In many areas of astronomy, the study of polarized
electromagnetic radiation from outer space is used to
probe interstellar magnetic field.
study of various aspects of early universe.
navigating near poles of earth's magnetic
field where neither sun nor stars are visible.
78. Radio Communication
All radio transmitting and receiving antenna are
intrinsically polarized, special use of which is made in
radar.
Most antennas radiate either horizontal, vertical, or
circular polarization. Their electric field plane
determines polarization or orientation of radio wave.
Vertical polarization is used when it is desired to
radiate a radio signal in all directions such as widely
distributed mobile units, AM and FM.
79. • Television uses horizontal polarization.
• Alternating vertical and horizontal polarization is
used on satellite communications (including
television satellites), to allow the satellite to carry
two separate transmissions on a given frequency,
thus doubling the number of customers a single
satellite can serve.
80. LCD
STRUCTU
RE
• LCD devices are used as read-outs in wrist
watches, calculators, clocks, electronic
instruments, laptop, computers etc.
• It consists of 10μm thick double refracting liquid
crystal supported between the assembly of glass
plates which are further sandwiched between two
polaroid sheets held in crossed configuration.
• During fabrication of LCDs, the liquid crystal
molecules are aligned in such a way that their long
axis undergoes 90o rotation, also referred to as
twisted molecular arrangement.
Liquid Crystal Display
81. When light is incident on the assembly, the front polarizer
polarizes it. The linear polarization of light is rotated
through 90o by the twisted molecular arrangement.
The light passes unhindered through the rear polarizer
whose transmission axis is perpendicular to that of the
front polarizer.
A reflector at the back of rear polarizer sends the light back
which emerges unobstructed from the front polarizer. As
such the display appears uniformly illuminated.
When external voltage is applied to the device, the
molecules lying in the region between electrodes untwist
and align along the field direction.
Consequently the light vector is not rotated when it passes
through this region. The rear polarizer blocks the light and a
dark digit or character is seen in that region.