polarization

POLARIZATION OF LIGHT

Dr. J.K.GOSWAMYUIET, PANJAB UNIVERSITY,

CHANDIGARH.

09/10/10 1Polarization of light : Dr. J.K. Goswamy, UIET, P.U.C.

09/10/10 Polarization of light : Dr. J.K. Goswamy, UIET, P.U.C. 2

WHAT IS POLARIZATION ?

It is the phenomenon of restricting the electric vector

vibrations of the light along a plane which may or may not

rotate about the direction of propagation.


BASICS OF PLANE WAVES

• A plane light wave is infinitely long and has wide wavefront.

• The transverse nature of light requires that the electric and magnetic fields oscillate in directions perpendicular to each other and also to the direction of propagation.

• For the light waves propagating in air or vacuum, the electric and magnetic vector vibrations have same frequency and are in same phase.

• Light wave that propagates in the x direction can be expressed mathematically as:

zt)-kxcos(B)tx,(B

yt)-kxcos(E)tx,(E

0zz

0yy

ω

ω

=

=


UNPOLARIZED OR ORDINARY LIGHT

The electric vector amplitude is

~378 times greater than the

magnetic vector amplitude.

Hence the magnetic field vector

oscillations can be ignored.

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.


• 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 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.


• The shape traced out by vibrating electric vector as

a plane wave propagates defines the State of

Polarization (SOP) of light.


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 in which light oscillations take place is called plane of vibration. The other plane devoid of light oscillations is called plane of polarization.

Phenomenon of Polarization


STATES OF POLARIZATION

Linearly Polarized Light

Elliptically Polarized light

Circularly Polarized Light


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 . These wave resulting from superposition of these two waves is to be analyzed.

z)t-kxcos(E)tx,(E

yt)-kxcos(E)tx,(E

0zz

0yy

θω

ω

−=

=

ϕ


• Both the light waves have electric field oscillations in YZ plane. We wish to study their time variation in a plane (say x=0), which will define relation between instantaneous displacements of two waves and their relative phase

difference. Hence:

( )

( )

θθ

θθ

θωθωθω

ωθωω

2

22

2

2

sincos2

:,

1sincos

sinsincoscoscos

1sin;cos;cos

=

−

+

−±

=

−==−

−±==−=

oy

y

oz

z

oz

z

oy

y

oy

y

oy

y

oz

z

oz

z

oy

y

oz

z

oy

y

E

E

E

E

E

E

E

E

getweequationabovetheSolving

E

E

E

E

E

E

ttE

Et

E

Et

E

Et

E

Et


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:

θθ 2

22

sincos2 =

−

+

oz

z

oy

y

oz

z

oy

y

E

E

E

E

E

E

E

E

PolarizedCircularlyEE

PolarizedlyEllipticalEE

PolarizedLinearly

ozoy

ozoy

==

≠=

=

2

2

,0

πθ

πθ

πθ


LINEAR POLARIZATION• 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 direction of propagation no longer exists.

±=

0z

0y

z

y

E

E

E

E


ELLIPTICAL POLARIZATIONThe 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 either do not have the same amplitude and/or are not 90o out of phase, the resultant electric vector traces out an ellipse in the plane of vibration also called the polarization ellipse.

1E

E

E

E2

0z

z

2

0y

y =

+


REP: Right Elliptic Polarization (CW rotation of electric vector while approaching the observer)

LEP: Left Elliptic Polarization (ACW rotation of electric vector while approaching the observer)

An ellipse can be represented by 4 quantities:size of minor axissize of major axisorientation (angle)sense of rotation (CW or ACW)

SENSE IN ELLIPTICAL POLARIZATION


CIRCULAR POLARIZATION

• If two linearly polarized light waves with phase difference = 90º 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 depending upon the sense of rotation of electric vector as wave approaches the observer.

1E

E

E

E2

0y

y

2

0z

z =

+


MIXED STATES OF POLARIZATION

• Unpolarized

• Linearly polarised + Unpolarized

• Elliptically polarized + Unpolarized

• Circularly Polarized + Unpolarized

• Elliptically polarized + Linearly polarized

• Circularly Polarized + Linearly polarized


METHODS OF POLARIZATION

DICHORISM

REFLECTION

SCATTERING

BIREFRINGENCE


POLARIZATION BY DICHORISM

Technique of selective absorption of electric vector vibrations in one of the two orthogonal directions.


WIRE-GRID POLARIZERS Grid is formed by an array of

parallel conducting wires with their spacing comparable to the wavelength of observation.

Electric field vector parallel to the wires is attenuated because of currents induced in the wires.

Energy dissipation of this component occurs through Joule’s heating of wires.

Mainly used for polarization of the IR and longer wavelengths.

Not useful for light waves but the technique paved way for atomic and molecular grids.


DICHORISM

Certain crystals strongly absorb

the incident light oscillations

along one direction while

easily transmit the light

oscillations in the direction

perpendicular to it. The

direction of strong absorption

of electric vector is called

absorption axis while other of

easy propagation forms optic

axis of the crystal.

Tourmaline, Quartz


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 crystals. 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.

• This Polaroid gives hazy appearance due to scattering of light by numerous crystallites.


H-SHEET (GRID OF POLYMER CHAIN)

A sheet of polyvinyl alcohol is gently heated and stretched in a

given direction resulting in alignment of hydrocarbons molecules

into long molecular chains.

It is then dipped in ink solution rich in iodine which impregnates

the plastic and gets attached to long polymeric chain of molecules,

effectively forming the chain of its own. The free electrons of

iodine move along the chain as if they were long wires.

The electric field component of light parallel to chain gets absorbed

while the perpendicular component is easily transmitted.

In H-sheets, there is no hazy appearance as scattering is caused by

molecules rather than submicroscopic crystals.

The H-sheets are effective polarizers over entire visible spectrum.


• K-Polaroids are made by stretching polyvinylene sheet by slight heating in the presence of dehydrating agent such as HCl. These 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 near infra-red region.

• Other Polaroids: There are also available dichoric sheet linear polarizers which are effective in the UV region of electromagnetic spectrum.


POLARIZATION BY REFLECTION

Transparent surfaces reflect selectively one component of electric vector vibrations at a particular angle of incidence.


POLARIZATION BY REFLECTION

• The reflection coefficient for light which has electric field

oscillations parallel to the plane of incidence reduces to zero at

some angle between 0° and 90°.

• 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.

• The angle at which this occurs is called the polarizing angle or

Brewster angle. At other angles, the reflected light is partially

polarized.

• The transmitted or refracted light remains partially polarized at

all angles of incidence of unpolarized light.




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 to 90°. The use of Snell's law gives

an expression for the Brewster angle.


POLARIZATION BY STACK OF PLATES

2

2

12nn

m

m

II

IIP

−+

=+−

=⊥

⊥



POLARIZATION BY SCATTERING

Scattering of light in orthogonal direction yields polarized light.



• The scattering of light off air molecules produces linearly

polarized light in the plane perpendicular to the direction

of propagation of the incident light.

• The scatterers (air molecules or suspended particles) can

be visualized as oscillating tiny dipole antennae which radiate in all directions other than their 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 is

linearly polarized.







DOUBLE REFRACTION OR

BIREFRINGENCE

Anisotropic media splits ordinary light into two purely

polarized beams having vastly different properties.


WHAT IS DOUBLE REFRACTION ?

• Double refraction, is the splitting of a

ray of light into two rays when

passing through certain anisotropic

materials such as Calcite, Quartz.

• This was reported by Erasmus

Bartholinus in 1669.

• Both rays of light are plane polarized

with their planes of polarization

mutually perpendicular.


• The O-ray obeys Snell’s law and has electric vector

vibrations perpendicular to optic axis of double refracting

crystal.

• E-ray doesn’t obey Snell’s law and has electric vector

vibrations along optic axis of the crystal.

NaCl Quartz


• The refractive indices of the double refracting medium is

different for O- & E-rays. Two rays propagate with

different speeds in the same medium. This property is

referred to as Birefringence.

• All transparent crystals, except those in cubic form, are

double refracting. However separation of two images is

usually not large enough to be observable.


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.

• Such an oscillating dipole radiates electromagnetic energy

in all directions except along its line of oscillation.

• The emitted secondary wavelets combine to form the

refracted wave-front.


• 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 atoms.

• Since there is anisotropy in forces binding the atoms as well as

electrons, this results in directional dependence in refractive index of

medium.

• The reason for birefringence is the fact that in anisotropic media the

electric field vector and the dielectric displacement can be non-

parallel for the E-polarization, although being linearly related.


BIREFRINGENCE: UNIAXIAL CRYSTALS

• The optic axis is the direction in the birefringent crystal along

which E-ray and O-ray propagate with same speed.

• If the material has single optical 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 called positive (negative) if O-ray

propagates faster (slower) than E-ray.

• Non-cubic transparent crystals having hexagonal or tetragonal

unit cells are uniaxial in nature.


Uniaxial Material no ne Δn =ne-no

Beryl Be3Al2(SiO3)6 1.602 1.557 -0.045

Calcite CaCO3 1.658 1.486 -0.172

Calomel Hg2Cl2 1.973 2.656 +0.683

Ice H2O 1.309 1.313 +0.004

Magnesium fluoride MgF2 1.380 1.385 +0.006

Quartz SiO2 1.544 1.553 +0.009

Ruby Al2O3 1.770 1.762 -0.008

Rutile TiO2 2.616 2.903 +0.287

Sapphire Al2O3 1.768 1.760 -0.008

Sodium nitrate NaNO3 1.587 1.336 -0.251

Tourmaline (complex silicate ) 1.669 1.638 -0.031

Zircon, high ZrSiO4 1.960 2.015 +0.055

http://en.wikipedia.org/wiki/Birefringence






BIREFRINGENCE: BIAXIAL CRYSTALS• Biaxial birefringence, also known as tri-refringence, describes an

anisotropic material that has more than one axis of anisotropy. • For such a material the refractive index will have three distinct values

which are labeled nα, nβ and nγ.

• These crystals are orthorhombic/ monoclinic/ triclinic in shape.

Material nα nβ nγ

Borax 1.447 1.469 1.472

Epsom salt MgSO4·7(H2O) 1.433 1.455 1.461

Mica 1.595 1.640 1.640

Mica, muscovite 1.563 1.596 1.601

Olivine (Mg, Fe)2SiO4 1.640 1.660 1.680

Perovskite CaTiO3 2.300 2.340 2.380

Topaz 1.618 1.620 1.627





09/10/10 45

NICOL PRISM

• It was the first type of polarizing prism invented by William Nicol of Edinburgh in 1828.

• It consists of a calcite crystal of length thrice its width.

• This faces of this have initial angles of 71o and 109o.

• The crystal faces crystal are cut so as to have angles of 68° and 112o.

• The crystal is split diagonally and surfaces of two halves are polished.

• The two halves are joined again using a layer of canada balsam.

Polarization of light : Dr. J.K. Goswamy, UIET, P.U.C.


NICOL PRISM CONSTRUCTION

71o

AA’

B

D

C’C

E-ray

O-ray

68o


• 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

(refractive index n = 1.55). This ray is absorbed by the

blackened surface on the sides of the 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.

09/10/10 48

MALUS LAW


LAW OF MALUS

Amplitude of light transmitted by polarizer:

Intensity = Const .(Amplitude)2


CROSSED POLARIZERS




ANALYSIS OF LIGHT

It is the procedure to umambiguously determine the

state of polarization of given light wave.


RETARDERS

• Retarders cause the delay in phase of one state of

polarization with respect to the other one.

• There is phase difference between the two

components of polarization which may (or may not)

alter the state of polarization when two components

superpose to yield the emergent wave.

• Most retarders are birefringent materials (quartz,

mica, polymers) having different indices of

refraction dependent on the state of polarization of

the incoming light.


HALF-WAVE PLATE

• Retardation of half wave or phase of 180º for one state of polarization.

• Used to flip the linear polarization or change handedness of circular polarization.


QUARTER-WAVE PLATE

• Retardation of quarter wave or phase delay of 90º for one of the polarizations.

• Can convert linear polarization to elliptical.

• For the incoming light polarized at 45º with respect to the retarder’s axis then the quarter plate can be used for conversion from linear to circular polarization (vice versa)


CIRCULAR POLARIZERS

• It converts the unpolarized to circularly polarized one.

• Made of a linear polarizer glued to a quarter-wave plate with their optic axes oriented at 45º with respect to one another.


DETERMINATION OF STATE OF POLARIZATION

Polaroid introduced in the path of light and rotated about axis coinciding with direction of propagation of light.

There is ambiguous situation in obtaining state of polarization in situations 2 and 3.

1.

Complete extinction of intensity at two orientations of polariod

Linearly polarized beam

2. No variation in the beam intensity

Unpolarized

Circularly polarized

Unpolarized + Circularly polarized

3. Intensity variation but not complete extinction

Elliptically polarized.

Unpolarized + linearly polarized

Unpolarized + Elliptically polarized.


Situation 2: Quarter Wave Plate is introduced before the polaroid

• If light intensity on rotation of polaroid remains same then it is an unpolarized beam.

• If the light intensity suffers extinction at two orientations of rotating polaroid, then it is circularly polarized. This is because quarter wave plate transforms circularly polarized

light into two linearly polarized waves.

• However if there is variation in intensity without complete extinction, then it is mixture of unpolarized and circularly polarized light.


Situation 3: When the quarter wave plate is introduced with its optic axis parallel to transmission axis of crystal, then

• If complete extinction of intensity occurs for two orientations of rotating polaroid then beam is elliptically polarized.

• If the complete extinction does not occur and orientation of polaroid for positions of maximum intensities are same as

before, then beam is mixture of unpolarized and linearly polarized.

• Finally if the position of maximum intensity occur at different orientations of polaroid, then it is a mixture of elliptically polarized and unpolarized light.


The rotation of plane of polarization of a polarized light is optical activity and is a special type of birefringence.

OPTICAL ACTIVITY

09/10/10 61

• The rotation of the orientation of plane of linearly polarized

light was first observed in 1811 in quartz by French

physicist François Jean Dominique Arago.

• Jean Baptiste Biot also observed the similar effect in liquids

and gases of organic substances such as turpentine.

• In 1822, the English astronomer Sir John F.W. Herschel

discovered that different crystal forms of quartz rotated the

plane of linear polarization in opposite directions.

HISTORICAL DEVELOPMENTS



• Louis Pasteur (1848) recrystallized sodium ammonium tartarate (optically inactive). He noticed that the crystals were of two types which he separated physically. The two types of crystals were optically active and rotated the plane

of polarized light in opposite directions. He proposed that these molecules exist in two forms, “left handed” and “right handed”. Together, the mixture of the two forms is optically inactive.


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 rotates the plane of polarized light in clockwise direction when viewed through a polarimeter.

(+) or (d) do not confuse with D

Levorotatory rotates the plane of polarized light in counter-clockwise direction when viewed through a polarimeter.

(-) or (l) do not confuse with L


Specific Rotation is the angle of rotation of plane polarized light by a 1.00 gram per cm-3 sample in a 1 dm tube.

[α ]D (D = sodium lamp, λ = 589 nm)

where α = observed rotation l = length (dm)d = concentration (g/cm3)

Alanine [ α ]D = +8.5 Lactic acid [α ]D = -3.8

The angle of rotation of plane polarized light by an optically active substance is proportional to the number of atoms in the path of the light.

[ ]ldD

αα =


SCHEMATIC DIAGRAM OF A POLARIMETER

An instrument used to measure optical activity.

Analyzer

Sample tube

Light source

Polarizer

Eye

Rotation of analyzer


WAVE 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.

LHCi

RHC EeEE θθ

2+=


In an optically active material the two circularly polarized waves experience different refractive indices. The difference in the indices quantifies the strength of the optical activity

This difference is a characteristic of the material (for substances in solution it is given as the specific rotation).

After traveling through length L of material the two polarizations will have a relative phase of

• Consequently, the final polarization is rotated to θ + Δθ.

LHCRHC nnn −=∆

λπθ nL∆=∆ 2

2

09/10/10 68

APPLICATIONS OF

POLARIZATION


POLARIZING FILTERSPolarizing filters exclude all light not

vibrating in the preferred direction 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, selectively

exclude the polarized portion of light

reflected by the horizontal surface.


Polarizing Microscopes

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 is allowed to pass through a

sample by the two polarizer arrangement which is further

used to study of properties of rocks or minerals.

09/10/10 Polarization of light : Dr. J.K. Goswamy, UIET, P.U.C.

70






Polarization PhotographyWithout Polarizer With Polarizer

Visual Effects of Polarization

Polarization by scattering is observed as light passes through the 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.

Polarization Photography : Reduces Reflections

Visual Effects of Polarization….cont’d



BiologyMany animals like octopus, squid, cuttlefish, insects and bees perceive a component of the polarized light and use it for the following:

navigational purposes.

orienting their communicative dances. Astronomy:

In many areas of astronomy, the study of polarized electromagnetic radiation from outer space is used

• to probe interstellar magnetic field.

• to study the early universe.

• navigating near the poles of the Earth's magnetic field where neither the sun nor stars are visible.


ChemistryPolarization is principally of importance in chemistry due to optical activity exhibited by chiral molecules.

GeologyThe property of birefringence is widespread in crystalline minerals and is frequently exploited using polarization microscopes, for the purpose of identifying minerals.

Art• Visual artists work use birefringent materials to create colorful,

sometimes changing images. The artist works by cutting hundreds of small pieces of cellophane and other birefringent films and laminating them between plane polarizing filters.

• 3-D films make use of polarized light and polarization filters in order to generate the 3D effect.


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. The electric field or E-plane determines the polarization or orientation of the 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.

• 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.



STOKES PARAMETERS

In 1852 Sir George Gabriel Stokes took a very different approach and discovered that polarization can be described in terms of observables using an experimental definition.


STOKES PARAMETERS

( ) ( ) ( ) ( ) 20y0x

20y0x

220y

20x

220y

20x εsinEE2εcosEE2EEEE =−−−+

The polarization ellipse is only valid at a given instant of time (function of time):

εsinεcos(t)E

(t)E

(t)E

(t)E2

(t)E

(t)E

(t)E

(t)E 2

0y

y

0x

x

2

0y

y

2

0x

x = −

+

To get the Stokes parameters, do a time average (integral over time) and a little bit of algebra...

εsinEE2V

εcosEE2U

E E Q

EEI

0y0x3

0y0x2

20y

20x1

20y

20x0

==

==

−==

+==

S

S

S

SThe 4 Stokes parameters are:


STOKES VECTOR

The Stokes parameters can be arranged in a Stokes vector:

• Linear polarization

• Circular polarization

• Fully polarized light

• Partially polarized light

• Unpolarized light 0VUQ

VUQI

VUQI

0V 0, U0,Q

0V 0, U0,Q

2222

2222

===++>++=

≠===≠≠

( ) ( )( ) ( )

( ) ( )

−°−°

°−°=

−+

=

LCPIRCPI

135I45I

90I0I

intensity

εsinEE2

εcosEE2

EE

EE

V

U

Q

I

0y0x

0y0x

20y

20x

20y

20x


STOKES PARAMETERS …..cont’d

09/10/10 85

THANKS FOR NICE AUDIENCE


polarization

Education

light vibrations

light vector oscillations

plane of polarization

ordinary light wave

polarized light waves

transverse nature of

polarization of lightdr

electric vector vibrations