polarization concept

Polarization ConceptEdited by iqBaLgoh [11/03/08]

Content by http://hyperphysics.phy-astr.gsu.edu/

Scope of Polarization

Classification of Polarization

Classification of Polarization• Light in the form of a plane wave

in space is said to be linearlypolarized.

• Light is a transverse electromagnetic wave, but naturallight is generally unpolarized, allplanes of propagation beingequally probable.

• If light is composed of two plane waves of equal amplitude by differing in phase by 90°, then thelight is said to be circularlypolarized.

• If two plane waves of differingamplitude are related in phase by 90°, or if the relative phase isother than 90° then the light issaid to be elliptically polarized.

Classification of PolarizationLinear Polarization• A plane electromagnetic wave is

said to be linearly polarized. Thetransverse electric field wave isaccompanied by a magnetic fieldwave as illustrated.

Classification of PolarizationCircular Polarization• Circularly polarized light consists of two perpendicular

electromagnetic plane waves of equal amplitude and 90° d ifferencein phase. The light illustrated is right- circularly polarized.

• Circularly polarized light may be produced by passing linearlypolarized light through a quarter-wave plate at an angle of 45° to the opticaxis of the plate.

Classification of PolarizationCircular Polarization (cont)

• If light is composed of two plane waves ofequal amplitude but differing in phase by 90°, then the light is said to be circularlypolarized. If you could see the tip of theelectric field vector, it would appear to bemoving in a circle as it approached you.

• If while looking at the source, the electricvector of the light coming toward youappears to be rotating counterclockwise, the light is said to be right-circularlypolarized.

• If clockwise, then left-circularly polarizedlight. The electric field vector makes onecomplete revolution as the light advancesone wavelength toward you.

• Another way of sayingit is that if the thumb ofyour right hand werepointing in the direction of propagation of thelight, the electric vectorwould be rotating in thedirection of yourfingers.

Classification of PolarizationElliptical Polarization• Elliptically polarized light consists

of two perpendicular waves ofunequal amplitude which differ in phase by 90°. The illustration shows right- elliptically polarizedlight.

• If the thumb of your right hand were pointing in the direction ofpropagation of the light, the electricvector would be rotating in thedirection of your fingers.

Method for Achieving Polarizationof Light


Polarization by Reflection 1. CalculationReflected Intensity

• Fressnell Law (reflection theory)

• Snell Law (refraction theory)

2. CalculationDerivation ofBrewster's angle (polarization by reflection)


Polarization by Scattering• The scattering of light off air molecules

produces linearly polarized light in theplane perpendicular to the incident light.

• The scatterers can be visualized as tinyantennae which radiate perpendicular to 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 beamdirection, the scattered light is linearlypolarized. This causes the light whichundergoes Rayleigh scattering from theblue sky to be partially polarized.


Blue Sky• The blue color of the sky is

caused by the scattering ofsunlight off the molecules of theatmosphere. This scattering, called Rayleigh scattering, ismore effective at short wavelengths (the blue end of thevisible spectrum). Therefore thelight scattered down to the earth ata large angle with respect to thedirection of the sun's light ispredominantly in the blue end ofthe spectrum.

Polarization by Scattering


Rayleigh Scattering• Rayleigh scattering refers to the scattering of light off of the molecules of

the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light. It is Rayleigh scattering off themolecules of the air which gives us the blue sky. Lord Rayleigh calculated the scattered intensity from dipole scatterers much smallerthan the wavelength to be:

• Rayleigh scattering can beconsidered to be elastic scatteringsince the photon energies of thescattered photons is not changed. Scattering in which the scatteredphotons have either a higher or lowerphoton energy is called Raman scattering. Usually this kind ofscattering involves exciting somevibrational mode of the molecules, giving a lower scattered photon energy, or scattering off an excitedvibrational state of a molecule whichadds its vibrational energy to theincident photon.

Polarization by Scattering


Birefringent Materials• Crystalline materials may have different indices of refraction associated with

different crystallographic directions. A common situation with mineralcrystals is that there are two distinct indices of refraction, and they are called birefringent materials. If the y- and z- directions are equivalent in terms of the crystalline forces, then the x-axis is unique and is called theoptic axis of the material. The propagation of light along the optic axis wouldbe independent of its polarization; it's electric field is everywhereperpendicular to the optic axis and it is called the ordinary- or o-wave. Thelight wave with E-field parallel to the optic axis is called the extraordinary- or e-wave. Birefringent materials are used widely in optics to producepolarizing prisms and retarder plates such as the quarter-wave plate. Putting a birefringent material between crossed polarizers can give rise to interference colors.

• A widely used birefringent material is calcite . Its birefringence is extremelylarge, with indices of refraction for the o- and e-rays of 1.6584 and 1.4864 respectively.


Calcite • Calcite is used in polarizing prisms such

as the Nicol prism, the Glan-Foucaultprism, and the Wollaston prism.

• A simple demonstration of the large birefringence of calcite is to put a dot on a piece of paper and put the calcite crystal over it. You see two distinct dots. By putting a piece of polaroid over thecrystal and rotating it, you can show thatthe two images of the dot are made upof light polarized at 90° with respect to each other.

• Rotating the polaroid will show one dot, then both in transition, and then just thesecond dot as you reach 90°.


Calcite

Because of its birefringence, calcite forms two images of the arrow. Rotating a polarizer over them shows that the light which forms the twoimages is polarized at right angles.

Two images throughcalcite crystal

Polarizer transmits theordinary ray

Polarizer rotatedabout 90°

transmits theextraordinary ray.


Prisms for Polarization• A number of polarizing prisms have been

devised which make use of birefringence to separate two beams in a crystallinematerial. Often they make use of total internal reflection.


Nicol Prism• Polarization can be achieved with

crystalline materials which have a different index of refraction in different crystal planes. Suchmaterials are said to bebirefringent or doubly refracting.

• The Nicol prism is made up fromtwo prisms of calcite cementedwith Canada balsam . Theordinary ray can be caused to totally reflect off the prismboundary, leaving only theextraordinary ray.


Quarter-Wave Plate• A quarter-wave plate consists of a carefully adjusted

thickness of a birefringent material such that the light associated with the larger index of refraction is retardedby 90° in phase (a quarter wavelength) with respect to that associated with the smaller index.

• The material is cut so that the optic axis is parallel to the front and back plates of the plate. Any linearlypolarized light which strikes the plate will be divided intotwo components with different indices of refraction. Oneof the useful applications of this device is to convertlinearly polarized light to circularly polarized light andvice versa. This is done by adjusting the plane of theincident light so that it makes 45° angle with the opticaxis. This gives equal amplitude o- and e-waves.

• When the o-wave is slower, as in calcite, the o-wavewill fall behind by 90° in phase, producing circularlypolarized light.


Quarter-Wave PlateLinear to Circular Polarization• If linearly polarized light is incident on a

quarter-wave plate at 45° to the optic axis, then the light is divided into two equal electricfield components. One of these is retarded by a quarter wavelength by the plate. This producescircularly polarized light. Incident circularlypolarized light will be changed to linearlypolarized light.


Quarter-Wave Plate Applications• The Wollaston prism is a polarizing beam splitter, preserving both the O- and

E-rays. It is usually made from calcite or quartz.

• The Wollaston prism is made up of two righttriangle prisms with perpendicular opticaxes. At the interface, the E-ray in the firstprism becomes an O-ray in the second andis bent toward the normal. The O-raybecomes an E-ray and is bent away fromthe normal.

• The beams diverge from the prism, givingtwo polarized rays. The angle of divergence of these two rays is determined by thewedge angle of the prisms.

• Commercial prisms are available withdivergence angles from 15° to about 45°. They are sometimes cemented withglycerine or castor oil, and sometimes notcemented if the power requirements are high.


• Quarter-Wave Plate Applications


Polarization by Absorption• 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 iscalled dichroism.

• There are several naturally occurring dichroic materials, and thecommercial material polaroid also polarizes by selective absorption.

• Link : Crossed polarizer


Dichroic Materials• Materials which have different absorption for perpendicular incident

planes for light are said to be dichroic. The mineral tourmaline is the bestknown of natural materials. Tourmaline refers to a class of boronsilicates. A tourmaline crystal has a unique optic axis, and any electricfield vector which is perpendicular to that axis is strongly absorbed.

• Polaroid is strongly dichroic and therefore an effective polarizer. If thetransmission axes of ideal polarizers are perpendicular, no light istransmitted. The light tranmitted at other angles follows the Law ofMalus.

Link :• Crossed polarizer• Liquid crystal display


Dichroic MaterialsLaw of Malus

• When a second polarizer is rotated, the vector component perpendicular to its transmission plane is absorbed, reducing its amplitude to :

• Since the transmitted intensity isproportional to the amplitude squared, the intensity is given by:

Example• If = 30 degree• Then = 0.75


Dichroic MaterialsLiquid crystal display

A dichroic polarizer covers the liquid crystal display. The polarized light fromthe background is transmitted, but the part which makes up the numeralshas been rotated 90° and is blocked, forming the dark are as. If a polarizerwith axis perpendicular to the surface polarizer is placed over the display as in the top right image, the entire display looks black.

Watch liquidcrystal display

A polarizer parallel to that ofthe front layer does not

obscure the display.


Polaroid Material• Polaroid is the trade name for the most commonly used dichroic material. It

selectively absorbs light from one plane, typically transmitting less than 1% through a sheet of polaroid. It may transmit more than 80% of light in theperpendicular plane.

• The word "polaroid" usually refers to polaroid H-sheet, which is a sheet ofiodine-impregnated polyvinyl alcohol. A sheet of polyvinyl alcohol is heatedand stretched in one direction while softened, which has the effect ofaligning the long polymeric molecules in the direction of stretch. Whendipped in iodine, the iodine atoms attach themselves to the aligned chains. The iodine atoms provide electrons which can move easily along thealigned chains, but not perpendicular to them. Light waves with electricfields parallel to these chains are strongly absorbed because of thedissipative effects of the electron motion in the chains. The direction perpendicular to the polyvinyl alcohol chains is the "pass" direction since theelectrons cannot move freely to absorb energy.


Polaroid Material• The polaroid material used in sunglasses makes use of dichroism, or

selective absorption, to achieve polarization.

Analyze Polarization


Crossed Polarizers• An ideal polarizer produces linearly polarized light from

unpolarized light. Two ideal polarizers would eliminateall light if their transmission directions are placed atright angles. The two sheets of polaroid at left are crossed and placed on an overhead projector.

• Polaroid materials accomplishpolarization by dichroism. Atangles other than 90°, thetransmitted intensity is givenby the Law of Malus.


Polarizer Puzzle• If crossed polarizers block all

light, why does putting a thirdpolarizer at 45° between themresult in some transmission oflight?

Third Crossed Polarizers


Third Crossed PolarizersPolarizer Puzzle• In dichroic materials like polaroid, the component of the field perpendicular to

the transmission plane is selectively absorbed. This achieves a rotation of theplane of polarization, but the mechanism is different from that in opticallyactive materials.

• In the image at left above, thepolaroids are crossed, resulting in minimum transmission. At right above, a third sheet of polaroid is insertedbetween the crossed polarizers. In thesituation shown, the transmittedintensity can be calculated by applyingthe Law of Malus twice. If the centerpolarizer is placed at 45° betweencrossed polarizers, 25% of the light willbe transmitted.


Polarization and Interference Colors• Many common transparent materials exhibit bands of

color when placed between crossed polarizers. Ordinarymaterials such as cellophane and polyethylene exhibitthem. Natural mica and even ice chips exhibitinterference colors.

• Selected thicknesses of birefringentmaterials can be used to form colorfulshapes like this butterfly when placedbetween crossed polarizers. Thesegments change color when yourotate the front polarizer, but are colorless in ordinary light. These are examples of interference colors.


Polarization and Interference ColorsWhen light is passed through a polarizer to produced linearly polarized light and that light isthen passed through a piece of birefringentmaterial, the light is broken up into twocomponents. Since the index of refraction of oneof them is larger, that component will lag in phase. Then if the light is passed through a crossedpolarizer, only that part of each of the components which is in the transmission plane will emerge. That means you have two coplanar components with a phase difference. If different colors have different indices, then for a given thickness ofbirefringent material, some colors will undergodestructive interference and some constructive, giving an interference pattern of varying colorsreminiscent of the interference colors of a thin film.


Polarization and Interference Colors

• This material shows a fan-shapedcolor variation when the polariod isrotated.



• This sample appears to be ordinarycellophane tape, but it shows a dramatic change in color as thesecond sheet of polaroid is rotated.



• This sample is taken to be a thin slice of a mineral. It shows color changes as it is rotated between crossedpolarizers.


Optical Activity

• A material which rotates the plane of incident linearly polarized light is said to be optically active. Viewing the light head-on, somesubstances rotate the electric field clockwise (dextrorotatory) andsome produce a counterclockwise rotation (levorotatory). Theproperty was discovered in quartz in 1811 by Arago. Two differentcrystalline structures of quartz produce d-rotatory and l-rotatorybehavior. The two crystalline forms are said to be enantiomorphs ofeach other. The optical activity of quartz is associated with its crystalstructure, as evidenced by the fact that neither molten quartz or fused quartz demonstrate optical activity.

• In the case of many naturally occurring organic compounds such as sugar, tartaric acid and turpentine, optical activity is exhibited in theliquid state. This shows that the activity is associated with theindividual molecules themselves.


Photoelasticity• Some materials become optically

anisotropic when a mechanicalstress is applied. This phenomenon is variously referredto as photoelasticity, stress birefringence, or mechanicalbirefringence. It is useful for thevisualization of mechanical stress in otherwise transparent materials. The colors are seen when thestressed materials are placedbetween crossed polarizers.

• Photoelastic materials are used for thin-film strain gauges for the studyof mechanical stresses in mechanical parts. If a replica of a cast part is made out ofphotoelastic material and thensubjected to stresses like thoseanticipated for the finished part, themaximum stress points in the shapecan be identified. This could lead to the strengthening of the design atthose points and eliminate costlybreakdowns.