polarization 1

8/14/2019 Polarization 1

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Polarisation of light

The polarisation of light is scarcely

discernable with our eyesPolarisation describes the behaviour of the electric

field associated with lighttypes of polarisation are linear , elliptical , circular ,unpolarised

Remember that in isotropicmaterials, light is atransverse wave

Direction

of travel

Plane of electricfield

z x

y


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Linear polarisation

The direction of the electricfield at a point stays constantin time

its direction is the direction of

linear polarisationits components along the x andy axes must always stay in stepmathematically, the 2 components of E at point zalong the wave can be written

z

x

y E

Directionof travel

Linearly polarised light

( ) ( )( ) ( )t kz E t z E

t kz E t z E

oy y

ox x

=

=

cos,

cos,


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A note on components of E

E , the electric field, has

a direction and a sizeit is a vector , like adisplacement

Every electric field of magnitude E o has

components, Eox and E oythe sizes of the components depend onthe angle between E o and the x axis

Polaroid transmits the component of E along itsaxis (see later)

x

y

Eoy

Eox

Eo

Eox along x +

Eoy

along y is equivalent to

Eo

( )( )==

sin

cos

ooy

oox

E E

E E


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Haidingers brush

Some people can detect the directionof linear polarisation of light

A very faint figure is visible inlinearly polarised light a few degreesacross in the centre of your field of view

if you rotate a piece of polaroid in front of your eye, thisfigure rotates with the polaroid

The figure is called Haidingers brush

linear polarisationdirection


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Relationship between irradiance

of light and electric field ELight meters measure irradiance, cameras

and our eyes respond to irradianceThe irradiance, I, is proportional the

average square of the electric field:

Polarisation phenomena are about thedirection and amplitude of the electric field

wave, E

2 E I


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Polaroid sheet

Polaroid produces linear

polarisation of light bytransmitting the electric vector along the axis of the polaroid

and absorbing the perpendicular electric vector

Polaroid placed in front of polarised lighttransmits the most when its axis is rotated || to the

direction of polarisation and least when

Direction of transmission

Polaroid sheet

Directionof

absorption

Polarisedlight

Polaroid

E


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% of polarisation

Light can be partially polarisedMeasure the maximum intensity I max and the

minimum intensity I minCalculate the % polarisation in the direction of

maximum intensity

Example:if I

max= 2I

min, then % polarisation = 100/3 = 33%

MeasuringImax

Named direction

Measuring

Imin

( )( ) 100II

II%

minmax

minmax +

=on polarisati


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Circular polarisation

With circular polarisation, the x and y amplitudesare both equal (call them E o) but there is a phase

difference of /2 between themCircular polarisation comes in

two flavoursright circular polarisation, in which Erotates clockwise looking back downalong the direction of propagation

left-hand circular polarisation circular polarisation cant be distinguished through a sheet of polaroid

x

yLooking

back towards the

source

Circularly polarised light( )( )t kz E E

t kz E E

o y

o x

=

=

sin

cos


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Combination of opposite circular

polarisationsIf you combine right-handed and left-handed circular

polarisation in equal amounts, you get linear polarisation

The polarisation angle (i.e. the direction of the linear polarisation) depends on the phase difference between one

component (e.g. x component) of the two handsrelevant to interpreting other polarisation phenomena

+Right

circular

Left

circular linear

( )( )t kz E E

t kz E E

o y

o x

=

=

sin

cos( )( )t kz E E

t kz E E

o y

o x

=

=

sin

cos ( )t kz E E o x = cos2

=


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Application of circular

polarisation

Backgroundincident light

Incident lightcircularly polarised

Reflected light withopposite circular polarisation

Display

Displayonly seen

Circular polariser

Circular polarisers are used to

enhance the contrast of LEDdisplaysBackground light is circularly

polarised before it reaches thereflecting front of the displayThe handedness of the

polarisation is changed by the

reflection and it fails to get back through the polariser

The direct light from the

display does pass through the polariser


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Elliptically polarised light

With elliptical polarisation,the amplitudes of x and y

components are generally notequal and neither are phases

between the componentsanything special

Elliptical polarisation is the most general case = 0 is the special case of linearly polarised light = /2 and Eoy = E ox gives circularly polarised light

x

yLooking

back towards the

source

Elliptically polarised light( )( )+=

=

t kz E E

t kz E E

oy y

ox x

cos

cos


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Unpolarised light

Unpolarised light consists of light where

the direction of E varies at random betweensuccessive measurements at one pointany direction is equally likely

Unpolarised light can beconsidered as a combination

of equal amounts of linear polarisation in two directionsat right angles, where the two

components are incoherent

x

yE values insuccessiveinstants

Unpolarised light


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Producing linear polarisation

Polaroid sheetTransmission through a wire grid

the distance between wires < /4 modern polaroid sheet works in a similar way

Scattering of sunlight by the atmosphere bees and other insects use polarised light to navigate

Reflecting lightreflections can be reduced by looking though polaroidsunglasses oriented to cut out the strongest polarisation

Transmission through birefringent materialsused in the petrological microscopeanalysis of strain in transparent materials

Transmission direction

Wire grid polariser


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Maluslaw

Malus law gives the irradiance transmitted by an analysing

polariser, I A, set at angle to the direction of polarised lightof irradiance I oThe irradiance of the light transmitted varies as cos 2

this is just what youd expect from our earlier sectionon the relationship between irradiance and amplitudee.g. a polariser is set at 30 to the direction of polarised light, howmuch is transmitted by the polariser?

fraction transmitted = 0.75

x

y

z

Unpolarisedlight

1st polaroid, polariser

Linearly polarised,amplitude E o,

intensity I o

2nd polaroid,analyser

Polarised,amplitudeEA = E ocos

= 20 cos I I A

( ) oo A I I I 75.030cos 2 ==


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Rotating the direction of

polarisationSeveral sheets of polaroid

in succession will rotate thedirection of polarisation of

lightSome molecules, such as sugar solutions

and quartz, can do the same only moreefficiently. This ability is called opticalactivity , or sometimes rotary polarisation

3 polarisers rotated by 20 to each other

Io


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Optical

activityOptically active materials rotate the direction of

polarisation as the light propagates throughdextro-rotatory ; levo-rotatory

measured by specific rotation , in mm -1 for solidsCause is that left and right circularly polarised

light have different refractive indices n R and n L.linearly polarised light travels through as twocircularly polarised rays, at slightly different speeds

as their phase difference varies, so the direction of linear polarisation alters

SamplePolarised beam

z


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Chiral molecules

Optical activity is caused by

molecules that have a helicaltwist, called chiral moleculesAll chiral amino acids are l-

rotatory why? Natural sugars like dextrose

are d-rotatory(Some optical activity can becaused by twisted molecular arrangements)

bondsH- blue

C-yellow

0- red

Dextrose


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Liquid crystal displays

An LCD pixel uses crossed polarisers to producethe dark state and an electrically induced change

of polarisation to produce the bright stateThe popular twisted nematic LCD:

Linear polariser

Glass

Thin conductinglayer

Liquid crystal(~10 m)

Conducting layer

GlassCrossed polariser Mirror

LCD


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Molecular orientations with an

LCDThe alignment of molecules is induced by a surfactant

to produce a highly optically active cellA small voltage is sufficient to re-align the molecules

No voltage Natural state with built-in 90 twist.

+ve

ve

Applied voltageMolecules away from surface re-align


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Polarisation by scattering

Vibrating electrons emit lightasymmetrically

most light is emitted to their vibration directionno light is emitted along their vibration direction

Light scattered through 90 is strongly polarised

The blue sky is polarised, particularly at 90 fromthe sun

use is made of this by insects, particularly bees, for navigating

Unpolarisedincident light

Electron

vibration

Electric field most

strongly seen


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The Brewster angle

The Brewster angle, B, is the angle at which thereflected light is 100% polarised, to the plane of

incidenceThe reflected and transmitted rays are at 90

Example: for n = 1.5, B = 56.3

n B =tan

reflected

incident

transmitted

I

Parallel polarisation

Perpendicular olarisation

B

Refractiveindex n

Strong transmitted beam


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Polarisation by

reflectionFraction of light reflected at

different angles of incidencedepends on its linear poln

Observation in nature

Pile of plates polariser

Fraction reflected versus angle of incidence for n=1.5

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80

I

I||

i

Weak Brewster anglereflection, polarised to

plane of diagram

Incidentlight

Pileof

plates

Strong transmitted beam polarised in plane of diagram

Brewster angle


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The polarising microscope

The polarising microscope

incorporates a polariserthe sample is illuminated bylinearly polarised light

An analyser allows the polarisation of the image to beinvestigated

the analyser is often set at 90to the polariser

the geologists version is thepetrological microscope

source

condenser

polariser specimenobjective

eyepiece

analyser

observer


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Birefringence

Birefringence is a new range of

phenomena opened up by theanisotropy of materials to the propagation of light

These materials usually transmitlight as two rays, even when one isincidentCaCO 3 (calcite, Iceland spar) is

the archetypical solidaxishexagonalup

viewedCaCO 3


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Ordinary & extraordinary rays

The ordinary ray obeys Snells lawThe extraordinary ray deviates in a plane

containing the optic axis direction of the crystalsuch a plane is called a principal plane

Both rays are linearly polarised at right angles toeach other

E

O

Top view of rhomb

Principal plane

EO

Side view of rhomb in principal plane

.

indicates polarised to principal plane

indicates polarised

|| to principal planelocates image of dot below surface


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ChristiaanHuygens:

euraka!

drawings

packing

Huygens'


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Waves in a uniaxial crystal

Calcite optic axis || 3-fold axis

Ordinary rays are propagated byan expanding spherical wave

the electric vector is optic axisrefractive index n o = c/v

Extraordinary ray is propagated by an expanding ellipsoidal wave

the electric vector is || princ. plane

smallest refractive index n e=c/v || a

b

Section optic axis


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Propagating ordinary waves

Ordinary waves

propagate as youwould expect fromHuygens principleThe refractive index

no for calcite is 1.658

ne for calcite is 1.486calcite is an example of a negative uniaxial crystal,

because n e< n o

Crystal

surface

Spherical waveletsof ordinary waves

Propagatingordinary

wavefronts incrystal

light

P ti f


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Propagation of

extraordinarywaves

Remember thatextraordinary wavelets

propagate as ellipsoidalwavefronts

The axes of the ellipsoids are inclined to the surface

The common tangent cuts the ellipsoids off to the sideThe direction of the propagating ray is therefore not perpendicular to the surface

inside an anisotropic crystal, the extraordinary light is generally nota purely transverse waveBiaxial crystals have 2 extraordinary rays; they are complicated

Crystal

surface

ellipsoidal waveletsof extraordinarywaves

Propagatingextraordinary

wavefronts incrystal

light

Bi f i i l d l l


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Birefringence is related to crystal classCubic isotropic

Tetragonal, Hexagonal, Rhombohedral uniaxial

Orthorhombic, Monoclinic, Triclinic - biaxial

(Trigonal)


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Light incident || optic axis

Both rays travel together, producing no

special effects

Opticaxis

Edge-on view of plate

Light incident when the optic axis is to the plate no interesting effects

Platethickness

Li h i id i i


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Light incident optic axis

The 2 polarisations travel at speeds c/n oand c/n e, acquiring a phase difference

Opticaxis Edge-on view of plate

Light incident when the optic axis is || to the plate

indicates polarisedplane of diagram

indicates polarised|| plane of diagram

y

z

x into planePlate

thickness

Polarisation change during


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Polarisation change during

propagationThe phase change between the 2

rays is z(n o-ne)2/ vacIf the 2 rays start off with equal

amplitude, then the diagram showshow the polarisation changes withz, the distance travelled

the sequence happens every 3 m incalcite100 m is more typical of minerals 45

90

135

180

225

270

315

360

Phasedifference

z

0

Mi l d th i


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Minerals and the microscope

Anisotropic material appears black; birefringent materialappears with polarisation colours

the most intense colours are when the optic axis is at 45extinction occurs when the optic axis is || or to the polariser

additional colouring is provided by pleochroism , selective polarisation dependent absorption of some colours

Polariser

Sample

Analyser

et.fsu.edumicro.magn:courtesy picture

Appearanceof Moon

rock in the polarisingmicroscope

Demonstration example


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Demonstration example

The first picture shows several sheets of mica of different thicknesses seen in ordinary light

The second picture, the same sheets between

crossed polaroids


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Strain in transparent materials

Colours are caused

by strain induced birefringence

also by variations of thicknessfor a 1 mm thick material,360 phase shift is causedwhen (n o n e) 510 -4

Sl


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Retarders

A retarder is a uniform plate of birefringent

material whose optic axis lies in the plane of the plate. Retarders can be used tomake circularly polarised light

analyse elliptically polarised lightinterpret colours in the polarising microscope

Slow axis is optic axis for calcitefast axis is slow axis

Phase retardation , in radians

Fast axisThicknessd

Slowaxis

fast slowvac nnd k =

Retardance


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RetardanceA full-wave plate retards the slow wave

relative to the fast wave by 2 radians

A quarter-wave plate retards by /2in terms of phase, the retardance is chromaticthe retardance may be measured

in wavelength e.g. a retardance of 250 nm, which is

d(n slow - n fast )Why bother?

e.g. in the polarising microscope, slidingin a retarding plate between sample andanalyser enables a microscopist to decidehow birefringent the sample is, helpingidentification of the sample

Making circularly polarised light


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Making circularly polarised light

Circular polarisationis made by shining

linearly polarised lightat 45 onto a quarter-wave retarder

The output looks like:

the + sign occurs if the slow axis is || y direction,giving right circularly polarised output

-ve sign for slow axis to y axis, giving left circularly polarised light

( )( )t kz E E

t kz E E

o y

o x

=

=

sin

cos

Polarisingaxis Quarter-wave

plate axis at 45 tothe polaroid axis

Circular polarisation

out

Any polarisation

in

A circular polariser

Linear polarisingsheet x

y

polarization 1

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