POLARIZATIONPOLARIZATION

Course Content:*Polarized and unpolarized light, linearly polarized light *Polarizer &

Law of Malus

*Superposition of two mutually perpendicular linearly polarized light,

circularly and elliptically polarized light

*Polarization due to reflection (Brewster's law) & scatteringPolarization due to reflection (Brewster s law) & scattering

*Polarization by double refraction and phenomena of double refraction

in uniaxial crystals

*Quarter and Half wave platesQuarter and Half wave plates

*Production of circular and elliptical polarized light,

*Nicole prism, Faraday rotation

Polarization

Property of waves that can oscillate with more than oneorientation

Electromagnetic waves, suchas light, gravitational waves

Sound waves in a gas or liquiddo not have polarization:as light, gravitational waves

exhibit polarizationdo not have polarization:as medium vibrates only along thedirection in which the waves are travelling.

Polarization of light is described by specifying the orientation of theGeneral Convention:

wave's electric field at a point in space over one period of theoscillation

When light travels in free space, in most cases it propagates asa transverse wave

Polarization is to the wave's direction of travel

Significant use in optics, seismology, telecommunications and radar science

The polarization of light can be measured with a polarimeter.

A polarizer is a device that affects polarizationA polarizer is a device that affects polarization.

Polarized and unpolarized lightp gLinearly polarized waves: E-fieldoscillates at all times in the plane of

l i ti

Unpolarized light: E–field in randomdirections. Superposition of waves withE ib ti i diff t di tipolarization E vibrating in many different directions

Circular and elliptical polarization Circularly polarized light: superposition of 2 waves of equal amplitude

with orthogonal polarizations, and 900 out of phase.

The tip of E describes a circle(counterclockwise = RH and clockwise =

LH depend on y component ahead or behind)LH depend on y component ahead or behind)

If this wave were approaching an observer its electric vector wouldIf this wave were approaching an observer, its electric vector wouldappear to be rotating counter clockwise. This is called right circularpolarization

If the thumb of your right hand were pointing in the direction of propagationof the light, the electric vector would be rotating in the direction of yourfi

If amplitudes differ elliptical polarizationElliptical polarization

fingers

Elliptical polarization

• Linear + circular polarization = elliptical polarization

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

What is the quantitative approach ???optic axis of the plate.

Mathematical description of the EM wave

Light wave that propagates in the z direction:

t)k(E)t(E

y)t-kzcos(E)tz,(E

xt)-kzcos(E)tz,(E

0yy

0xx

y)(),( 0yy

to the equation of an ellipse (using trigonometric identities, squaring, adding):q g, g)

22 EEEE

2

0y

y

0x

x

0y

y

0x

x sincosEE

EE2

EE

EE

Master equation for polarization of light

Case-I: If there is no amplitude in x (E0x = 0), there is only one component in y (vertical)one component, in y (vertical).

Case‐II: Polarization at 45o

If there is no phase difference ( = 0) and

E0x = E0y, then Ex = Ey

t)k(E)t(E Case‐III: Circular polarization

y)t-kzcos(E)tz,(E

xt)-kzcos(E)tz,(E

0yy

0xx

If the phase difference is = 90o and E0x = E0y

then: E / E = cos  ,   E / E = sin then: Ex / E0x  cos  ,   Ey / E0y  sin and we get the equation of a circle:

1sin cosEE

EE 22

2

y2

x

EE 0y0x

Case‐IV: Elliptical polarizationIf the phase difference is  = 90o and E0x E0y

we get the equation of an ellipse:g q p

Summary:

Direction of propagation

Summary:

90o 90o90 90o

Producing polarized light

Polarization by selective absorption: material that transmits waves whose E-fieldvibrates in a plane parallel to a certaindirection and absorbs all othersdirection and absorbs all others

Polarizers and Malus’s LawIf li l l i d li ht ( l f l i ti i di t d b dIf linearly polarised light (plane of polarization indicated by redarrow) of intensity I0 passes through a polarizing filter withtransmission axis at an angle along y directiontransmission axis at an angle along y direction

jθcosEiθsinEE 00i jθcosEiθsinEE 00inc

After the polarizer

jθcosEE 0transm

So the intensity transmitted is

θcos IθcosE αI 20

220transm

2*Transmitted intensity: I = I0 cos2 = intensity of polarized beam on analyzer (Malus Law)

Unpolarised light on polarisers

Only I0/2 is transmitted of unpolarized light by a polarizer and it isy 0 g ypolarized along the transmission axis

An analyzer rotated at an angle respect to the polarizertransmits 100% of the incident intensity when = 0 and zero when = 90o = 90o

Relative orientation of the polarizer

Transmitted amplitude is E0 cos (component of polarization along polarizer axis)

Transmitted intensity is I0 cos2

(square of amplitude)(square of amplitude)

Perpendicular polarizer give zero intensity

Malus’ law: Example

1) Light transmitted by first polarizer is vertically polarized. I1 = I0/22) Angle between it and second polarizer is = 45o. I2 = I1

2(45o) 0 5 I 0 25 Icos2(45o)= 0.5 I1 = 0.25 I03) Light transmitted through second polarizer is polarized 45o from

vertical. Angle between it and third polarizer is = 45o.vertical. Angle between it and third polarizer is 45 . I3 = I2 cos2(45o)= 0.125 I0

Polarization by reflection

Unpolarized light reflectedp gfrom a surface becomespartially polarized

Degree of polarizationdepends on angle of incidence

If reflected and refractedbeams are orthogonal completebeams are orthogonal completepolarization occurs

Brewster’s law: angle of Brewster s law: angle ofincidence is given by tan p = n(n = index of refraction)

Reflection of light off of non-metallicsurfaces results in some degree of( ) surfaces results in some degree ofpolarization parallel to the surface