Lect 1,2 Polarization

Polarization Polarization Interference and Diffraction

Wave nature of LightPOLARIZATION ?

Wave nature of Light POLARIZATION ?

Longitudinal?Longitudinal?

Transverse?• E M wave • S wave in seismic wave• S-wave in seismic wave

Light is an electromagnetic wave andtransverse in naturetransverse in nature.

Natural light or ordinary light is unpolarized in natureNatural light or ordinary light is unpolarized in nature.

Vibrations take place symmetrically in all directions in theplane perpendicular to the direction of propagation of lightplane perpendicular to the direction of propagation of light.

Why????Why????

Electric field only going up and down ⇒ linearly or plane polarized

The process of transforming unpolarized light intopolarized light is known aspolarized light is known as

Representation of Plane polarized light

Plane polarized light withp gVibration perpendicular tothe Plane of paper (S-

l i d)polarized)

Plane polarized light witha e po a ed g wvibrations parallel to the planeof paper (P-polarized)

Plane of vibration & polarization:

Plane of vibration: A plane containing the direction ofpropagation and direction of vibrationp p g

Plane of polarization: A plane containing the direction ofpropagation and perpendicular to plane of vibrationpropagation and perpendicular to plane of vibration

Mathematical representation of Pl l i d li ht

Suppose light is propagating in z

Plane polarized light

Suppose light is propagating in z-direction. Mathematically a planepolarized light can be represented as: xpolarized light can be represented as:

ˆ z)cos(ˆ),( 0 tkzEitzE xx ω−=

ˆ )cos(ˆ),( 0 tkzEjtzE yy ω−=

How to detect unpolarized & polarized light …

Unpolarized: if no change in the intensity during full rotationUnpolarized: if no change in the intensity during full rotation

Polarized: if intensity changes during full rotation of the crystalPolarized: if intensity changes during full rotation of the crystal

Production of polarized lightf p z g

1 B R fl ti B t ’ L1. By Reflection: Brewster’s Law

2 B Refraction: Mal s La2. By Refraction: Malus Law

3 By selective absorption: Dichroic material3. By selective absorption: Dichroic material

4 By double refraction:4. By double refraction:

-Nicol Prism-Nicol Prism

- Wave platesWave plates

Polarization by reflection: Brewster’s Law

• Unpolarized light is incident atl i i l th di l t ipolarizing angle on the dielectric

medium the reflected light iscompletely plane polarizedcompletely plane polarized.

θμ tan= pθμ tan=

Note : The polarizing angle is different for differentfl i freflecting surfaces.

Polarization by reflection: Brewster’s Law Polarization by reflection: Brewster’s Law

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

1

21tannn

pθ⎠⎝ 1n

n1 22πθθ =+ pthatShow

n2

2

sintan 2 μ

θθ === p n

'

costan

1

μθ

θp

p

lawssnellandn

sinsin 221 θθ =p

thereforenn

)90(cossincos 22

π

θθθ −==p

therefore

22πθθ =+p

Polarization by reflection: Brewster’s Law Polarization by reflection: Brewster’s Law

For air-water interface, n1 = 1 and n2 = 1.33 (say) then Brewster’s angle is:then Brewster s angle is:

θ tan-1(1 33) 530θp = tan 1(1.33) ~ 530

Thus if the sunlight is incident on the sea at an angleclose to the polarizing angle, the reflected light isclose to the polarizing angle, the reflected light isalmost polarized. Now if view through the rotationpolaroid, the sea will appear more transparentpolaroid, the sea will appear more transparentwhen the polaroid blocks the reflected light.

Polarization by multiple reflection Malus’ LawLaw states thatintensity of lighttransmitted throughthe analyzer is directlyproportional to thesquare of the anglebetween thetransmission planes ofthe polarizer and

20 cosI I θ=

analyzer.

0 cosI I θ

• Unpolarized light have E field vibration in all directions.• Therefore I I <cos2θ> I /2• Therefore I = I0 <cos2θ> = I0/2

• Two consecutive polarizers.

Quest: 22.10 (page-22.38) Optics 4th ed by Ajoy Ghatak

(a)Consider two crossed Polaroids placed in the path ofan unpolarized beam of intensity I0. If we place a thirdp f y 0 f pPolaroid in between the two then, in general, somelight will be transmitted through . Explain thisg g pphenomenon.

(b)Assuming the pass axis of the third polaroid to be 450

to the pass axis of either of the polaroids, calculate thep f f p ,intensity of the transmitted beam. Assume that all thepolaroids are perfect.p p f

Ans: I0/8

Quest: An unpolarized light passes through aQuest: An unpolarized light passes through avertically placed polarizer having horizontalpolarization axis Subsequently it passes through apolarization axis. Subsequently it passes through apolarizer with its pass axis at 90o with respect to

l d l h h lvertical and two polarizers having their polarizationaxes at an angle 30o and 60o with verticalrespectively.What will be the intensity of the emergent light?What will be the intensity of the emergent light?

Ans : (3/32)I0

Use of Polaroid

Use of Polaroid

Without polarizer With polarizer

Use of Polaroid

Without polarizer With polarizer

Wire Grid Polarizer

Input light contains both polarizationsboth polarizations

The light can excite electrons to move along the wires, which theng g ,emit light that cancels the input light. This cannot happen perpen-dicular to the wires. Such polarizers work best in the IR.

Polaroid sheet polarizers use the same idea, but with long polymers.

Wire grid polarizer in the visibleUsing semiconductor fabrication techniques, a wire-grid polarizer was recently developed for the visiblerecently developed for the visible.

The spacing is less than 1 micron.

How do we make Polarized Light?

I. Polarizers-

Polarization by double refractionWhen an UPL enters ananisotropic crystal it splits intoanisotropic crystal, it splits intotwo beams, each of them beingcharacterized by a certain state ofcharacterized by a certain state ofpolarization. If by some method,we could eliminate one of thewe could eliminate one of thebeams then we would obtained aLPLLPL.

Methods of eliminating one of the beamMethods of eliminating one of the beam.1. By selective absorption - Dichroism.2. Total Internal Reflection.

Polarization by Selective Absorption – Dichroism

The electric field component of an incident light that is perpendicularto the optic axis (determined by its atomic configuration) is stronglyto the optic axis (determined by its atomic configuration) is stronglyabsorbed by the sample.

Thicker the sample, the more complete the absorption. Here thecrystal’s principal axis becomes polarizer’s transmission axis.

Polarization by Absorption: Dichroic materialsA number of crystalline materials absorb more light in oneincident plane than another so that light progressingincident plane than another, so that light progressingthrough the material become more and more polarized asthey proceed This anisotropy in absorption is calledthey proceed. This anisotropy in absorption is calleddichroism. There are several naturally occurring dichroicmaterials and the commercial material polaroid alsomaterials, and the commercial material polaroid alsopolarizes by selective absorption. Tourmaline crystal

is a dichroic materialis a dichroic material

By total internal reflection Polarization by Scattering

DOUBLE REFRACTION -BIREFRINGENCE

When a ray enters such a crystal, it splits into two rays. Thisphenomenon is known as double refraction or birefringence

A t i l hi h di l t diff t i di f f ti i id

phenomenon is known as double refraction or birefringence.

A material which displays two different indices of refraction, is saidto be ‘birefringent’.

Doubly Refracting Crystals

When a ray of unpolarised light is incident on a certaini l t l (d bl f ti t l) th tspecial crystal (doubly refracting crystal) there are two

refracted rays. Such crystals are of two types

1 Unaxial e g : calcite (Iceland spar) tourmaline and1. Unaxial e.g.: calcite (Iceland spar) , tourmaline andquartz

2 Bi axial e g : topaz and aragonite Copper Sulphate2. Bi-axial e.g.: topaz and aragonite, Copper Sulphate,cane sugar and Mica

GEOMETRY OF CALCITE CRYSTAL

Two images throughcalcite crystal

Polarizer transmits theordinary ray.

Polarizer rotated about 90°transmits the extraordinaryray.

GEOMETRY OF CALCITE CRYSTALIt is colorless transparent crystal. It is chemically crystallized CaCO3and occur in nature in different forms all of which give rhombohedranand occur in nature in different forms, all of which give rhombohedranon cleavage as shown in figure.

A and H are Blunt Corner

GEOMETRY OF CALCITE CRYSTALOptic axis: direction along a line passing through any oneof the blunt corners and making equal angles each of theof the blunt corners and making equal angles each of thethree edges which meet at the corner.

GEOMETRY OF CALCITE CRYSTALPrincipal Section: A plane containing the optic axis of the crystaland perpendicular to its two opposite faces is called the Principaland perpendicular to its two opposite faces is called the Principalsection of the crystal for that pair of faces. As Crystal has sixfaces there are three principal sections corresponding to eachpair of the opposite faces.