Polar Ssr.pdf

PART of the NOTES ARE taken from WAVE SOURCES

Polarisation

XY – Plane: Plane of polarisation

POLARISATION Light is a transverse electromagnetic wave. We have not really discussed the direction of the Electric field other that that it is perpendicular to the direction of motion. If the E field points in a constant direction it is linearly polarised. However this direction is not always unchanging.

Unpolarized light Polaroid: Transmits along the pass axis and absorbs along the perpendicular axis (Transmission and Extinction axis)

Malus law I  E  ( Eo cos )  I o cos  2

2

2

Unpolarized light

Io I  I o cos   2 2

Degree of polarisation If the incident light is a mixture of unpolarised light of intensity Iu and polarised light of intensity Ip, then the transmitted light is given by:

Iu 2 I   I p cos  2 Iu Iu I max   I p ; I min  2 2 I max  I min P I max  I min

What if the E fields point in different directions? Consider 2 waves travelling in the z (k) direction but one has an E field pointing in the x (i) direction and one with E field pointing in the y (j) direction. Then Adding the electric fields gives:

The resultant E field is a vector pointing in a different direction but with components in the x (i) and y (j) direction. This wave is still linearly polarised but with a

You can have Linear, circular, elliptical polarizer

Polarisers are based on one of four mechanisms -Dichroism (selective absorption) -Birefringence (double refraction) -Reflection -Scattering

Wire Mesh

Example: If the vertically polarised component of The E field causes the electrons in the atom to oscillate vertically. This then generates light in all directions except in the vicinity of the dipole axis ie not vertically.

Reflection

Birefringence It means Double Refraction. When the electric field of the light is parallel to the Optical Axis the light experience an Extraordinary Refracting Index, on the perpendicular direction of the Optical Axis the light experience an Ordinary Refracting Index.

The polarised light can have component of E field parallel to the optic axis (as well as one perpendicular to the optic axis). Rays polarised parallel to the axis are extraordinary rays or e-rays. O-rays and e-rays experience different refractive indices, no and ne and so travel at different velocities. For calcite, no =1.66, while ne = 1.49.

Why do we have ne and n0 How it polarised? Why it is useful? PLEASE read the class notes

Retarders Please check class notes Optical Path Difference

Quarter wave, Half wave and Full wave Plates or Retarders

On passing through a quarter wave plate, one of these componentsis shifted relative to the other by Δϕ=π/2 (900) Then we go from linear light to circularly polarised light.

Similarly, if the initial polarisation angle is other than 450 we gofrom linear light to elliptically polarised light. These processes can also happen in reverse to turn circularlypolarised light into linear light or elliptically polarised light into linear light.

- Polarisation Plane of polarisation is same as plane of incidence - Polarisation Plane of polarisation is perpendicular to the plane of incidence

Polarisation by reflection

Polarisation by double refraction - Two refracted beams emerge instead of one - Two images instead of one

Optic Axis: Uniaxial crystals exhibit cylindrical symmetry. There is a unique direction in a uniaxial crystal called the optic axis. Values of physical parameters along optic axis are different from the values perpendicular to it.

Calcite

Quartz

Polarisation by double refraction Isotropic Medium : Velocity Spherical Anisotropic Medium : Velocity ellipsoid

Uniaxial and Biaxial Crystals Uniaxial : Calcite, Quartz Biaxial: Mica

- Polarisation Plane of polarisation is same as plane of incidence (principal plane)

This definition is considered in absence of Principal Plane

- Polarisation Plane of polarisation is perpendicular to the plane of incidence (principal plane) Plane of incidence : plane contains incident ray, reflected/refracted ray, surface normal Plane of polarisation : plane contains electric field vector and direction of propagation

Principal plane : Plane contains optic axis and the direction of propagation

e-ray : Plane of polarisation is same as principal plane e-ray in general does not obey the laws of refraction except in case of special cut of crystal (optic axis)

o-ray : Plane of polarisation is perpendicular to the principal plane o-ray always obeys the laws of refraction Always e-ray carries -polarisation and o-ray carries -polarisation

Polarisation by reflection

Brewster angle unpolarised polarised

linearly polarised

partially polarised

Glass

Brewster’s law

= Brewster angle

Half wave plate Quartz

Linearly Polarized Beam

A Linearly Polarized Beam of light can be thought of as the addition of a lefthand circularly polarized and a right-hand circularly polarized beam

Circularly Polarized Beam A Circularly Polarized Beam of light can be thought of as the addition of two lineraly polarized beams.In this case you have to add phase to one beam, which basically means you shift it by 1/4 wavelength with respect to the other beam.

Circular Polarization is closely related to photon spin or elliptical polarization. Some photons have Elongated Spin, some have Quite Round Spin. So that, beams of light made of one photon can be polarized in all the same ways that beams of light made of two photons.

Photons have spins with different elongations pointing at different directions.

EXTRA NOTES POLARIZATION MATHS EQUATIONS

Part I: Polarization states

Mathematical description of the EM wave

Light wave that propagates in the z direction:   E x (z, t )  E0x cos(kz -  t) x   E y (z, t )  E0y cos(kz -  t   ) y

Polarization of Light: Basics to Instruments

40

Part I: Polarization states

Graphical representation of the EM wave (I) One can go from:

  E x (z, t )  E0x cos(kz -  t) x   E y (z, t )  E0y cos(kz -  t   ) y

to the equation of an ellipse (using trigonometric identities, squaring, adding): 2

Ey  Ex   Ey  E x  2     cos  sin 2    E 0x E 0y  E 0x   E 0y  2

Polarization of Light: Basics to Instruments

41

Part I: Polarization states

Graphical representation of the EM wave (II) An ellipse can be represented by 4 quantities: 1. size of minor axis 2. size of major axis 3. orientation (angle) 4. sense (CW, CCW) Light can be represented by 4 quantities... Polarization of Light: Basics to Instruments

Part I: Polarization states, linear polarization

Vertically polarized light   E x (z, t )  E0x cos(kz -  t) x   E y (z, t )  E0y cos(kz -  t   ) y

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

Polarization of Light: Basics to Instruments

Part I: Polarization states, linear polarization

Polarization at 45º (I)   E x (z, t )  E0x cos(kz -  t) x   E y (z, t )  E0y cos(kz -  t   ) y

If there is no phase difference (=0) and E0x = E0y, then Ex = Ey

Polarization of Light: Basics to Instruments

44

Part I: Polarization states, linear polarization

Polarization at 45º (II)

Polarization of Light: Basics to Instruments

45

Part I: Polarization states, circular polarization

Circular polarization (I)   E x (z, t )  E0x cos(kz -  t) x   E y (z, t )  E0y cos(kz -  t   ) y

If the phase difference is = 90º and E0x = E0y then: Ex / E0x = cos  , Ey / E0y = sin  and we get the equation of a circle: 2

 Ex   Ey    cos2  sin 2  1     E  E 0x    0y  2

Polarization of Light: Basics to Instruments

46

Part I: Polarization states, circular polarization

Circular polarization (II)

Polarization of Light: Basics to Instruments

47

Part I: Polarization states, circular polarization

Circular polarization (III)

Polarization of Light: Basics to Instruments

48