Polarization

Lecture-1 Polarization Polarization is a property of transverse waves which describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel.

IT MUST BE KNOWN 1. Basics of Polarization 2. Electromagnetic Wave

3. Brewster’s law : ptan=μ , Where μ is the refractive , p is polarizing angle. Distinction between Unpolarized and Polarized light :

The difference between the Polarized light and Unpolarized light is difference in symmetry of vibrations of electric vectors about the direction of propagation of light. In Unpolarized light the light vector vibrates along all possible straight lines in

a plane perpendicular to the direction of propagation . Infact Unpolarized light may be considered to consist of an infinite number of waves , each having its own direction of vibration . In polarized light there is a lack of symmetry about the direction of light Polarization as the violation of symmetry of light vibrations As in case if Unpolarized light the electric vibrations are in all possible directions perpendicular to the wave’s direction .(fig ) . In case of polarized light the vibration are not symmetrical about the direction of light but the vibrations are confined to only to a single line in the the plane perpendicular to the direction of propagation .Such light is called ‘Plane Polarized’ or ‘ linearly polarized’ light . According to the theory of ‘electromagnetic theory of light’ a light wave consists of electric and magnetic vectors vibrating in mutually perpendicular planes , both being perpendicular the direction of propagation of light . The electric vector acts as a ‘light vector’

The following figure show some examples of the evolution of the electric field vector (blue) with time (the horizontal axes), along with its x and y components (red/up and green/down), and the path traced by the tip of the vector in the plane (purple): Plane of Vibration : The plane containing the direction of vibration and the direction of propagation of light is called the ‘plane of vibration’ . Plane of Polarization : The plane passing through the direction of propagation and containing no vibration is called ‘Plane of Polarization’.

IT MUST BE KNOWN 1. Optic axis of the crystal 2. principal section of the crystal

double refraction(birefringence)

It is a optical property in which a single ray of unpolarized light ( polarization) splits into two components traveling at different velocities and in different directions. One ray is refracted at an angle as it travels through the medium, while the other passes through unchanged. The splitting occurs because the speed of the ray through the medium is determined by the orientation of the light compared with the crystal lattice of the medium. Since unpolarized light consists of waves that vibrate in all directions, some will pass through the lattice without being affected, while others will be refracted and change direction. Materials that exhibit double refraction include ice, quartz, and sugarDouble Refraction Doubly –Refracting Crystals There are certain crystals which split a ray of light incident upon them into two refracted rays .Such crystals are called ‘doubly refracting crystals’ . Types :

1. Uniaxial crystal e.g. – calcite , tourmaline , quartz 2. Biaxial crystal e.g. - topaz, aragonite .

When ray of unpolarized light is incident on calcite or quartz crystal , it splits up into two refracted rays out of which one is found to obey the laws of refraction , that is , it always

lies in the plane of incidence and its velocity in the crystal is same in all directions. This ray is called ‘ordinary ray' ( O-Ray ). The refracted ray does not obey the laws of refraction .It travels in the crystal with different speeds in different directions .Hence it is called ‘Extraordinary ray’ ( E-ray ) .Along the optic axis ,however, the O-ray and E-ray both have the same velocity and hence same refractive index .

Polarization of the Rays

A ray of light is incident normally on a crystal , a principal section of which is shown . The ray is split up into two rays O and E ray . The O ray passes through the crystal undeviated While the E-ray is refracted at some angle .(from fig.) . As the opposite face of the crystal are parallel , the rays emerge parallel to the incident ray . but relatively displaced by a distance proportional to the thickness of the crystal . The ordinary and extraordinary rays obtained by double refraction are plane- polarized .The O-ray polarized in the principal section (i.e. it has vibration ⊥ to the principal section ) while E-ray polarised perpendicularly to the principal section (i.e. it has vibration parallel to the principal section ).

Lecture-2 Nicol prism A Nicol prism is a type of polarizer, an optical device used to generate a beam of polarized light. It was the first type of polarizing prism to be invented, in 1828 by William Nicol (1770-1851) of Edinburgh. It consists of a rhombohedral crystal of calcite (Iceland spar) that has been cut at a 68° angle, split diagonally, and then joined again using Canada balsam.

Unpolarized light enters one end of the crystal and is split into two polarized rays by birefringence. One of these rays (the ordinary or o-ray) experiences a refractive index of no = 1.658 and at the balsam layer (refractive index n = 1.55) undergoes total internal reflection at the interface, and is reflected to the side of the prism. The other ray (the extraordinary or e-ray) experiences a lower refractive index (ne = 1.486), is not reflected at the interface, and leaves through the second half of the prism as plane polarized light.

Nicol prisms were once widely used in microscopy and polarimetry, and the term "crossed Nicols" (abbreviated as XN) is still used to refer to observation of a sample between orthogonally orientated polarizers. In most instruments, however, Nicol prisms have been supplanted by other types of polarizers such as Polaroid sheets and Glan-Thompson prisms.

Uses The Nicol prism can be used both as ‘Analyser’ and Polariser . Production of different types of Polarised light Plane Polarised light – If however the light vector (electric vector) vibrates a fixed line in the plane , the light is said to ‘plane polarised’ or ‘linearly polarised’ . Circularly polarised light When two plane polarised waves are superimposed ,under certain conditions , the resultant light vector rotates with a constant magnitude in a plane perpendicular to the direction of propagation . The tip of the vector traces a circle and the light is said to be ‘Circularly polarised light’. Elliptically Polarised light If however the magnitude of the resulted of light vector varies periodically during its rotation ,the tip of the vector traces an ellipse , and light ids said to be ‘elliptically polarised’.

Lecture-3 Superposition of two Plane-Polarised waves having perpendicular vibrations Let a beam of Plane-Polarised light be incident normally on a calcite plate cut with its optic axis parallel to is faces . Let the linear vibration in the incident light be along PA , making an angle θ with the optic axis . Let A be the amplitude of vibration in the incident light. On entering the crystal , the amplitude of the incident light wave splits into two components , A cosθ along PE and A sinθ along PO . The component A cosθ having vibration parallel to the optic axis forms E-wave and the component A sinθ having vibration perpendicular to the optic axis forms the O-wave . The two waves emerge from the plate with a phase difference δ between them .Thus if Asinωt be the incident wave , the two emergent plane- polarised E-ray and O-ray would be represented respectively by

)sin(cos δωθ += tAx and tAy ωθ sinsin=

Let us put θcosA = a bA =θsin . Then we have

)sin( δω += tax ………………………..(i)

tby ωsin= ……………………………..(ii) The nature of resultant vibration can be obtained by eliminating t from (i) and (ii) . from (i)

we have .

δωδω sincoscossin ttax

+=

= δωδω sinsin1cossin 2 tt −+

But from eq. (ii), byt =ωsin

δδ sin)1(cos 2

2

by

by

ax

−+=

δδ 22

22

sin1cos ⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟

⎠⎞

⎜⎝⎛ −

by

by

ax

δδ 22

2

2

2

sincos2=−+

abxy

ax

by ………….(iii)

This is in general , represent an ellipse .Hence the light emerging from the crystal plate is , in general , elliptically polarised .

Special cases : (i) If the thickness of the plate is such that δ=0, 2π , 4π …………, then cosδ=1 and sinδ=0. Then eq. (iii) gives

022

2

2

2

=−+abxy

ax

by

02

=⎟⎠⎞

⎜⎝⎛ −

by

ax

0=⎟⎠⎞

⎜⎝⎛ −±

by

ax

xaby ±=± ……………………………………….(iv)

This represent a pair of coincident straight lines through the origin having a positive slope b/a (fig) . This means that the emergent light is linearly-polarised with the same direction of vibration as the incident light . (ii) If δ= π , 3π, 5π …………; then cosδ= -1 and sinδ=0 , then eq. (iii) reduces to

022

2

2

2

=++abxy

ax

by

02

=⎟⎠⎞

⎜⎝⎛ +

by

ax

0=⎟⎠⎞

⎜⎝⎛ +±

by

ax

xaby m=±

This is again a pair of coincident straight lines but with a slope (-b/a) . Hence the emergent light is linearly polarised with the vibration making an angle

θ2tan2 1 =⎟⎠⎞

⎜⎝⎛−

ab with that of the incident light (fig) . This case is the

basis of half wave plate .

(iii) If δ= π/2 , 3π/2, 5π/2 …………, then cosδ=0 and =1 . Then equ. Reduces to

δ2sin

12

2

2

2

=+ax

by ………………………………(iv)

This represent an ellipse . Hence light emerging from plate is elliptically polarized if the angle of vibration becomes 450 then x and y component of elliptic

vibration are equal .Then a=b , equ. (iv) becomes 222 ayx =+Hence in this case the emergent light is circularly polarized light .This case is the basis of Quarter Wave Plate

Lecture-4 Quarter Wave plate : A doubly refracting crystal plate having a thickness such as to produce a path difference of 4/λ , or a phase difference of π/2 , between the ordinary and extraordinary wave is called a ‘Quarter Wave Plate’ or 4/λ plate

Half Wave plate : A doubly refracting crystal plate having a thickness such as to produce a path difference of 2/λ , or a phase difference of π , between the ordinary and extraordinary wave is called a ‘Half Wave Plate’ or 2/λ plate

Detection of different types of polarized lights A rotating Nicol prism can distinguish between ordinary light and completely plane polarized light . It however cannot distinguish between the ordinary and circularly polarized light since in both cases there is no variation in intensity of light viewed through the rotating Nicol. If ,however the Nicol prism is used in conjunction with a quarter-wave plate , it is possible to distinguish between various kinds of light by applying the following tests .

Polarimetry is the measurement and interpretation of the polarization of transverse waves, most notably electromagnetic waves, such as radio waves and light. Typically polarimetry is done on electromagnetic waves that have traveled through or reflected, refracted, or diffracted from some material or object in order to characterize that object.

A polarimeter is the basic scientific instrument used to make these measurements, although this term is rarely used to describe a polarimetry process performed by a computer, such as is done in polarimetric synthetic aperture radar.

Specific Rotation : The specific rotation S of a substance at a given temp and for a given wavelength of light , is defined as the rotation in degrees produced when its concentration is 1 gm/cm3 . That is S=θ/l×c Biquartz Polarimeter This polarimeter is same as the laurent’s half –shade polarimeter , the only difference in the device and the source. In this setup the white light is used instead of monochromatic light . Laurent’s Half-Shade polarimeter

For measurement of angle of rotation of optically active substance in solution i.e. angle through which the plane of polarised light is roated on passing through a specific length of solution of known concentration, specific rotation may then be determined .the circular head is attached near the analyser and vernier movement on the scale enables the reading of optical rotation accuracy upto the accuracy of 0.1°.soleil's bi-quarts or laurents half shade device which makes the instrument accurate and sipmle for use with white light or sodium light.the polarimeter tubes.