PHASE RETARDATION

PLATES

SUBMITTED BY: SUBMITTED TO :

PRIYAMVADA CHUNDAWAT Mr. GOPAL CHOUDHARY

INTRODUCTION

Retarders serve to change the polarisation of an incident wave. In principle , the operation of a retarder is quite easy. One of the two constituent coherent P-states is somehow caused to have its phase lag behind that of the other by a predetermined amount. Upon emerging from the retarder , the relative phase of the two components is different than it was initially , and thus the polarisation state is different as well. Once we have developed the concept of retarders, it will be possible to convert any given polarisation state into any other and hence create circular and elliptic polarisers as well.

CLASSIFICATION

PHASE RETARDATION PLATE

A doubly refracting uniaxial crystal plate of uniform

thickness having refracting surface parallel to direction of

optic axis and capable of producing a definite phase

difference between the ordinary and the extraordinary ray,

is called phase retardation plate.

A retardation plate is an optically transparent material

which resolves a beam of polarized light into two

Orthogonal components; retards the phase of one

component relative to the other; then recombines the

components into a single beam with new polarization

characteristics.

INCIDENT MONOCHROMATIC LIGHT

EMERGENT LIGHT

SCHEMATIC VIEW :

E-ray

O-ray

Direction of optic axis

‘d’

PHASE DIFFERENCE : In calcite crystal , the velocity of E-ray (Ve) is greater than that of O-ray, the difference in time taken by these waves to cross the plate thickness ‘d’ can be given as :ΔT = To-Te ----- 1Here To and Te are the time taken by O-ray and E-ray to cross the plate of thickness d.To = d/Vo.Te = d/Ve.ΔT = (d/Vo) – (d/Ve).So, path difference occurs between E-ray and O-ray on passing through the plate, which can be given as :Δ = c . ΔTΔ= c {(d/Vo) – (d/Ve)}Δ= d {(c/Vo) - (c/Ve)}{n1= c/Vo , n2= c/Ve }Δ = d(n1-n2)Here n1 and n2 are the refractive indices of calcite crystal plate for O-ray and E-ray respectively. Hence phase difference between E-ray & O=ray is : o =( 2π*Δn *d) / λ

QUARTER WAVE PLATE

A doubly refracting uniaxial crystal plate having refracting

faces parallel to the direction of the optic axis , having a

thickness such as to create a path difference of λ /4 or a

phase difference of π/2 between the O-ray and the E-ray ,

is called Quarter wave plate.

For quarter wave plate :

Δ=(n1-n2)d= λ /4

where λ is the wavelength of the incident light.

d = λ /{4(n1-n2)}

A quarter-wave plate consists of a carefully adjusted thickness of a birefringent material such that the light associated with the larger index of refraction is retarded by 90° in phase (a quarter wavelength) with respect to that associated with the smaller index. Any linearly polarized light which strikes the plate will be divided into two components with different indices of refraction. The 2 components travel along same direction but with different speed and a phase difference of π /2 will be introduced between them. One of the useful applications of this device is to convert linearly polarized light to circularly polarized light and vice versa. This is done by adjusting the plane of the incident light so that it makes 45° angle with the optic axis. This gives equal amplitude o- and e-waves. When the o-wave is slower, as in calcite, the o-wave will fall behind by 90° in phase, producing circularly polarized light.

LINEAR TO CIRCULAR POLAQRISATION

If linearly polarized light is incident on a quarter-wave plate at 45° to the optic axis, then the light is divided into two equal electric field components. One of these is retarded by a quarter wavelength by the plate. This produces circularly polarized light. Incident circularly polarized light will be changed to linearly polarized light.

.

APPLICATION OF QUARTER WAVE PLATE

VARIOUS POLARISATION STATES

Q.W.P

Q.W.P

E.P.L

C.P.L

P.P.L

P.P.L

NOT 45°

45°

HALF WAVE PLATE

A doubly refracting uniaxial crystal plate having refractive faces parallel to the direction of the optic axis ,having a thickness such as to create a path difference of λ /2 or a phase difference of π between the O-ray and the E-ray ,is called a Half wave plate.Here, Δ=(n1-n2)d= λ /2and d = λ /{4(n1-n2)}A retarder that produces a λ/2 phase shift is known as a half wave retarder. Half wave retarders can rotate the polarization of linearlypolarized light to twice the angle between the retarder fast axis and the plane of polarization. Placing the fast axis of a half wave retarder at 45° to the polarization plane results in a polarization rotation of 90°.

A half-wave plate. Linearly

polarized light entering a wave plate can be resolved into two waves, parallel (shown as green) and perpendicular (blue) to the optical axis of the wave plate. In the plate, the parallel wave propagates slightly slower than the perpendicular one. At the far side of the plate, the parallel wave is exactly half of a wavelength delayed relative to the perpendicular wave, and the resulting combination (red) is orthogonally polarized compared to its entrance state.

A half wave plate is used for changing the direction of

plane of vibration of the plane polarized light .When it is

incident normally on a half wave plate , emergent ray is

also plane polarized but the plane of vibration of emergent

ray rotates through an angle 2 theta.

Anti-clockwise clockwise

(c.p.l) H.W.P (c.p.l)

APPLICATION OF HALF WAVE PLATE :

DISTINCTION BETWEEN QUARTER - WAVE PLATE, HALF- WAVE PLATE AND AN ORDINARY GLASS PLATE :

To distinguish between QWP, HWP and GP light from monochromatic source is allowed to pass through a nicol prism say (N1) called polarizer as it gives plane polarized light (PPL). Now the plate to be analyzed is inserted in the path of PPL with its plane normal to the incident light and analyze the emergent ray by another nicol prism ,say (N2) called analyzer.

U.P.L N1 P.P.L Plate N2 eye

DURING ONE ROTATION OF NICOL PRISM N2 :

i. If the emergent light shows intensity two times maximum and two times minimum but not 0, then the plate will be QWP , due to conversion of PPL into elliptically polarized light (EPL) by this plate.

ii. If emergent light shows uniform intensity , then also the plate would be QWP , due to conversion of PPL to circular polarized light (CPL).

iii. If the emergent light shows intensity 2 times maximum and 2 times zero intensity, then the plate may be QWP, HWP or GP.

iv. For this case , rotate the test plate by some angle and then turn nicol N2 through one rotation.

EMERGENT LIGHT

SHOWS INTENSITY 2 TIMES MAXIMUM AND MINIMUM

BUT NOT 0OR UNIFORM INTENSITY

=> QWP

SHOWS TWO TIMES MAXIMUM AND

TWO TIMES 0 INTENSITY, THEN

THE PLATE IS HWP OR GP

NOW REMOVE THE TEST PLATE AND THEN ADJUST THE ANALYZER N2 FOR EMERGENT LIGHT TO BE OF 0 INTENSITY. INSERT THE TESTPLATE & TURN IT THROUGH 1 COMPLETE ROTATION, IF THERE IS

INTENSITY VARIATION THEN IT IS HWP & IF 0 INTENSITY,THEN IT IS GP

CONCLUSION

In this application note we have given a basic description of light polarization and some of the tools used to control the polarization state of light. Retarders and polarizers were used in simple devices that provide some of the common manipulations required wherever light is being measured. We have seen that quarter wave plate as previously explained will change linear polarization to circular and visa-versa. It can be shown that propagation through a half wave plates will keep linear polarization linear, however it will be rotated through an angle of 2q; where q is the angle between the incident polarization direction and the crystal’s fast axis. For this reason half wave plates are often referred to as polarization rotators.

THANK YOU .

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