polarisation

1. PHASE
RETARDATION
PLATES
SUBMITTED BY: SUBMITTED TO :
PRIYAMVADA CHUNDAWAT Mr. GOPAL CHOUDHARY

2. 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.

3. CLASSIFICATION

4. 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.

5. INCIDENT MONOCHROMATIC LIGHT
EMERGENT LIGHT
SCHEMATIC VIEW :
E-ray
O-ray
Direction of
optic axis
‘d’

6. 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 ----- 1
Here 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 . ΔT
Δ= 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

7. 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)}

8. 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.

9. 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.

10. 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°

11. 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 /2
and 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 linearly
polarized 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°.

12. 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.

13. 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 :

15. 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

16. 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.

17. EMERGENT LIGHT
SHOWS INTENSITY 2 TIMES
MAXIMUM AND MINIMUM
BUT NOT 0
OR 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 TEST
PLATE & TURN IT THROUGH 1 COMPLETE ROTATION, IF THERE IS
INTENSITY VARIATION THEN IT IS HWP & IF 0 INTENSITY,THEN IT IS
GP

18. 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.

19. THANK YOU
.
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