Polarization-Physics-Lab Report, Exercises of Physics

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To study nature of polarization of laser light

Submitted to:

Dr. Asloob Ahmed Mudassar

Submitted by:

Yasir Ali

M.Phil. Physics DPAM

PIEAS

Any electromagnetic radiation consists of two components, the electric and the magnetic, which

are mutually perpendicular. The plane, in which one component lies say electric component, is

known as the plane of oscillation for that wave.

During excitation and de-excitation an atom emits EM radiation. During single such event, the

EM radiation emitted has fixed plane of polarization. But when a large number of such events combine, the plane of radiation is random for all such events. Such light is called randomly

polarized or un-polarized. In un-polarized light, electric field of light continuously changes its

electric field. As in EM radiation electric field and magnetic field are perpendicular to each

other, so magnetic field also continuously changes its field. But we always can resolve E-field

into its horizontal and vertical components.

As light is also an electromagnetic radiation so we discuss a particular case. In light electric field

continuously changes its direction so its components, when direction of propagation is along z-

axis, are gives as

Ey = E 1 sin(ωt - kz+δ) Ex = E 2 sin(ωt - kz)

This means that one component is delayed by phase difference δ which is random for un-

polarized light. The angle which this resultant electric field makes with the X axis can be

expressed as,

tan θ = Ez / Ey = (E 1 sin(ωt - kz + δ)) / (E 2 sin(ωt - kz))

From angle Ѳ we can define different categories of light depending on orientation of electric

field.

Un-polarized light:- For random phase difference δ, angle Ѳ between two components of

light is also random so light is called

randomly polarized or un-polarized. As we

can see that plane of electric field oscillates

around the direction of propagation of light.

This is called un- polarized light.

Fig.

Unpolarized

light

Plane polarized light:- If phase difference between x-axis component and y-component of

electric field is such that δ=0 or δ = π then angle Ѳ between the two components is constant and

light in this case is known as linearly polarized light.

In linearly of plane polarized light electric field is confined only in one plane and is

perpendicular to direction of propagation of light.

Circularly polarized light:- If phase difference is δ = π/2 and E 2 = E 1 then angle of electric

field with x-axis is given as

tan θ = ((E 2 sin(ωt - kz) / (E 1 sin(ωt - kz + π/2)))

tan θ = tan(ωt - kz)

or θ = ωt – kz

Circular polarization occurs when the component fields are precisely 90 degrees out of phase,

one component reaching its maximum when the other is reaching its zero-crossing. Actually it is

a mixture of equal amounts of two linear polarizations at right angles to one another, and 90

degrees out of phase to one another. For circularly polarized light, magnitude of electric field is

given as

E^2 = Ey^2 + Ez^2

= E 12 cos^2 (ωt - kz) + E 12 sin^2 (ωt - kz)

=E 12

This means that intensity or magnitude of resultant electric field remains constant even angle

varies with time.

In circularly polarized light electric field of light waves rotates around the direction of

propagation light. Its intensity is constant during rotation. Circularly polarized light can be left or

right circularly polarized, depending on its directions of rotation of electric field.

A circularly polarized light is produced from plane polarized light using quarter wave plate.

Quarter wave plate:- A quarter wave plates is a non linear material of such a thickness that

can produce a phase difference of π/2 between two perpendicular components of light. A quarter

wave plates is placed at π/4 angle to polarization direction of light, so this light is equally divided

into two orthogonal components, one of which is delayed in phase by π/2. This light from λ/ plate has electric field such that it appears o rotate around direction of propagation of light.

Quarter wave plate is made from birefringent material and having two refractive indices. Light

polarized along the direction with the smaller index travels faster and thus this axis is termed the

fast axis. The other axis is the slow axis.

Elliptically polarized light :- If phase difference δ = π/2 between two components of

electric fields and the two components are not equal in magnitude, then light appears such that its electric field rotates around the direction of propagation of light but its magnitude varies and so its electric field appears making an ellipse light produced will be elliptically polarized. It can also be left or right elliptically polarized like circularly polarized light.

Elliptically polarized light is produced by passing linearly polarized light through quarter wave plate when angle between polarization direction and fast axis of quarter wave plate is other than 45 o. In case of elliptically polarized light, intensity does not change. Only decomposing a single vector into its rectangular components with some phase difference does not change magnitude on vector. Similar is case for elliptically polarized light. We can also produce linearly polarized light from circularly or elliptically polarized light by passing it through quarter wave plate. Experiment:- Apparatus used in our experiment is, two polarizers, two quarter wave plates, photo detector to measure intensity, He-Ne laser. Objective:- To study nature of polarization of different kinds through polarizer and quarter wave plates.

Procedure:- Steps in which the experiment was performed are following.

1. Direction of polarization:- First of all we found direction of polarization of laser light. This was done by placing a polarizer in the path of laser beam and rotating it smoothly. At certain point maximum intensity of light passed through polarizer. At that point direction of polarized light and free axis of polarizer were aligned. So this is polarization direction of light. This was verified by rotating polarizer by 90o^ from previous position and observing that minimum intensity passed in this new position, which showed 90o angle between polarizer and light’s polarization direction.
2. Intensity and first polarizer:- For observing effect of polarizer’s angle with light’s polarization using first polarizer. We started from zero angle and noted intensity through detector. Then we changed angle between polarizer and polarization direction of light in small steps and noted intensity. From we can observe that intensity vary with angle. For angles 0o, 180o, 360o^ intensity has maximum value while for angles 90o, 270o^ intensity has minimum value shown in plot.

Fig. 3. Intensity through second polarizer Intensity and second polarizer:- Then we used another polarizer and observed variation on intensity due to rotation of polarizer. Plot of intensity of transmitted polarized light through polarizer for different angles between polarizer and direction of polarization of light is given.

These two components now will pass through another polarizer which is at nearly 45^0 angle to original direction of polarized light. Now according to Malus law, intensity passed through second polarizer is ( ) ( )

Fig. 6. Two components of polarized light through another polarizer. Intensity pattern observed are

Fig. 7Intensity through two polarizers

2. Polarizer 2 rotating and polarizer 1 fixed:- This part is same as above, the difference is only that now polarizer 1 is kept at 45^0 (almost) to direction of polarized incident beam and polarizer 2 is rotated for 360^0 angle. In this case polarizer 1 affected intensity on light by Malus law and also destroyed its polarization and give x-component and y-component of light which after passing through polarizer 2 again through Malus law and equation given above give intensity as shown. If polarizer 1 was exactly at 45^0 angle then intensity through both polarizers would be constant, but as we could not fixed that polarizer at 45^0 exactly so some small variations observed

as shown.

Fig. 8, intensity through two polarizers when first is fixed

5. QWP fixed and polarizer rotating :- In this case our desire was to fix QWP at 45^0 but it was not possible due to scale given on stand. Let first case QWP placed before the polarizer. If QWP is placed the polarizer and QWP is fixed and polarizer is rotated then QWP will change polarized light into circularly or elliptically polarized light which has two components of intensity (E field) as Ix and Iy. For rotating polarizer, intensity passed through it is given by Malus law as ( ) ( ) Where θ is the angle between Ix and free axis of polarizer. This formula is written for first quadrant but can be used for full revolution of polarizer. If θ=45^0 then I=Ix( or Iy). But if θ has values other than 45^0 then intensity has some variations given as

In second case polarizer which was placed before QWP is rotated while QWP was kept fixed at 45^0 (almost). In this case again QWP did nothing with light coming from polarizer and intensity pattern showing effect of only polarizer. Again normalized intensity plot against angle of rotation of polarizer for 45^0 of QWP is shown.

Again θ is angle between free axis of polarizer and direction of polarization of light along x-axis obtained from QWP. At any other angle of rotation of QWP with polarization direction of light, elliptically polarized light was produced which had different components of electric field (or equally intensity) along x-axis and y-axis. If I 0 is incident intensity then

√ ( ) And

√ ( ) Square and square root is taken to discard negative values of intensity which are impossible. These values of intensity along x-axis and y-axis fields when passed through polarizer placed at 45^0 9almost) gave pattern of intensity like.

Normalized intensity with Imax = 261