Chapter Three : Polarization of Light Waves

3.1 POLARIZATION OF LIGHT

To talk about the polarization of an electromagnetic wave, it s easiest to look at polarized light. Just remember that whatever applies to light generally applies to other forms of electromagnetic waves, too. So, what is meant by polarized light? It s light in which there s a preferred direction for the electric and magnetic field vectors in the wave. In unpolarized light, there is no preferred direction: the waves come in with electric and magnetic field vectors in random directions. In linearly polarized light, the electric field vectors are all along one line (and so are the magnetic field vectors, because they re perpendicular to the electric field vectors). Most light sources emit unpolarized light, but there are several ways light can be polarized.
One way to polarize light is by reflection. Light reflecting off a surface will tend to be polarized, with the direction of polarization (the way the electric field vectors point) being parallel to the plane of the interface.
Another way to polarize light is by selectively absorbing light with electric field vectors pointing in a particular direction. Certain materials, known as dichroic materials, do this, absorbing light polarized one way but not absorbing light polarized perpendicular to that direction. If the material is thick enough to absorb all the light polarized in one direction, the light emerging from the material will be linearly polarized. Polarizers (such as the lenses of polarizing sunglasses) are made from this kind of material.
If unpolarized light passes through a polarizer, the intensity of the transmitted light will be 1/2 of what it was coming in. If linearly polarized light passes through a polarizer, the intensity of the light transmitted is given by Malus law
, (13.1)
where ? is the angle between the direction of polarization of the incident light and the polarization axis of the polarizer.
A third way to polarize light is by scattering. Light scattering off atoms and molecules in the atmosphere is unpolarized if the light keeps traveling in the same direction, is linearly polarized if at scatters in a direction perpendicular to the way it was traveling, and somewhere between linearly polarized and unpolarized if it scatters of at another angle.
There are plenty of materials that affect the polarization of light. Certain materials (such as calcite) exhibit a property known as birefringence. A crystal of birefringent material affects light polarized in a particular direction differently from light polarized at 90 degrees to that direction; it refracts light polarized one way at a different angle than it refracts light polarized the other way. Looking through a birefringent crystal at something, you d see a double image.
Liquid crystal displays, such as those in digital watches and calculators, also exploit the properties of polarized light.

POLARIZATION BY REFLECTION

One way to polarize light is by reflection. If a beam of light strikes an interface so that there is a 90° angle between the reflected and refracted beams, the reflected beam will be linearly polarized. The direction of polarization (the way the electric field vectors point) is parallel to the plane of the interface.
The special angle of incidence that satisfies this condition, where the reflected and refracted beams are perpendicular to each other, is known as the Brewster angle. The Brewster angle, the angle of incidence required to produce a linearly-polarized reflected beam, is given by
. (13.2)
This expression can be derived using Snell s law, and the law of reflection. The diagram below shows some of the geometry involved.

Figure 13.1

Using Snell s law we obtain
. (13.3)
This gives the Brewster relationship
. (13.4)
Light is a transverse wave. The directions of the oscillations electric and magnetic vectors being at right angles to the direction of propagation (Fig. 13.2).


Figure 13.2

However light is emitted by an enormous number of atoms. That is why the plane of oscillations of -vector is not kept the same in space. The orientations of this vector as well as are arbitrary (Fig. 13.3).

Figure 13.3

Light wave is moving toward the observer. This is so called natural light. Vectors of are not shown. If there is an interaction of light and substance the effect of polarization takes place. A plane-polarized wave is shown in Fig. 13.4.

Figure 13.4

One may say that the plane of oscillations of - vector is regu-lated. Thus if location of the oscillation plane is constant the light is called plane–polarized. There are three ways of producing a polarized light:
1) polarization by transmission of light through anisotropic substances;
2) reflection of light;
3) refraction of light.
A tourmaline crystal, quartz, Iceland spar are used usually in order to turn natural light into polarized. The reason of this effect is that these crystals is said to be optically anisotropic. A substances are called optical anisotropic if its optical properties vary in different directions. The scheme of device for investigation of polarized light shown in Fig. :


Figure 13.5

The first crystal (polarizer) is used for polarization of natural light. The second one (analyzer) is used for investigation of polarized light. The analyzer and polarizer are the same crystals. If analyzer rotate about the direction of light beam the transmitted intensity changes.
Now the thin sheet of polarized material is used. It is called polaroid. Polaroid consists of dichroic crystal herapatite (guinine sulfide periodide), that is in the thin film of celluloid.