# Polarized Light

Light is an electromagnetic wave. Nature of the wave is that a temporarily varying electric field provokes a magnetic field, and vice versa, a temporarily varying magnetic field provokes an electric field.

Electric and magnetic field are determined by their total amount and their direction, both are vectors. They are perpendicular to each other. Generally, light is unpolarized. If either the direction or the amount of the vectors remain (except for the sign) during the change, one talks about polarized light.

Let us consider first the case that the direction of the electric vector remains, except for the change of sign. Together with the propagation of light, a plane is formed. Simply speaking, the light is oscillating in a plane. A physicist talks about linear polarization. This is displayed in the upper part of Figure 1.

To cancel the polarization, one could try to superpose a second wave where the electric vector just has the opposite sign of the first one. However, this would be destructive interference, and the light would vanish at all. If the plane of the second wave is selected perpendicular to the first one, the light remains existing, but without preferred direction. This is illustrated in the middle part of Figure 1. Since the polarization disappears by such a superposition, one can consider the first wave positive linearly polarized and the second one negative linearly polarized. In the  Stokes-system, one calls the first case +Q and the second case –Q.

Is the polarization plane of a wave under 45 degrees with respect to the +Q-case, one deals with an independent linear polarization state, which is called Stokes-U, as illustrated by the green curve in the lower part of Figure 1.

If the amount of the electric vector remains constant, its direction must change permanently. One speaks about Circular Polarization, if the electric vector rotates around the propagation axis. This case is illustrated in Figure 2. According to the sense of rotation, it is called left or right circular polarization, and the symbols  +V and –V are used in the Stokes-system.

To measure polarized light, one can use double refractive crystals. Such crystals have a preferred plane in which linearly polarized light travels a bit faster than in the plane perpendicular to it, depending on the internal structure of the crystal. The fast beam is also called the ordinary beam and the slow one is the extraordinary. If the light enters in a certain direction, the  extraordinary beam is deflected by a small angle, what can be used to separate positive and negative polarized light (polarizing beam splitter). Light polarized under 45 degrees or circularly polarized light is split into equal parts.

Is the incidence direction perpendicular to the case above, the ordinary and extraordinary beams are not deflected, but there is a phase shift between them. Such optical elements are called phase plates. Linearly polarized light is not affected if it corresponds to the plane of the ordinary beam (the so-called fast axis). Is there an angle between the planes of the incensing light and the plane of the ordinary beam, the light will be separated into ordinary and extraordinary beam and recombined at the exit of the phase plate. Is the retardation corresponding to half of the wavelength (half wave plate), the plane of linearly polarized light is rotated by twice the angle. Is the angle 45 degrees, +Q will change into –Q. Circular polarization remains unaffected by a half wave plate.

In the case of  quarter wave plate, the the retardation is only a quarter of the wavelength. If the rotation angle is 45 degrees, the amount of the electric vector after leaving the phase plate is constant, but is is rotating around the propagation axis. Linear polarization becomes circular polarization, and vice versa, circular polarization becomes linear polarization.

Now we  can build a polarimeter which consists of a half wave plate, a quarter wave plate and a polarizing beam splitter. With the special  rotation angles of the phase plates, we can change any polarization state into +Q and –Q, which are then separated by the beam splitter. The difference of the intensities in the two beams, divided by the sum, gives the degree of polarization. A scheme of such a polarimeter is given in Figure 3

For modern polarimeters, ferroelectric liquid crystals are often used. They can be switched between two orientations of the fast axis by changing the external electric field. Another possibility are variable liquid crystals  where the retardation depends on the external electric tension.