The Faraday effect
Figure 2.1: Polarization of light and Faraday rotation of plane-polarized wave by angle β.
The Faraday effect, discovered by Michael Faraday in 1845, was the first experimental evidence that light and electromagnetism are related. This effect occurs in most optically transparent dielectric materials (including liquids) when they are subjected to strong magnetic fields. Light, and in general, electromagnetic radiation (EMR) takes the form of self-propagating waves in vacuum or in matter. These waves consist of alternating magnetic and electric field components that oscillate perpendicular to one another and to the direction of motion of the wave. By convention, the electric field vector E~ defines the polarization angle of the wave at any instant of time. A beam is said to be unpolarized when the E~ orientation of the component waves is a random mixture of all possible angles. Figure 2.1 depicts some electric field E~ oscillations striking a polarizer grid with a vertical polarization axis. A polarizer selectively transmits only the component of E~ that is parallel to the polarization axis of the polarizer, in this case E~y. Recalling that E~ = E~x + E~y, then the vertical wave is transmitted fully (E~y = E~ ), the horizontal wave is attenuated fully (E~x = 0), and the diagonal waves transmit only their E~y component, although this is not shown in the diagram. The transmitted beam is said to be plane-polarized because all the E~y point in the same direction, as shown by the arrow on the viewing screen. The Faraday effect or Faraday rotation is a magneto-optical phenomenon, or an interaction between light and the magnetic field in a dielectric, or non-conducting, medium. A magnetic field induces a rotation of the atomic magnetic dipoles in the dielectric, making it dielectrically polarized. This causes a beam of EMR entering the material to split into two beams by the effect of double refraction, or circular birefringence. These beams propagate throught the material at different speeds so that upon emerging from the material, they recombine with a phase shift that is expressed as a rotation in the polarization angle of the beam, as shown in Figure 2.1. The rotation angle β of the plane of polarization is proportional to the intensity of the component of the magnetic field B~ in the direction of the beam of light, as well as the length l of the sample:
β = νBl (2.3)
The Verdet constant ν is an optical parameter that describes the strength of the Faraday effect for a particular material; it varies with the temperature of the sample and the wavelength of the incident light.
16 Malus’ Law of polarization In 1809, Etienne-Louis Malus (1775-1812) observed that when a polarizer is placed in front of a beam of plane polarized incident light of intensity I0, the intensity I of the plane polarized transmitted beam is given by 2 I = I0 cos β, (2.4) where β is the angle between the light’s initial polarization E~ and the polarization axis of the polarizer. ◦ From Equation 2.4 it is apparent that when β = 0 ,I = I0 and the light is fully transmitted, when ◦ ◦ β = 90 ,I = 0 and the light is fully blocked, and when β = 45 ,I = I0/2. Equation 2.4 can be easily derived from the previous discussion of E~ components and by recalling that the intensity of a wave of amplitude A is I = A2.
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