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Light, as we have said, is a transverse electromagnetic wave. However, until this point we have only considered light for which the electric (and magnetic) field vector are oscillating in a single, fixed plane. Such light is called linearly polarized or plane polarized. In other words, although the electric field oscillates in magnitude and sign, its orientation is constant. A fixed plane of vibration contains both E and , the direction of propagation. However, natural light is generated by a large number of randomly oriented atomic oscillators. The light emitted from these oscillators will combine momentarily to form a linearly polarized wave, but this will persist for no longer than 10-8 seconds before different atomic oscillators emit new randomly polarized waves causing a different polarization of the resultant wave. The result is that the polarization of natural light fluctuates too rapidly to be detectable. This situation is called random polarization. In most light the polarization is neither completely random nor completely linear -- this is known as partially polarized light.
Consider two plane polarized waves propagating in the z direction, one oscillating in the x-direction and one in the y-direction:
|Ex(z, t)||= E0xcos(kz - σt)|
|Ey(z, t)||= E0ycos(kz - σt + ε)|
|E[E0x + E0y]cos(kz - σt)|
It is also possible for light to what is called circularly polarized. This occurs when E0x = E0y = E0 (in the case where the amplitudes are not equal the polarization is elliptical) and the phase difference between the component waves is ε = - Π/2±2Πm for m any integer. The resulting equation for the wave is:
|E = E0[cos(kz - σt) + cos(kz - σt)]|
A device which creates polarized light when natural light is incident upon it is called a polarizer. Polarizers work by one of four methods: selective absorption, reflection, scattering, or birefringence. For a linear polarizer, only light with a polarization parallel to a particular axis will be transmitted; this axis is called the transmission axis. Rotating the polarizer when natural light is incident will have no effect on the irradiance on the far side of the polarizer because of the random polarization of the light. However, if a second identical polarizer is placed behind the first and rotated with respect to the first, the irradiance will vary. This is because light passing through the first polarizer will be plane polarized. As the transmission axis of the second polarizer or analyzer is rotated only the component of the plane polarized light parallel to this axis will be transmitted. When the angle between the two polarizers reaches 90o the plane polarized light has no component parallel to the transmission axis of the analyzer. For angles in between the irradiance of the transmitted light is given by Malus' Law:
|I = I0cos2θ|
The simplest polarizer is called a wire-grid polarizer and consists simply of a number of closely spaced parallel wires.
The related phenomenon of birefringence occurs when a substance is optically anisotropic, or does not have the same optical properties in all directions. Most usually, this manifests itself as the property that light travels faster through the substance along one axis than it does along another. Thus the substance has two different refractive indices (refringence is an old word for refraction). This can arise from a difference in how strongly electrons in the atoms in the crystal structure are bound to their nucleus; electrons along one axis may be bound more strongly causing them to have a different resonance frequency (see the discussion of dependence on index of refraction on frequency).
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