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Polarization of Electromagnetic Waves
The electric component of an electromagnetic plane wave can oscillate in any direction normal to the
direction of wave propagation (which is parallel to the
vector) (Fitzpatrick 2008). Suppose that the wave is propagating in the
direction. It follows that the electric field
can oscillate in any direction that lies in the

plane. The actual direction of oscillation determines the polarization
of the wave. For instance, a vacuum electromagnetic wave of angular frequency
that is polarized in the
direction has the associated electric field

(564) 
where
. Likewise, a wave polarized in the
direction has the electric field

(565) 
These two waves are termed linearly polarized, since the electric field vector oscillates in a straightline.
However, other types of polarization are possible. For instance, if we combine two linearly polarized waves of equal amplitude, one polarized in the
direction,
and one in the
direction, that oscillate
radians out of phase, then we obtain a circularly polarized wave:

(566) 
This nomenclature arises from the fact that the tip of the electric field vector traces out a circle in the plane normal to the
direction of wave propagation.
To be more exact, the previous wave is a righthand circularly polarized wave, since if the thumb of the right hand points in the direction of
wave propagation then the electric field vector rotates in the same sense as the fingers of this hand. Conversely, a lefthand
circularly polarized wave takes the form

(567) 
Finally, if the
 and
components of the electric field in the previous two expressions have different (nonzero) amplitudes then
we obtain righthand and lefthand elliptically polarized waves, respectively.
This nomenclature arises from the fact that the tip of the electric field vector traces out an ellipse in the plane normal to the
direction of wave propagation.
Next: Laws of Geometric Optics
Up: MultiDimensional Waves
Previous: Oscillation of an Elastic
Richard Fitzpatrick
20130408