Plane and Circularly Polarized EM Waves
Electromagnetic waves are transverse in the sense that associated electric
and magnetic field vectors are both perpendicualr to the direction of wave
propagation. The Poynting vector defined by
S = E x H (W/m^2),
indicates not only the magnitude of the energy flux density (energy flow
rate per unit area per unit time, Watts/m^2) but also the direction of
energy flow. For simple electromagnetic waves, the Poynting vector is in
the same direction as the wavevector, k.
The first animation shows propagation of sinusoidal plane electromagnetic
waves in the z direction. The electric field is assumed in the x direction,
and the magnetic field in the y direction.
A plane electromagnetic wave can be considered as vector combination of
two circularly polarized waves rotating in opposite directions. The animation
below shows propagation of electric field associated with a circularly
polarized wave with postitive helicity. (Positive helicity is the case
such that a screw would move in the direction of wave propagation if rotated
with the electric field. In optics, it is called "left hand" circualr polarization.
Negative helicity (right hand polarization) refers to rotation in the oppsite
direction.) The moving end of the helix indicates the head of the electric
field vector which is rotating about the z axis as shown in the right figure.
Animation below shows vector sum of two circularly polarized waves with
opposite helicities which results in formation of a plane wave. Electromagnetic
waves emitted by charged particles undergoing circualr motion (e.g., electrons
trapped in a magnetic field) are in general circularly (or elliptically)
polarized. Circularly polarized waves carry angular momentum as well as
energy and momentum. The angular mometum flux density is given by
R = r x (E x H)/c,
as discussed in Example 6, p. 161 of the textbook.
To repeat animation, click "Back" then "Forward" buttons.
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