Question

What kind of polarization has a plane electromagnetic wave if the projections of the vector E on the x and y axes are perpendicular to the propagation direction and are defined by the following equations:

(a) Ex = E cos (ωt — kz), Ey = E sin (ωt kz);

(b) Ex = E cos (ωt — kz), Ey = E cos (ωt — kz + π/4);

(c) Ex = E cos (ωt — kz), Ey = E cos (ωt — kz + π)?

Answer 1

The wave is moving in the direction of z - axis

so the of the electric vector moves along a circle. For the right handed coordinate system this represents circular anticlockwise polarization when observed towards the incoming wave

This is clearly an ellipse. By comparing with the previous case (compare the phase of Ey in the two cases) we see this represents elliptical clockwise polarization when viewed towards the incoming wave.

We write the equations as

which is a straight line (y = -x). It corresponds to plane polarization.