Is Light Capable of Being Polarized in Multiple Directions?

[davidfur]

...two directions ?

I know light can be x, y or z-polarized. but can it be polarized both in x AND y or any combination of 2 directions ?

what about three directions ? can a light be polarized in 3 directions altogether (isotropicaly) ?

puzzling question...

thanks,

 

[vanhees71]

It's a question of what you mean by "light". Usual "thermal" light, say from the sun or a good old light bulb, is not polarized at all. It's an incoherent superposition of a lot of randomly polarized field modes (it's incoherent, because the relative phases of these modes are randomly distributed too).

If you have laser light, you have to a pretty good approximation, a coherent and monochromatic em. wave. Such a wave can be characterized by the electric field. Taking the $$z$$ direction of a Cartesian coordinate system as direction of wave propagation, it can be idealized as a plane-wave solution of the free Maxwell equations:

$$\vec{E}(t,\vec{x})=(A \vec{e}_x+B \vec{e}_y) \exp(-\mathrm{i} \omega t+\mathrm{i} \vec{k} \cdot \vec{x})+\mathrm{c.c.}$$

Here, $$A$$ and $$B$$ are arbitrary complex constants, that determine the polarization state as a superposition of horizontally and vertically polarized field modes. This most general polarization state is called elliptically polarized light.

Special cases are

linearly polarized light: B=r A with $$r \in \mathbb{R}$$, i.e., both parts of the wave are in phase

circularly polarized light: $$B=\pm \mathrm{i} A$$, i.e., there's a phase shift of $$\pm \pi/2$$ between the parts (called right or left circularly polarized em. wave).

 

[Meir Achuz]

...two directions ?

I know light can be x, y or z-polarized. but can it be polarized both in x AND y or any combination of 2 directions ?
what about three directions ? can a light be polarized in 3 directions altogether (isotropicaly) ?
puzzling question...
thanks,

Light propagating in the z direction can be polarized in any direction in the x-y plane. It cannot be polarized in the z direction.

 

[I like Serena]

There's a nice animation on http://en.wikipedia.org/wiki/Polarization_(waves).