# Unpolarized light vs. randomly rotating polarized light?

I am confused with physical picture about unpolarized light.

Is unpolarized light very fast rotating polarized light? or co-existing state of two orthogonal polarization? (or something else?)

If there is a linear polarizer which rotates very very fast and randomly (the polarizer in imagine), the output light is same to unpolarized light? I don't think so but I am not sure.

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or, instead of linear polarizer, a Faraday rotator with magnetic field whose amplitude is randomly chnaged can be considered, I think.

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Does randomly rotating polarized light mean linear polarized light but randomly direction of amplitude? –  qfzklm Aug 22 '13 at 9:03
yes. axis of linear polarizer is randomly rotating –  Jae-Hwang Jung Aug 22 '13 at 9:13

Unpolarized light can be thought of as a superposition of wave trains of a finite duration of order $0<\tau<\infty$, each of which has a certain pure polarization, which may be elliptical, with a random direction. The phases of the pulses and their start and end times are also random.

What this means in practice is that any unpolarized light source has a coherence time $\tau$. If you look at the polarization with higher temporal resolution than this, you will see a pure polarization (per spectral component! If the light source is not monochromatic the picture is more complicated). If you measure with a lower resolution, the randomly rotating polarization will average out and you will observe no polarization effects.

To put things in scale, the coherence length ($=c\tau$) of sunlight is about $6\,\mu\text m$. In practice this means that any polarization-dependent interferometry must involve path differences shorter than that, or you will be seeing the (lack of) interference between two different pulse trains with random relative polarizations and phases.

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The picture you have about unpolarized light is correct, I think, but I would try to avoid the idea of "rotating fast", because it gives an idea of continuity, that I think is what you try to avoid in the concept of unpolarized light.

So, in essence unpolarized light is modelled by short wave trains of some arbitrary pure polarization; this is because if you interfere this light with itself, the interference pattern will blur at some point, that correspond to the average length of these trains.

I never thought about the idea of getting unpolarized light from purely polarized light, but, I think what you propose could work in theory. Now, if you see a real Faraday rotator, I don't think it can do the job.

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