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.
--
or, instead of linear polarizer, a Faraday rotator with magnetic field whose amplitude is randomly chnaged can be considered, I think. 
 A: 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 $0.6\,\mu\text m$ (doi). 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.
A: 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.
A: I will give you my personal mental image of unpolarized light, maybe it
will help.
In a given point in space, the E field is a vector lying in the
plane perpendicular to the propagation. In this plane, if you put the
tail of the vector at the origin, then the tip of the vector is a point
jerking in a random fashion around the origin. The important thing is
that it is random, not periodic, as purely monochromatic light
cannot be unpolarized.
If the light is narrow-band, the movement will look kind of periodic
(and thus polarized) over short time scales. You would then be able to
define an “instantaneous polarization”. But this polarization will
slowly change over the time scale corresponding to the bandwidth. You
cannot assume anything about the instantaneous polarization: it could be
linear, elliptical or circular. I would assume though that it changes
continuously, unless the spectrum of the light is quite heavy-tailed:
discontinuities in the time domain always make heavy tails in the
frequency domain.
If it is white light, then the tip of the vector is just jerking
randomly, with a hardly discernible frequency corresponding to the
middle of the band. Maybe more a time scale than an actual frequency. It
would be very hard to identify an instantaneous polarization, because
such polarization would be changing practically in the same time scale.
You could describe both situations as the superposition of two fields
with perpendicular polarizations: the combined polarization can be
computed from the amplitudes and phases of the components. But since
those amplitudes and phases have a finite coherence time, then your
polarization is always changing.
