Re: Which Polarizer?

achilleaslazarides@xxxxxxxxxxx wrote:

David Littlewood wrote:

You can have a simple answer to that question, but not a simple
explanation.


Hello,

Could you please explain what is wrong with or complicated about the
following explanation:

Consider a completely polarised wave, the axis of polarisation of which
is vertical (along the z-axis). That is, the electric field is always
in the direction of the z axis. It now passes through a plate with the
property that, along a direction at 45 degrees clockwise from the z
axis and perpendicular to the direction of propagation, it passes light
with no change; along a direction at 45 degrees anticlockwise from the
z-axis and in the same plane, it retards the phase of this wave by 1/4
wavelength.

So, assume that the moment our wave arrives at this plane, the electric
field is at its maximum (top) position (this amounts to choosing the
origin of time, in this case). Its component along the +45 degree axis
is transmitted unchanged, but the one along the -45 degree axis is
retarded by 1/4 wavelength, ie, since it was at the top of its cycle,
it ends up at exactly zero and going up (of the previous cycle). So
there is a phase difference of pi/2.

After the plane, the +45 component starts decreasing from the max,
while the -45 increasing from zero, and, in general, they just continue
evolving as before. Some thought will show that their resultant will
rotate (clockwise). Hence circularly polarised light.

I know this is wordy, but if it's drawn, it's pretty simple really. Of
course, I may misunderstand what a "quarter wave plate is".


The circular polariser works exactly the same for coherent and
incoherent light. That's the easy bit.

The problem with explanations is that they usually ignore the
wave/particle dual nature of light. Explanations of polarisation always
focus on the wave part and ignore the photons. The simplest way to think
of it is that each photon behaves like a little burst of waves, with a
wavelength, a polarisation direction etc. In random light, each photon
will have its polarisation direction and the phase of its light
different. It will pass through polarisers, or not, according to the
relative orientations.


But why is it a problem? That light is made of particles is irrelevant
to this, as far as I can see. Could you explain why you think it is?


Coherent light consists of photons whose polarisation direction and
phase are all the same. However, each one follows the same rules when it
passes through a polariser; it's just that the results will all be the
same for each photon because of their identical polarisation/phase.

However, the "phase" in the description of retardation refers, not to
the phase of one photon relative to its neighbours, but to the phase
relationship between its O and E components as it passes through a
birefringent material. It is, if you like, its internal phase, not its
phase relative to its, er, relatives.


Well, I don't see how it is either useful or meaningful to talk of
photons passing through birefringent materials. Since, as far as I
(vaguely) remember, such materials are formally ones for which the
refractive index is tensorial, it seems the whole thing can be
understood using nothing but Maxwell's eqns.

Furthermore, you talk of the phase of a photon relative to others. But,
if you are going to think of this at such a microscopic level, photons
don't pass through matter, they get absorbed and reemitted and so on,
and in general, do very complicated things in there (if we insist of
thinking of photons in more or less classical terms; we don't insist,
the picture is completely different). So, which photon, and which
relative?

Or maybe you meant something completely different and I misunderstood?

Thanks.

See:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html

If you like math:
http://farside.ph.utexas.edu/teaching/qm/lectures/node7.html

Now it gets really "heavy:"
http://en.wikipedia.org/wiki/Photon
"However, in the framework of special relativity, this is not
the case for massless spin-1 particles, such as the photons. They
have only two spin projections, or helicities, which correspond
to the right- and left-handed circular polarizations of
classical electromagnetic waves. Linear polarizations are produced
by the superposition of the two spin projections of a photon."

In some places you'll find the description of a photon as always
being circularly polarized, which is what the above statement
alludes to.

Roger
.

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