Re: Planes of polarization

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

"John S. Denker" wrote:

> Ludwik Kowalski wrote:
> ...
> > Now consider a common picture illustrating Snell's law.
> > The two planes are no longer arbitrary, they are: (a) plane
> > of incidence (defined by the incoming beam and the normal)
> > and (b) plane perpendicular to it. Note that the plane (b) is
> > also uniquely defined by the beam direction.
>
> <nit> Uniquely except in the case of normal incidence </nit>
>
> > Similar situations exist in crystal optics. Thinking that
> > planes of polarization are arbitrary, rather than imposed
> > by atomic structures, may be an obstacle to understanding.
>
> I'm not sure I understand what the issue is here,
> but let me guess. ....

It was only an observation that planes of linear polarization,
into which a beam of light is decomposed, are usually not
arbitrary. This becomes an issue in crystal optics, for example,
when the index ellipsoid is constructed for a crystal like calcite.
The optical axis, z, and principal axes, x,y (defined in terms
of two mutually perpendicular principal planes) are imposed
by the internal atomic structure. The unique x,y,z axes turn
out to be mutually perpendicular while the cleavage surfaces
are not. This was counterintuitive to me. My impression used to
be that x and y are arbitrary directions perpendicular to the z axis.
Ludwik Kowalski





> 1) To understand unpolarized light you need to convince
> yourself of the lemma that if it's unpolarized in one
> basis it's unpolarized in any other basis.  In particular,
> try transforming from the vertical/horizontal basis to the
> right-circular/left-circular basis.
>
> 2) You won't succeed with item (1) unless you realize that
> you can't write down a wavefunction for unpolarized light.
> It exists only as a mixture, as an ensemble.
>
> 2a) The "density matrix" formulation comes in handy.
>
> 2b) If you and/or your students are not up-to-speed on
> density matrices, the following approach may help:
>
>  *) To make unpolarized light, combine vertical light
> with horizontal light _with an arbitary adjustable relative
> phase_.  (If you combine them with a definite phase, you
> don't have unpolarized light, you just have some cockeyed
> polarization.)
>
>  *) Perform whatever propagation, filtering, and/or basis
> changes you like.
>
>  *) Calculate the intensity by taking the absolute-square,
> taking the phase into account according to the usual rules.
>
>  *) Now take the average over all phases.
>
> ===================
>
> If this doesn't address the relevant points, please
> clarify the question.