A distinction between "optical activity" and "circular polarization" is
important to emphasize. In the first case the incoming ligh, linearly
polarized in one plane, comes out as linearly polarized in another plane.
This is also called "rotation of the plane of polarization". It is not a
case in which the next particle of the escaping light (or the next rope
segment, if you wish) is rotated more than the one before it. Each layer
of transparent material turns the plane of polarization a little more.
Circular polarization, as stated by many, calls for two linearly polarized
waves (mutually perpendicular and of equal amplitude) which are out of
phase by 90 degrees. Linearly polarized light can be mathematically
described as two circularly polarized waves of equal amplitude (left and
right being in phase with each other) but that does not turn it into
something more different than what it is. There is only one basic kind
of polarization, linear. Neither circular nor elliptical polarization is
possible when linear polarization is not allowed.
Mathematical decomposition of a plane wave into two components is purely
artificial in an isotropic material, such as glass. A simple analyzer
can be used to extinguish the outgoing light. But in some materials the
mathematical decomposition becomes much more than the artifact. This
happens when speed of light of one component is different from the other.
In that case the escaping components are phase-shifted, according to the
thickness, and the total extinction of light by a simple analizer is no
longer possible.
The real conceptual question is why is the speed of ligh in one plane
different from the speed of light in another? The old idea of Huygens,
according to which waves are absorbed and reemitted (from layer to
layer), has something to do with this. But how? Speed of light in glass
is about 2/3 of c (a well known factoid). And it can be expressed in
terms of the epsilon, or terms of the index of refraction, which are
also experimentally measurable material constants. I never saw a
calculation of such parameters in terms of numbers of electrons,
molecular potentials, etc. Do such calculations (of the speed of light)
exist?
Ludwik Kowalski