Re: A stinking explanation ?

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

After  reading John's reply I fail to see how it deals with
my original claim. I am not going to repeat what I already
said about two items from his message. The issue is an
apparent contradiction between what textbooks say
about polarized light. Optical activity is an experimental
fact. Fresnel said we can explain it by assuming that the
left and right circularly polarized waves propagate with
different velocities. This also can be tested experimentally.
I guess that many people have verified this.

Textbooks are talking about light propagating along the
optical axis, not perpendicularly, as in a quarter wave plate,
and not at an arbitrary angle. (For example, see the first
sentence in 28.3 of Jenkins and White, page 584, 4th
edition). If it is true that L-light and R-light propagate
along the optical axis with different speeds then it is not
possible to say that speed of light is the same for all
states of polarization along an optical axis. And yet that
is what is implied by Figure 26A, (page 545 in J.W).

However, as I read the textbook more carefully again,
I see that the authors are aware of the conceptual difficulty
which prompted me to start this thread. The two wave
surfaces (a sphere and an ellipsoid of revolution) do
touch for all uniaxial crystals, EXCEPT THOSE IN
WHICH OPTICAL ACTIVITY TAKES PLACE. In
these crystals two surfaces nearly touch each other.
I did not notice this "NEARLY" reservation till now.

In other words, a statement that "an optical axis is a
direction along which speed of light is the same for
all states of polarization is only approximately
correct for optically active substances, such a quartz.
A general statement should be that  "an optical axis
is a direction along which the difference between
the speed of E-light (polarized in the principal plane)
and O-light (polarized perpendicularly to the principal
plane) is the smallest". Or something like this, as
illustrated in Figure 28H, a.

I am no longer confused but I think that the topic is
not presented in the best possible way, even in this
great textbook. The definition of the "optical axis",
by the way, and that of a "principal plane", can be
found on page 507. I wish somebody asked me
write a pedagogical essay on polarization of light.
But nobody is asking and I am not going to write
it for myself.
Ludwik Kowalski

John Mallinckrodt wrote:

> On Wed, 22 Sep 1999, Ludwik Kowalski wrote:
>
> > An optical axis of a transparent crystal, such as quartz, is a
> > direction along which ordinary and extraordinary waves
> > propagate with the same phase velocity. A typical illustration
> > of this can be found in "Fundamentals of Optics" of Jenkins
> > and White (Fig 26A, p 545, 4th edition).
>
> This may be technically true, but I think it is a little misleading.  To
> consider a wave "extraordinary" it must have at least some component of
> its E-field parallel to the optic axis.  (I am restricting my
> consideration to uniaxial substances like quartz.)  If a wave
> propagates along the optic axis, then both linear polarizations are
> necessarily identical in every respect.
>
> > Consider a quartz plate whose optical axes are
>
> (?? I assume you mean to say "whose optical axis is")
>
> > also normal to its flat surfaces. In such plate a linearly polarized
> > light, at zero angle of incidence, will remain linearly polarized at the
> > exit, no matter how thick is the plate.
>
> True, but the plane of polarization will be rotated by an amount that
> depends on the thickness of the plate due to the fact that quartz is
> an optically active material (as you go on to note later.)
>
> > We explain this by saying that the wave velocity, for that direction of
> > propagation, is the same for all planes of polarization.
>
> Hmm.  It may be true in this case that the phase velocity is the same for
> all linear polarization states, but that certainly does *not* explain the
> observed rotation of the plane of polarization.
>
> > The explanation makes sense
>
> well...
>
> > but it conflicts with another so-called explanation, at least in my
> > mind. I am referring to Frenel's "explanation" of optical activity
> > (rotation of the plane of polarization by a quartz plate). According to
> > Jenkins and White (page 588) Frenel's explains the effect by assuming
> > that "two circular vibrations move forward with slightly different
> > velocities."
>
> Right
>
> > Please explain how velocities of right-handed and left-handed
> > components of linearly polarized light can be different for a
> > beam parallel to the optical axes.
>
> Because the material has a *rotational* asymmetry about its optical axis.
> Quartz (and certain other) crystals display such a rotational asymmetry
> and occur in versions ("enantiomorphs") that are mirror images of each
> other.  For waves propagating along the optic axis, the crystal structure
> encountered by different linear polarizations is identical, but it is
> *not* for right and left circular polarizations.
>
> John Mallinckrodt      mailto:ajm@csupomona.edu
> Cal Poly Pomona          http://www.csupomona.edu/~ajm