Re: A stinking explanation ?

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

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