Re: POLARIZATION

[Hugh Logan <hlogan@ix.netcom.com>]

LUDWIK KOWALSKI wrote:
> On 28 May 1998 19:33:24 Hugh Logan <hlogan@ix.netcom.com> wrote:
>
> > There is also a series of lecture demonstrations of elliptical and
> > circular polararization (mechanical analogies, microwave, and optical)
> > from the University of Maryland starting at
> > (http://www.physics.umd.edu/deptinfo/facilities/lecdem/m9-01.htm ).
> > Just press the "next demo" button to see successive demonstrations.
>
> I did just this. Who is supposed to benefit from such pictures, and from
> short descriptions below them? I suppose this stuff is for teachers who
> are already familiar with physics not for students who want to learn it.
I had the same feeling about the lecture demonstrations, but thought
that the pictures might be of interest to those who had seen similar
mechanical contraptions. (I thought the animation from Brigham Young
University was quite good. It is part of a much larger web
presentation). The microwave demonstrations are probably a relic of the
days when the long since out of print book, _Optics of 
the Electromagnetic Spectrum_ by C. L. Andrews, Prentice Hall, 1960, had
a following. In this text there are many microwave demonstrations of
optical phenomena, though not exactly the same as the U. of Md.
demonstrations, and I think some used these as a basis for student
experiments. The only microwave experiment that I did regularly was
Bragg diffraction with a simulated crystal made of ball bearings
embedded in styrofoam (also not one I found in Andrews). Although I
referred to Andrews years ago, I have only had a copy recently, having
found it in a used book store. This book does have some explanations and
microwave demonstrations that might help with your questions below. This
is not a topic on which I have spent much time.
 
> As I wrote before, I have a conceptual difficuly with the so-called
> "rotation of the plane of polarization" in some transparent materials.
> Each layer of oscillating electrons turns the vector E by a small
> angle, always in the same direction. Why? The usual answer "this is
> caused by molecular structures of atoms" is not sufficient. What
> prevents electrons from oscillating in the plane of E, as in glass or
> in water? We add some sugar to water and the vessel behaves differently.
Wouldn't it be more to the point to say that you have a layer of
molecules with a screw-like structure in which the electrons are more
free to oscillate in directions determined by the structure of the
molecules? What if the molecules are randomly oriented? As Jenkins and 
White point out (p. 594, 4th ed.), "One might at first sight think that
the random orientation of the molecules would cancel out the rotary
effect entirely. But each molecule has a screw-like arrangement of,
atoms and a right-handed screw is always right-handed, no matter from
which end it is viewed." Andrews (pp. 467-468) suggests demonstrating
this by advancing a nut along a bolt so that the nut moves toward the
class. Then reverse the direction of the bolt, and again turn the nut
so that it again moves toward the class. The direction of rotation
relative to the class is the same in either case. The bolt represents
the molecule and the turning of the nut, the turning of the electric
vector.(It would probably be better if students demonstrated this to
their own satisfaction with a nut and bolt -- even better with nuts and
bolts with both left hand and right hand threads). So each layer 
of molecules turns the E vector a little bit, even if they are randomly
oriented. Suppose you think of the layers of, say a solution of
dextrose, as being like a stack of n polaroid filters intended to rotate
the beam by an angle theta, each with its polarization direction at an
angle theta/n from the previous one. Apply Malus' law n times to get

		I/I(0) = (cos theta/n)^2n  .

For large values of n, the ratio approaches unity. Andrews does this
with microwaves, using several parallel wire grids as polarizers. One
gets the general sense of of a screw-like progression of preferred
direction in which the electrons can oscillate as one progresses 
through several such layers. Andrews goes a step further, modeling
individual molecules with pieces of circular waveguides (possibly tomato
cans with the lids removed). Conductors are placed diametrically inside
the circular waveguide in spiral staircase fashion. Andrews also
mentions that a rectangular waveguide maintains the direction of the
electric vector. Such a waveguide will rotate the E vector if twisted.
He fashions such a crude twisted waveguide from a stack of rectangular
pieces of wood held together with a dowel rod through the centers, each
piece of wood rotated slightly relative to the previous one. The edges
(outside of the waveguide) are painted with silver conducting paint.

If you refer to Andrews, I think there is a misprint on p. 468. I think
the angles 105, 120, and 135 degrees should be with respect to the
horizontal (assuming the E field initially vertical) so that the angles
with respect to the initial E field are 15, 30 , and 45 degrees as his
equation seems to imply.

This is the best I can do for now, as I am practically a beginner at
this topic. Jenkins and White (p. 593) mention the work of Max Born on
the electromagnetic theory of optical activity, referring to a summary
by E. U. Condon, Rev. Mod. Phys., 9:432-457 (1937). I wonder if Hecht or
Hecht and Zajac have anything meaningful on this topic. I don't have
access to these books at the moment.

Hugh Logan