Re: POLARIZATION

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

Some further thoughts based on some additional reading:

Donald E. Simanek wrote:
> The responses so far have several problems:
>
> The model of a polarizer as an array of "slits". Where did *that* model
> come from?
I think this came from the slits between the conductors in the microwave
model and the "slits" between the gold wires in the Bird and Parrish
experiment. I am not sure that the regions between the "strands" of
iodine in a Polaroid filter are really "slits" if the strands are in
more than one plane (I am not absolutely sure about this, but I have 
the impression that the "strands" are in more than one plane."

The most descriptive explanation of how the "strands" in Polaroid
filters work is the following comparison eith the microwave wire grid
polarizer (in _Introduction to Optics_ by Pedrotti and Pedrotti,
Prentice Hall, 1987): After mentioning that the conduction paths must
be closer together for visible light than for microwaves, he states,
"When a sheet of clear, polyvinyl alcohol is heated and stretched, its
long, hydrocarbon molecules tend to align in the direction of 
stretching. The stretched material is then impregnated with iodine
atoms, which become associated with the linear molecules and provide
'conduction' electrons to complete the analogy to the wire grid." 
After discussing naturally occurring dichroic materials, the Pedrotti's 
go on to say, "In non-metallic materials, the electrons acting as dipole
oscillators are not free. In this case the wave they generate is not out
of phase with respect to the incident wave, and complete cancellation of
the forward wave does not occur. The energy of the driving wave,
however, is gradually dissipated as the wave advances through the
absorber, so that the efficiency of the dichroic absorber is a function
of the thickness." I presume this applies to Polaroid sheets, so that
the analogy with the wire grid polarizer is less than exact. 
 
  Is it an extention of the infamous "rope through the
> picket-fence" model some textbooks foist on students as an analogy to
> polarization?
  Looked at as slits between conductors, I don't think it is an  
extension of the "ropes through the picket-fence" model. I don't
  think an ideal multislit - open slits separated by opaque strips _
  would produce polarization.

> The slit model and the picket fence model fail miserably when applied to
> the case of a sandwich of three polarizers. The second's axis is at, say,
> 45 degrees to the first. The third is at 90 degrees to the first. The
> picket fence and slit models would predict no light gets through. But it
> does get through. Then remove the middle polarizer and then light
> doesn't get through. Any model or analogy which can't deal with this case,
> a case so easily demonstrated, isn't worth a moment's consideration.
I think this certainly applies to the picket fence model. I never heard
of the "slit model" until now. (Perhaps I confused the wire grid with a
multislit in my first posting). But if the "slit model" refers to the
wire grid model, I think this can pass your test as mentioned in my
second posting. (As I mentioned in my second posting, the wire grid
works by division of components, not "sifting" as in the case of the
picket fence -- using Anderson's expressions).

If, by "slit model," you are thinking of polarization by a single slit
made of metal as I described, I think three of these, the outer two
crossed, would let more light through than just the outer two if the
middle one was at an intermediate angle. (I am not sure how close to
100% polarization by one slit is possible in practice). The polarization
of the light of a given wavelength (or narrow range thereof) that barely
gets through a slit narrowed until the light is just barely visible is
definitely polarized with the plane of polarization along the direction
of the slit as observed visually. I am not thinking of "the slit model"
as many of these single slits put together. The direction of the plane
of polarization is 90 degrees different. I have never read about
polarization of visible light by a single slit in any text. I did not
try it with a non-metallic slit, which would probably have been very
difficult to make sufficiently narrow, if not impossible.  

> Diffraction gratings (for light) in the laboratory are usually clear
> transmission gratings, replicas of a metal grating. Therefore they
> transmit light over their entire area, blocking none. They are essentially
> phase gratings.
But ruled, unblased, transmission gratings with the ruling on glass are
close to the pure multislit (Jenkins and White, 4th ed., p.368). The
rulings act as opaque areas since they scatter the light, the regions
between transmit regularly. True, such a grating is not a polarizer.
In echelette or blazed gratings the flat surfaces are at an angle to the
flat swide of a grating -- in edge view something like clapboards on the
exterior of a house.

Although I didn't find the original Bird and Parrish article, I found a
description of his gold wire polarization apparatus in _University
Optics_, Vol. 2, by D.W. Tenquist, R. M. Whittle, and J. Yarwood, Gordon
and Breach, 1970. Bird and Parrish started with what appears to be an
echellete transmission grating with 20,000 rulings per centimeter. This
means that the each "clapboard" occupies 500 nm, a typical visible light
wavelength. So far this is a diffraction grating, not a polarizer. Gold
is then deposited on the edges (perpendicular to the base of the grating
or nearly so) of the "clapboards" (my expression) about 100 atoms thick,
much less than the wavelength of the incident radiation and also much
less than the flat, sloped region of the "clapboards." Thus there are
20,000 thin, parallel gold wires per centimeter. The thickness
of the gold wires was limited to avoid appreciable induced currents
pependicular to the length of the wires and corresponding absorption in
energy. Unpolarized radiation incident on the wire grid becomes
polarized perpendicularly to the wires on transmission. According to the
text referred to, "The component parallel to the wires was absorbed." He
goes on to say that the induced currents "would dissipate rapidly the
energy in the parallel field components." This is what I recall reading
elsewhere. (The reflection grating in Anderson depends on backwards
reradiation due to the currents in the conductors). As mentioned
previously, the direction of the polarization doesn't agree with the 
"rope and picket fence model," aside from that model's failure to pass
the three polarizer test. As I see it, the Bird and Parrish apparatus
is both a polarizer and a transmission diffraction grating. Although
_University Optics_ fails to specify the wavelength of the incident
radiation, I recall that they used infrared - certainly with a
wavelength longer than the d = 500 nm spacing of the grating. I would
expect that such a grating would be more appropriate for shorter
wavelengths than the visible -- say the near ultraviolet if used for
diffraction. If one applied the diffraction grating equation 
( d*sin(theta)= n*lambda ) to incident infrared radiation (to the 
extent that the formula applies in this situation) with n = 1 (first
order), sin(theta) would again be greater than 1 -- impossible. Thus
only zeroth order transmission would take place, meaning no observed
diffraction. So it is only incidentally a diffraction grating.

> The microwave diffraction grating made of metal strips with spaces between
> works because of oscillatory motion of electrons along the strips. The
> electrons in these strips radiate.  The process is essentially classical,
> the electron motion in the metal being over distances large compared to
> the slit and wire widths.
>
> From the example of the microwave reflection grating, it is clear that
reradiation in the backwards direction takes place. But is reradiation
from the metal wires, and not just absorption, instrumental in
explaining the forward transmitted radiation in the wire grid polarizer
of Bird and Parrish (or the microwave version)?

Thanks for your excellent questions that helped to _start_ the
clarification of my thinking about models of polarizers.

Hugh Logan