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Re: POLARIZATION

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? Is it an extention of the infamous "rope through the
picket-fence" model some textbooks foist on students as an analogy to
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.

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.

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.

There's a model of light gratings which treats the process as a quantum
one of absorption/re-emission of photons in the solid material at the
edges of the slit. However, I see no reason why this process should be
coherent, preserving polarization direction, or biasing the direction of
the emitted photons, since only single atoms are involved in each event.
But someone here who knows more than I about such processes may come
forward to enligten us. The optics book by Ditchburn, or Born and Wolf,
should have something useful. Anyway, I wouldn't expect the grating to
polarize.

-- Donald

.....................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Professor of Physics FAX: 717-893-2048
Lock Haven University of Pennsylvania, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu http://www.lhup.edu/~dsimanek
.....................................................................

On Fri, 22 May 1998, Charles Crummer wrote:

I am missing a fundamental point and would welcome clarification if
possible.

A student asked "When does a polarizing filter stop polarizing if the
spacing is made greater and greater between the 'strands' in the
polarizing filter?"

To this I would add; Does a diffracting grating polarize light? (It
certainly doesn't appear to as we tried in lab).

I believe a clarification concerning polarization would be valuable if
anyone can help with this issue.

Thanks,


David Abineri

A polarizer transmits only light polarized in a certain plane. It absorbs
the rest. (We have several burned polarizers and no burned gratings.)
Gratings do not absorb much. They diffract light of any polarization. I
think the usual model of a polarizer as a lot of small slits is good if one
keeps the absorption in mind. Pasco's microwave apparatus can be used for
both diffraction and polarization. The metal in the grating absorbs. Why
don't polarizers diffract?

Charlie



I did not see the original message in this thread, as it is not in my
folder. I presume it is the one directly above. Regarding the statement
that a polarizer transmits only light polarized in a certain plane, this
is not true if one is talking about the light incident on the polarizer.
The relationship between the intensity of the transmitted polarized
light and its maximum value as a function of the angle of the incident
polarized light is given by Malus's law:

I(transmitted)= (I(max))*cos^2(theta).

If the incident polarized light's plane of polarization is not
perpendicular to the direction of polarization of the polarizing filter,
some light will get through in the direction determined by the filter.
To say that light only with its plane of polarization in the direction
of polarization of the filter is transmitted is in keeping with the
incorrect rope and picket fence analogy. Of course, the light coming
through the filter has a definite plane of polarization determined by
the filter. According to _Fundamentals of Optics_, 4th ed. by Jenkins
and White (p. 505) the "strands" I think were being referred to are
"long strings of iodine atoms all lying parallel to the fiber axis,
with a periodicity of 3.10 Angstroms." (in H-Polaroid). I am not sure
how well the grid of wires in the Bird and Parrish experiment (or of
the microwave grid of wires experiment) model the detailed behavior of
the chains of iodine atoms, but the overall result is similar. The
text _Optics of the Electromagnetic Spectrum_ by C. L. Andrews,
Prentice Hall, 1960 shows a wire screen (parallel wires) reflection
diffraction grating for microwaves (p. 395). Anderson points out that
microwaves incident on the wire screen with the E vector parallel to
the wires are completely reflected as a result of the reversal of phase
of the electric field, but not the magnetic field of the reradiated
waves, the Poynting vector being reversed. Microwaves with the E vector
perpendicular to the wires should be transmitted. (Anderson stipulates
that the wires should be "no more than 0.1 wavelength apart and not less
than 0.01 wavelength in diameter. A finer wire presents too high a
surface resistance." Although I do not have the literature available,
perhaps it is this surface resistance in the microscopic gold fibers
of the Bird and Parrish experiment that accounts for the absorption,
rather than complete reflection, of the infrared waves polarized
parallel to the fibers that I believe I read about in connection with
the experiment. Anderson nicely illustrates (p. 395) that polarization
by a wire screen is not a sifting process (as in the case of the rope
and picket fence analogy), but rather a division into components.
I agree with Donald that I should not have compared the polarizer
with a transparent diffraction grating, but I believe the more advanced
literature on diffraction goes beyond Huygens' principle, even the
Kirchoff formulation, to take into account electromagnetic theory and
the electromagnetic properties of the material surrounding the
aperture. I think that any of the polarizing devices based on a grid
of wires would obey Malus's law and satisfy David's three polarizer test
just as would a Polaroid filter.
I mentioned polarization by a single slit, not as a model for a
Polaroid filter, but because I don't think the effect is very well
known, and the direction of polarization contrasts with that for a grid
of wires. There are results of detailed experimental studies of single
slit diffraction using microwaves in:

L. R. Aldridge, "Tandem Slit Diffraction Measurements,"
Technical Report No. 176, Cruft Laboratory, Harvard University
(May 1953).

As to why polarizers don't diffract, I am not sure. It might have
something to do with the fact that not all the parallel strands
of iodine atoms are in the same plane. It occurred to me that something
like Bragg scattering might apply, but for d of the order of
3 Angstroms and a wavelength lambda of visible light (thousands of
Angstroms), there would be no possible angle of relection theta in
2*d*sin(theta)= n*lambda unless the order n were very high, in which
the Bragg reflected intensity would be extremely low. This is just a
guess, but if the light couldn't be Bragg reflected, it might go
straight through. The periodicity of the iodine strands was studied by
diffraction of X-rays of much shorter wavelength than visible light.

Hugh Logan