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[Phys-L] Re: Travel distance in a waveguide.



Let's see how the following two points sound... plus another question at
the end.

(1) If I measure the group delay of a light pulse through a fiber optic
cable, I can divide the cable length by the group delay to find the
group velocity for that light pulse in that cable. For my particular
situation, the students measure about 100 ns for a 20-m cable, giving
2E8 m/s for the group velocity.

(2) If I divide the speed of light in vacuum by the group velocity I get
the group refractive index of the cable. In my particular case, this is
3E8/2E8 giving 1.5 as the group refractive index for my cable. In a
previous message I called this the effective refractive index. One of
the nice references Bob Sciamanda posted calls this the group refractive
index.

Question...

In a graded index cable there isn't a single refractive index, so we
can't have a hunk of the material that we could form into a prism with
which we could determine the refractive index using a spectrometer or
via a critical-angle technique.

However, in a step-index cable there is a single refractive index, so we
could have a hunk of that material for which we could determine the
refractive index by other means.

How would the group refractive index measured for a step-index fiber
optic cable compare to the refractive index measured for the bulk
material using a prism in a spectrometer or using a flat hunk of the
material in an Abbe refractometer (critical-angle technique)?

Bob Sciamanda implied that we can think of the refractive index measured
in a hunk of the material as a group refractive index because even in
the hunk of material we should think of the velocity as a group
velocity. But it seems to me this group refractive index will be
different than the group refractive measured for the same material in a
fiber optic cable because the geometry is different. (The group
velocity in a wave guide depends on the dimensions of the wave guide.)
Is this correct reasoning that the bulk refractive index and the fiber
optic group refractive index would be different?


Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu