--- On Sun, 10/12/08, ludwik kowalski <kowalskil@mail.montclair.edu> wrote:
"But I have a difficulty with the first sentence: "Self-focused
laser filament tracks in various glasses and polymers were chemically
etched . . ." They probably wanted to say that "filament tracks,
created by a laser beam, were etched . . . " It is the "self-focused"
part that confuses me. It probably refers to a laser beam, not to its
track. How can a beam be "self-focused" ? It can be focused by a
mirror or a lens. What am I missing?"
I do not know much about etching, but I think that your question
about
self-focusing has to do with a non-linear optical effect.
According to it, the index of refraction can be considered as an
intrinsic optical characteristic of a medium only at sufficiently
low light intensities. At high enough intensities, the passing beam
of light affects the optical characteristics of the medium through
which it is passing. In some mediums, the index of refraction is
"boosted up" by laser light so that it gets higher where the light
is brighter.
So if you have a Gaussian beam, which is more intense along its axis,
then in such a medium the index of refraction will become accordingly
higher on the axis than at the periphery of the beam. As a result, the
beam finds itself trapped by the dielectric wave-guide (effective
"optical fiber") formed by the beam itself. Its peripheral parts bend
toward the axis similar to the atmospheric refraction when the sun light
bends toward denser
atmospheric layers.
The beam is literally "focusing itself", hence the name of the
corresponding effect.
The actual process is much more complicated, since the propagation
state may be unstable, and the initial beam can split into a bundle of
"filaments", each pinched at its respective "focal points", but the abov
description can serve as the first approximation.
"If, however, the lattice is not quite perfect, we don’t get perfectly
coherent forward scattering. If the sample is large enough and/or
imperfect enough, we get localization. If
the little scatterers are situated on a perfect crystal-like
lattice, but the scattering parameters (e.g. size) is variable from site
to site, then we get Mott localization. If the sizes are uniform but
the locations are randomized, we get Anderson localization. See
reference 1. We still have some forward scattering, but it is
no longer coherent. If you try to do a Huygens construction but
randomize the phases of the contributions, you get nothing.
(This is a standard result for waves, and for vectors generally:
Given a large number of vectors with random orientation, they add
up to zero.)"
In my opinion, this is not a very good analogy. In a black-body
radiation, the propagation vectors, as well as polarization vectors,
are distributed randomly, which does not make the radiation density
zero.
"So what happens to all the light that can’t go forward, and can’t
be absorbed? It rattles around for a while and then gets tossed out
the front surface of our lattice of scatterers. The outgoing light
has a wide distribution of angles. Our lattice looks white."
This explanation is also misleading. An object looks white not
because of wide distribution of angles, but because of wide
distribution of its spectrum over the frequency range. In the same
experiment, one can make the same surface look red if it is
illuminated with red light, even with the same "wide distribution
of angles".