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Re: A list of textbook miscon: spatial coherence



-----Original Message-----
From: William Beaty <billb@eskimo.com>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Friday, February 13, 1998 12:08 AM
Subject: Re: A list of textbook miscon: spatial coherence


On Thu, 12 Feb 1998 SCIAMANDA@edinboro.edu wrote:

William Beaty wrote:
(By "coherent" I mean "having large spatial coherence length.)

William J. Beaty SCIENCE HOBBYIST
website

Bill,
Before this discussion gets mired in semantics, let me just point out
that you seem to be confusing what I believe to be the common notions
of spatial vs. temporal coherence:

Hi Bob! What part of my long diatribe seems to be discussing temporal
coherence? While writing it, I was visualizing a set of atoms which emit
perfectly monochromatic light ("temporally coherent"), so temporal
coherence issues can be ignored. Either some of my thoughts are confused,
or I didn't succeed in stating them clearly.

William J. Beaty SCIENCE HOBBYIST website
billb@eskimo.com www.eskimo.com/~billb


Hi Bill!
Perhaps there is our problem : temporal coherence cannot be ignored, it is
paramount! The radiation of the atoms from an ordinary "monochromatic"
source consists of truncated sine waves of finite length. The Fourier
transform of a truncated sine wave is a sinc function in frequency space,
with a non-zero line width which is inversely proportional to the duration
of the truncated sine segment in time.

In these ordinary sources, spontaneous emission dominates and there is no
correlation among the start and stop phases of the truncated sine wave
emissions of the various atoms. It is my understanding that the laser
process is dominated by stimulated emission, in which an incident wave is
"cloned" by synchronizing an already excited molecule to emit before its
time, and in phase with the incident (stimulating) wave. Spontaneous
emission is random in time (phase), there is no reference to which it might
be synchronized. The distinction is really a QED matter; I speak of the
effects in Maxwellian terms.

Other considerations which may be at issue:
In order for stimulated emission to dominate, one needs a population
inversion. The mirrors provide the positive feedback which turns an
amplifier into an oscillator. The spatial wavefront pattern at right angles
to the propagation direction (spatial coherence) is a function of the
"waveguide modes" imposed by the mirror shapes.

Getting far away from a source will improve its use in a Young double slit
experiment (because you are asking only a tiny fraction of its immense
wavefront to be spatially coherent), but it will not improve its use in a
Michaelson interferometer - a measure of temporal coherence - related to the
duration of the separate (and randomly connected) wave trains [coherence
measured along the direction of propagation]. These phase discontinuities
do not "wash out" just by removing the source to a large distance away,
which is what I read you as saying.

Hope this gets us at least talking the same language.
-Bob

Bob Sciamanda sciamanda@edinboro.edu
Dept of Physics trebor@velocity.net
Edinboro Univ of PA http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA (814)838-7185