Re: A list of textbook miscon: spatial coherence

["Bob Sciamanda" <trebor@velocity.net>]

-----Original Message-----
From: William Beaty <billb@eskimo.com>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Wednesday, February 18, 1998 11:01 AM
Subject: Re: A list of textbook miscon: spatial coherence


> On Fri, 13 Feb 1998 SCIAMANDA@edinboro.edu wrote:
>
> > Bill Beaty wrote:
> > > . . .
> Perhaps the problem is that I have misconceptions regarding the nature
of
> spatial coherence.  I imagine it this way: spatial coherence without
> temporal coherence looks like broadband starlight.  Temporal coherence
> without spatial coherence looks like a large, diffusely glowing,
extended
> object which emits perfectly monochromatic light without even any sudden
> jumps in phase of the emitted waves.


Especially that last sentence is enigmatic .  . .If at y=0 the
x-travelling wave is sin(kx-wt), what is it at y=+/- delta (and how do
you do that)?  Hmmm . . .You may superimpose many very narrow and
unrelated parallel laser beams side by side into a larger beam (I guess I
just answered my own question!).  But each laser beam still has its own
coherence (of both kinds).  I guess this would have to be your "large,
diffusely glowing, extended, monochromatic object".  How else would you
do it?  Note that these laser beams are not "diffuse"; they don't
superimpose; they stay separated.  Your extended diffuse glowing source
would mix beams as they travel and spread and lose even temporal
coherence (unless they are synchronized, and then the whole thing has
both temporal and spatial coherence.).

You are tying my poor little brain in knots . . . so you may be getting
gibberish -

Let's see . . . Given a Hg vapor source, a sharp filter to let through
only a single green Hg line would improve the temporal coherence
(monochromaticity) of the output beam.  Adding a pinhole in front of the
Hg source would improve the spatial coherence - in the extreme you might
consider that you are now letting through the emissions of only a single
atom so that there is no superposition of radiations from different atoms
and each truncated wave train of the chosen atom makes a single,
partially coherent wavefront.  There are discontinuities in phase (in
time and along the beam propagation direction), but even these
discontinuities are coherent (synchronized) across the wavefront.

Before the laser, these techniques were the way to get a moderate amount
of both types of coherence (sacrificing brightness) in the visible.
Using only one or the other (filter vs pinhole) will enhance only one of
temporal vs spatial coherence (and bring back some brightness).  I think
we both agree on these techniques, I'm really just thinking out loud.

> If my examples are OK, then my laser misconception can be restated thus:
>
>   I understand how lasers create nearly-perfect monochromatic light,
but
>   how do lasers create point-source light?

Important point: the typical laser beam is unlike that of a point source.
It has (in the simplest mode) a Gaussian wavefront going smoothly to zero
transversely. This smooth "apodization" is necessary for spatial
coherence.  Unless a beam is infinitely wide (eg., plane or sphere) it
has edges. At the edges the intensity must taper gradually to zero or it
will spread and develop spatial incoherence.

>    . . . Textbooks seem to claim that
>   spatial coherence is caused by the mechanism which also creates
>   temporal coherence.  Either they are extremely wrong, or I am
extremely
>   confused.
I guess this is your bottom line point (iconoclast! :) ).  The resonant
modes of the mirrorred cavity select the set of frequencies which can be
excited. The lasing mixture provides and amplifies these frequencies.
Each mode requires a longitudinal fit (frequency/temporal coherence) and
a transverse fit (spatial coherence).  The two dimensional character of
the cavity  inextricably intertwines the two.  Mathematicaly, the
transverse and longitudinal separation constants are related, they are
not independent.

PS.  I think your model of parallel plane mirrors effectively removing
the source to infinity (and thus getting spatial coherence) is not
apropos. The plane mirror cavity is very unstable; alignment is very
critical, or beams "walk out"; it tries to produce a plane wave of finite
width and sharp cutoff  and so will quickly spread.  I don't think it is
much (if ever) used.  (There are configurations using one plane and one
spherical mirror.)

> ((((((((((((((((((((( ( (  (   (    (O)    )   )  ) ) ))))))))))))))))))
)))
> William J. Beaty                                  SCIENCE HOBBYIST
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> billb@eskimo.com                                  www.eskimo.com/~billb
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Sorry to ramble.  I'm no expert.
-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