Re: Prony method for resonator loss calculations
- To: mathgroup at smc.vnet.net
- Subject: [mg102121] Re: Prony method for resonator loss calculations
- From: AES <siegman at stanford.edu>
- Date: Thu, 30 Jul 2009 05:30:46 -0400 (EDT)
- Organization: Stanford University
- References: <h4p3b3$ijb$1@smc.vnet.net>
In article <h4p3b3$ijb$1 at smc.vnet.net>, gcarlson <gcarlson at xannah.org>
wrote:
> I am trying to compose a Mathematica notebook to implement the Prony
> method as described by Siegman and Miller ("Unstable Optical Resonator
> Loss Calculations Using the Prony Method." Applied Optics 9:2729-2736
> (1970)).
My God! A topic from a past which seems a long, long time ago! I feel
a small amount of pride in having adapted and used the Prony method to
do some useful resonator calculations at that time, and it was a
learning experience as well.
Since electrons are cheap, and you or someone might have a minor
interest, I might even recount how this came about. At that time (as
best I recall) we faculty members scattered around campus could talk to
Stanford's IBM 360 (?) mainframe over in Pine Hall from ADM-3 terminals
(?) in our offices (or was it still punched cards), but we had to walk
over there to pick up our blue bar printouts from our slots in the
printer room.
I had an EE colleague, Dave Tuttle, a very distinguished electric
network and circuit analyst and protege of Guilleman at MIT
<http://www.eecs.mit.edu/great-educators/guillemin.html>
who did the same thing from another building. One day Dave happened to
take a short cut through our building, stuck his head in my door, and
asked what I was doing.
By pure serendipity I was struggling trying to understand the higher
order modes of unstable optical resonators (which, via another equally
serendipitous event, I had invented, or discovered, or whatever, four or
five years earlier). So, I told Dave about this; he immediately
identified the link between my involvement with the (nonorthogonal,
biorthogonal) higher order modes in unstable laser resonators and his
own background in the (nonorthogonal, biorthogonal) modes of lossy
lumped circuits; told me about the Prony method, which he knew about
from his circuit work (he had, I think, spent time in France, spoke
French, and had written about Prony); pointed me to some references; and
things went from there.
But I have to say: If you're exploring this today, it seems to me it
has to be for love, or play, or historical interest, or just plain
curiosity (all of which are great forces in this world, and not to be
denigrated). But computers have evolved in power and memory to the
point that if you just want results for resonator modes, powerful matrix
root finders (a la Streifer) are probably the way to go.
Also have to say, I'd love to go back to that topic and get involved in
a discussion about it -- but my curiosity is leading me at the moment
into gain-guided and index-guided (and anti-guided) fibers and
dielectric waveguides (stable or unstable), and questions like "Does
gain guiding always trump index guiding or anti-guiding?"; and between
that and other things, I just don't think I can engage with your project
in a substantive way at this point. But good luck!
--AES