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Re: Prony method for resonator loss calculations

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  • Subject: [mg102121] Re: Prony method for resonator loss calculations
  • From: AES <siegman at>
  • Date: Thu, 30 Jul 2009 05:30:46 -0400 (EDT)
  • Organization: Stanford University
  • References: <h4p3b3$ijb$>

In article <h4p3b3$ijb$1 at>, gcarlson <gcarlson at> 

> 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
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!


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