Understanding Stability Conditions for Unsymmetric Optical Resonators

[hideelo]

I am trying to understand the conditions for an optical resonator with unsymmetric reflectors, i.e. the focal lengths of the two reflectors are different. According to wikipedia (http://en.wikipedia.org/wiki/Optical_cavity#Stability) 0 < (1 - L/R1)(1 - L/R2) < 1 is the equation that will guarantee stability and they say that this can be derived from ray matrix transfer analysis but when I try to do it (I'm assuming it's an eigenvalue problem) I keep getting these long intricate conditions that don't at all resemble this simple result.

1) Are there any conditions on the system that need to be put in?
2) is there anywhere that goes through this derivation step by step?

TIA

Edit: Sorry I didnt capitalize the thread title, I noticed it after I posted and can't seem to change it

 

[Andy Resnick]

Anthony Siegman's published work is the authoritative source for this information. Absent that, here's a website that may help:

http://www.wlu.ca/documents/38467/NotesCh12.pdf

I'm not sure what you mean by 'unsymmetric'- asymmetric? There's not much information about those:

http://arxiv.org/pdf/chao-dyn/9806017.pdf
http://www.eng.yale.edu/stonegroup/publications/OpticalProcesses2003.pdf

 

[hideelo]

I guess what I was looking for is in the first one, but the part m looking for is exactly where he says that he will skip the details :-( . As far as what I meant by unsymmetric, I explain that in the first sentence. I mean a system where the two reflectors have different focal lengths.