Chapter 22: Unstable Optical Resonators
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Source: Anthony E. Siegman, *Lasers* (1986), Chapter 22.
Use each section/problem identifier with the book; the original prompts are
not reproduced here.  Each entry gives the governing model, the decisive
solution route, and a physical verification.

Section 22.1: Elementary Properties
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Problem 22.1.1 — Geometrical output coupling for double-ended unstable resonators
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List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Build the round-trip ABCD matrix and solve :math:`q=(Aq+B)/(Cq+D)`; for real systems apply :math:`|A+D|<2` before selecting the physical root with :math:`\operatorname{Im}(1/q)<0`.
Back-propagate the eigenmode through one round trip to verify self-consistency and compare its aperture loss with the assumed stability regime.