Chapter 22: Unstable Optical Resonators

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

Problem 22.1.1 — Geometrical output coupling for double-ended unstable resonators

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 \(q=(Aq+B)/(Cq+D)\); for real systems apply \(|A+D|<2\) before selecting the physical root with \(\operatorname{Im}(1/q)<0\). Back-propagate the eigenmode through one round trip to verify self-consistency and compare its aperture loss with the assumed stability regime.