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
Brief solution
1. Method.
List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
2. Decisive step.
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 \(\operatorname{Im}(1/q)<0\).
3. Verification.
Back-propagate the eigenmode through one round trip to verify self-consistency and compare its aperture loss with the assumed stability regime.
Show detailed steps
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.