Chapter 28: Passive Mode Locking
Source: Anthony E. Siegman, Lasers (1986), Chapter 28. 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 28.1: Pulse Shortening In Saturable Absorbers
Problem 28.1.1 — Pulse shortening in fast saturable absorbers
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.
Expand \(k(\omega)\) about the carrier, retain the requested orders, and use \(v_g=(dk/d\omega)^{-1}\) with \(k''\) controlling quadratic dispersive broadening.
3. Verification.
Check the transform-limited and zero-dispersion limits, and conserve pulse energy when only phase is changed.
Show detailed steps
List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation. Expand \(k(\omega)\) about the carrier, retain the requested orders, and use \(v_g=(dk/d\omega)^{-1}\) with \(k''\) controlling quadratic dispersive broadening. Check the transform-limited and zero-dispersion limits, and conserve pulse energy when only phase is changed.
Problem 28.1.2 — Pulse shortening in slow saturable absorbers
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.
Expand \(k(\omega)\) about the carrier, retain the requested orders, and use \(v_g=(dk/d\omega)^{-1}\) with \(k''\) controlling quadratic dispersive broadening.
3. Verification.
Check the transform-limited and zero-dispersion limits, and conserve pulse energy when only phase is changed.
Show detailed steps
List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation. Expand \(k(\omega)\) about the carrier, retain the requested orders, and use \(v_g=(dk/d\omega)^{-1}\) with \(k''\) controlling quadratic dispersive broadening. Check the transform-limited and zero-dispersion limits, and conserve pulse energy when only phase is changed.
Problem 28.1.3 — Shortening of square input pulses
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.
Expand \(k(\omega)\) about the carrier, retain the requested orders, and use \(v_g=(dk/d\omega)^{-1}\) with \(k''\) controlling quadratic dispersive broadening.
3. Verification.
Check the transform-limited and zero-dispersion limits, and conserve pulse energy when only phase is changed.
Show detailed steps
List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation. Expand \(k(\omega)\) about the carrier, retain the requested orders, and use \(v_g=(dk/d\omega)^{-1}\) with \(k''\) controlling quadratic dispersive broadening. Check the transform-limited and zero-dispersion limits, and conserve pulse energy when only phase is changed.