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
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Expand :math:`k(\omega)` about the carrier, retain the requested orders, and use :math:`v_g=(dk/d\omega)^{-1}` with :math:`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
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Expand :math:`k(\omega)` about the carrier, retain the requested orders, and use :math:`v_g=(dk/d\omega)^{-1}` with :math:`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
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Expand :math:`k(\omega)` about the carrier, retain the requested orders, and use :math:`v_g=(dk/d\omega)^{-1}` with :math:`k''` controlling quadratic dispersive broadening.
Check the transform-limited and zero-dispersion limits, and conserve pulse energy when only phase is changed.