Chapter 30: Hole Burning and Saturation Spectroscopy
====================================================

Source: Anthony E. Siegman, *Lasers* (1986), Chapter 30.
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 30.2: Elementary Analysis Of Inhomogeneous Hole Burning
---------------------------------------------------------------

Problem 30.2.1 — Exact expression for inhomogeneous saturation at line center
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Integrate the velocity-class response with the homogeneous saturation denominator, keeping pump and probe detunings separate before evaluating the Lamb-dip or hole width.
Check that the unsaturated line is recovered at zero intensity and that power broadening increases the homogeneous width.

Problem 30.2.2 — Exact expression for hole burning in a Lorentzian inhomogeneously broadened line
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Integrate the velocity-class response with the homogeneous saturation denominator, keeping pump and probe detunings separate before evaluating the Lamb-dip or hole width.
Check that the unsaturated line is recovered at zero intensity and that power broadening increases the homogeneous width.

Problem 30.2.3 — Oscillation mode spectrum and power output for a strongly inhomogeneous laser oscillator
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Integrate the velocity-class response with the homogeneous saturation denominator, keeping pump and probe detunings separate before evaluating the Lamb-dip or hole width.
Check that the unsaturated line is recovered at zero intensity and that power broadening increases the homogeneous width.

Section 30.6: Inhomogeneous Laser Oscillation: Lamb Dips
--------------------------------------------------------

Problem 30.6.1 — Frequency pulling in an inhomogeneously broadened laser
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Integrate the velocity-class response with the homogeneous saturation denominator, keeping pump and probe detunings separate before evaluating the Lamb-dip or hole width.
Check that the unsaturated line is recovered at zero intensity and that power broadening increases the homogeneous width.

Problem 30.6.2 — Oscillation spectrum and power output versus pumping in a doppler-broadened gas laser
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Evaluate both cases from the same symbolic expression before taking their ratio; this keeps normalization and sign conventions from obscuring the comparison.
Integrate the velocity-class response with the homogeneous saturation denominator, keeping pump and probe detunings separate before evaluating the Lamb-dip or hole width.
Check that the unsaturated line is recovered at zero intensity and that power broadening increases the homogeneous width.

Problem 30.6.3 — Anomalous frequency pulling at line center in a doppler-broadened laser
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Integrate the velocity-class response with the homogeneous saturation denominator, keeping pump and probe detunings separate before evaluating the Lamb-dip or hole width.
Check that the unsaturated line is recovered at zero intensity and that power broadening increases the homogeneous width.

Problem 30.6.4 — Inverse Lamb dip analysis
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

List the supplied quantities in one unit system, isolate the requested variable symbolically, and retain guard digits until the final evaluation.
Integrate the velocity-class response with the homogeneous saturation denominator, keeping pump and probe detunings separate before evaluating the Lamb-dip or hole width.
Check that the unsaturated line is recovered at zero intensity and that power broadening increases the homogeneous width.