  We investigate the limits of intracavity absorption spectroscopy with
nonlinear media. Using a common theoretical framework, we compare the detection
of a trace gas within an undriven cavity with gain near and above threshold, a
driven cavity with gain kept just below threshold, and a cavity driven close to
the saturation point of a saturable absorber. These phase-transition-based
metrology methods are typically quantum-limited by spontaneous emission, and we
compare them to the empty cavity shotnoise-limited case. Although the
fundamental limits achievable with nonlinear media do not surpass the empty
cavity limits, we show that nonlinear methods are more robust against certain
technical noise models. This recognition may have applications in spectrometer
design for devices operating in non-ideal field environments.
