  We study the non-linear interaction of a cold sample of strontium-88 atoms
coupled to a single mode of a low finesse optical cavity in the so-called bad
cavity limit and investigate the implications for applications to laser
stabilization. The atoms are probed on the weak inter-combination line $\lvert
5s^{2} \, ^1 \textrm{S}_0 \rangle \,-\, \lvert 5s5p \, ^3 \textrm{P}_1 \rangle$
at 689 nm in a strongly saturated regime. Our measured observables include the
atomic induced phase shift and absorption of the light field transmitted
through the cavity represented by the complex cavity transmission coefficient.
We demonstrate high signal-to-noise-ratio measurements of both quadratures -
the cavity transmitted phase and absorption - by employing FM spectroscopy
(NICE-OHMS). We also show that when FM spectroscopy is employed in connection
with a cavity locked to the probe light, observables are substantially modified
compared to the free space situation where no cavity is present. Furthermore,
the non-linear dynamics of the phase dispersion slope is experimentally
investigated and the optimal conditions for laser stabilization are
established. Our experimental results are compared to state-of-the-art cavity
QED theoretical calculations.
