  Advances in integrated photonics open exciting opportunities for
batch-fabricated optical sensors using high quality factor nanophotonic
cavities to achieve ultra-high sensitivities and bandwidths. The sensitivity
improves with higher optical power, however, localized absorption and heating
within a micrometer-scale mode volume prominently distorts the cavity
resonances and strongly couples the sensor response to thermal dynamics,
limiting the sensitivity and hindering the measurement of broadband
time-dependent signals. Here, we derive a frequency-dependent photonic sensor
transfer function that accounts for thermo-optical dynamics and quantitatively
describes the measured broadband optomechanical signal from an integrated
photonic atomic-force-microscopy nanomechanical probe. Using this transfer
function, the probe can be operated in the high optical power, strongly
thermo-optically nonlinear regime, reaching a sensitivity of $\approx$ 0.4
fm/Hz$^{1/2}$, an improvement of $\approx 10\times$ relative to the best
performance in the linear regime. Counterintuitively, we discover that higher
transduction gain and sensitivity are obtained with lower quality factor
optical modes for low signal frequencies. Not limited to optomechanical
transducers, the derived transfer function is generally valid for describing
small-signal dynamic response of a broad range of technologically important
photonic sensors subject to the thermo-optical effect.
