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 $approx 10times$ 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.
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