In order to extract the actual microresonator response χ(ω) from the experimentally photodetected χ(ω), the frequency response χdet(ω) of our entire experiment setup and detection chain needs to be calibrated first. This is realized by direct detection of the pump power modulation δP(ω)χdet(ω) in the absence of the probe laser and the pump filter. The measured response χ(ω) is normalized to the setup response χdet(ω), and thus the actual microresonator response χ(ω)=χ(ω)/χdet(ω) is retrieved, with a constant factor. This constant factor is removed when retrieving χtherm(0)/χKerr(0) from the fitting of χ(ω) using a fitting function

with κprobe, pump/4π being the cavity cutoff frequencies for the pump and probe fields, respectively. The normalized thermal response function χtherm(ω)/χtherm(0) used in the fitting is retrieved from COMSOL simulation. In Fig. 5d, f, only the normalized response χ(ω)/χKerr(0) is shown, with the constant factor removed.

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