Fig. 2. Retrieval of the transient nanoscale response function.

a Theoretical framework to quantitatively relate the measured pump-induced near-field signal change ΔE_NF to the transient complex dielectric function $\mathrm{\Delta }{\widetilde{ϵ}}_{\mathrm{NF}}$. b Example ground-state complex dielectric function ${\widetilde{ϵ}}^{\left(0\right)}\left(\overline{\nu }\right)$ and its pump-induced change $\mathrm{\Delta }{\widetilde{ϵ}}_{\mathrm{NF}}\left(\overline{\nu }\right)$ for a model vibrational response, with the ground-state resonance at ${\overline{\nu }}_{\mathrm{gs}}$ and the frequency-shifted excited-state resonance at ${\overline{\nu }}_{\mathrm{ex}}$. c Simulated heterodyne IR s-SNOM interferograms for the ground-state I_NF(t) and its pump-induced change ΔI_HPP(t). d $E_{\mathrm{NF}}\left(\overline{\nu }\right)$ and $\mathrm{\Delta }{E}_{\mathrm{NF}}\left(\overline{\nu }\right)$ in frequency-domain, obtained from Fourier transform and $E_{\mathrm{LO}}\left(\overline{\nu }\right)$ deconvolution of the time-domain interferograms in panel c.