Fig. 1

Illustration of damping compensation for sensing enhancement through synthesized complex-frequency waves. a The extinction spectra of the molecular layer at real frequency (the light blue curve) and at CFW (the dark blue curve). The vibrational peaks are marked by the vertical lines. b The extinction spectra of the graphene nanoribbon at real frequency (the light green curve) and at CFW (the dark green curve). c The extinction spectrum of the molecular layer enhanced by GP at real frequency (the light red curve) and at CFW (the dark red curve). d–f The extinction maps under different \({E}_{\mathrm{f}}\) (d) with \({\gamma }_{\mathrm{M}}=60\; {\mathrm{cm}}^{-1}\) at real frequency, (e) with \({\gamma }_{\mathrm{M}}=0\; {\mathrm{cm}}^{-1}\) at real frequency and (f) with \({\gamma }_{\mathrm{M}}=60\; {\mathrm{cm}}^{-1}\) at CFW. All CFW results are use Eq. (2) to calculate from the corresponding real frequency results