Fig. 2: Decoupled optical forces from different physical mechanisms.

a AFM topography of a nanorod. b Overall force map of the nanorod, \({F}_{opt}(\mathop{r}\limits^{\rightharpoonup })\). The illumination is left-handed circularly polarized. The field of view is 150 nm by 150 nm. c The phase of the optical force with the background phase correction \({\varphi }_{opt}(\mathop{r}\limits^{\rightharpoonup })-{\varphi }_{PA}+{90}^{\circ }\). The optical gradient force, \({F}_{G}(\mathop{r}\limits^{\rightharpoonup })\), is dominant at two ends of the nanorod, where the phase is close to 180 degrees. The photothermal force, \({F}_{PT}(\mathop{r}\limits^{\rightharpoonup })\), is dominant at the body of the nanorod, where the phase is between 0 and 90 degrees. The photoacoustic force is dominant outside of the nanorod, where the phase is around 90 degrees. The decoupled amplitude of the measured (d) photothermal force and (e) the optical gradient force. f Measured decoupled optical gradient force and photothermal force along the dashed line as shown in (d) and (e). Simulated (g) photothermal force map and (h) optical gradient force map at 100 ns after the raising edge. i The line profile of simulated optical gradient and photothermal forces along the dashed line as shown in (g) and (h). j Measured optical force spectra on the substrate (black), at the end (red), and the center (blue) of the nanorod, as indicated in (a). The laser modulation, \({f}_{opt}\), is at the same frequency as the mechanical resonance frequency of the cantilever, \({f}_{0}\). The frequency difference \({f}_{d}-{f}_{0}\) is 1 kHz. The error bars indicate the standard deviation, and the data points indicate the mean values of three measurements. k The simulated optical force spectra at the end and the center of the nanorod are given by the optical gradient force and the photothermal force, respectively.