The heterodyne technique is used to detect short-range forces. Using the heterodyne technique, we demonstrate photoinduced force microscopy (PiFM) imaging and z-spectroscopy without the artifact of photothermal vibration. The rejection ratio was at least 99.975% under a high-scattering condition. In addition, the heterodyne technique employs the optimal amplitude at the first resonance frequency of the cantilever to detect the photoinduced force sensitively. According to our calculation, the optimal ratio of the amplitude to the distance between the dipole of the tip and that of the sample is 0.4448. The heterodyne technique can be employed to perform PiFM without the artifact by using the optimal amplitude.

Three-dimensional (3D) information of the optical response in the nanometre scale is important in the field of nanophotonics science. Using photoinduced force microscopy (PiFM), we can visualize the nano-scale optical field using the optical gradient force between the tip and sample. Here, we demonstrate 3D photoinduced force field visualization around a quantum dot in the single-nanometre spatial resolution with heterodyne frequency modulation technique, using which, the effect of the photothermal expansion of the tip and sample in the ultra-high vacuum condition can be avoided. The obtained 3D mapping shows the spatially localized photoinduced interaction potential and force field vectors in the single nano-scale for composite quantum dots with photocatalytic activity. Furthermore, the spatial resolution of PiFM imaging achieved is ~0.7 nm. The single-nanometer scale photoinduced field visualization is crucial for applications such as photo catalysts, optical functional devices, and optical manipulation.

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We present a theoretical study on the measurement of photoinduced force microscopy (PiFM) for composite molecular systems. Using discrete dipole approximation, we calculate the self-consistent response electric field of the entire system, including the PiFM tip, substrate, and composite molecules. We demonstrate a higher sensitivity for PiFM measurement on resonant molecules than the previously obtained tip-sample distance dependency, z−4, owing to multifold enhancement of the localized electric field induced at the tip-substrate nanogap and molecular polarization. The enhanced localized electric field in PiFM allows high-resolution observation of forbidden optical electronic transitions in dimer molecules. We investigate the wavelength dependence of PiFM for dimer molecules, obtaining images at incident light wavelengths corresponding to the allowed and forbidden transitions. We reveal that these PiFM images drastically change with the frequency-dependent spatial structures of the localized electric field vectors and resolve different types of nanoparticles beyond the resolution for the optically allowed transitions. This study demonstrates that PiFM yields multifaceted information based on microscopic interactions between nanomaterials and light.