Fig. 1. Setup of s-SNOM experiment based on homodyne detection

Fig. 2. Point-dipole model of tip-sample interaction

Fig. 3. Point-dipole model (left) compared with finite-dipole model (right)

Fig. 4. Schematic of self-homodyne detection

Fig. 5. Schematic of (quadrature) homodyne detection

Fig. 6. Schematic of heterodyne detection

Fig. 7. Schematic of pseudoheterodyne detection

Fig. 8. Overlapping usage scenarios of mainstream near-field signal extraction techniques. (a) Near-field characterization of α‑MoO₃ hyperbolic phonon polariton (pseudoheterodyne detection technology)^[83]; (b) effect of Mo isotope-enriched of α‑MoO₃ on polariton loss of hyperbolic phonons was investigated by near field microscopy (pseudoheterodyne detection technology)^[91]; (c) near-field characterization of hyperbolic phonon polaritons coated with α-MoO₃ by thin-layer of hexagonal boron nitride (self-homodyne detection technology)^[92]; (d) grid-dependent propagation properties of hyperbolic phonon polariton of α-MoO₃ were investigated by near-field microscopy (quadrature homodyne detection technique)^[93]; (e) self-homodyne detection technique^[64] and (f) pseudoheterodyne detection technique^[94] were used to characterise graphene plasmonic Doppler effect

Fig. 9. Extracting near-field phase information using quadrature homodyne detection or pseudoheterodyne detection. (a) Near-field phase and morphology images of water film growth on gibbsite nanoparticle (quadrature homodyne detection)^[26]; (b) near-field phase and corresponding line profile images of 3C—SiC nanowires with low stacking fault density (left) and high stacking fault density (right) (pseudoheterodyne detection)^[19]; (c) scanning electron microscope image of silicon nanowires and near-field phase image showing distribution of p-i-n junctions (quadrature homodyne detection)^[28]

Fig. 10. Near-field imaging of Au nanobar arrays. (a) Image of height of Au nano-antenna arrays obtained from AFM measurement; (b) image of near-field signal intensity using self-homodyne detection; (c) near-field phaseand (d) amplitude images obtained by quadrature homodyne detection; (e) near-field phase and (f) amplitude images obtained by pseudoheterodyne detection