Fig. 1. (a) Principle of using NV centers to detect the vectorial distributions of a light field. The single NV centers with different but well-defined axes interact with the same light field. The corresponding fluorescence emission is then analyzed to obtain the vectorial distributions of the light field. (b) Normalized fluorescence intensity of the single NV center versus the x–y plane laser polarization angle α. α = 0º corresponds to x axis. (c) Diagram of the NV center with symmetry axis of [0,63,33]. The white sphere represents the nitrogen atom, the red sphere represents the vacancy, and the blue sphere represents carbon atom. The translucent circle represents the surface perpendicular to the NV center axis and is noted as M.

Fig. 2. (a) DPP deep neural network overview. RV, random vector; OBJ, objective. (b) Calculated intensity and phase distributions of the radially polarized beam in the focal plane under the tight focus condition (NA = 0.9). The intensity distribution results are normalized by total intensity. (c) Schematic of the experimental setup with a home-built confocal nanoscopy. PBS, polarization beam splitter; VR, vortex retarder; GL, galvo scanning mirrors; SPCM, single-photon counting module; LP, long-pass filter; DM, dichroic mirror; OBJ, objective; PZT, piezoelectric displacement table. Scale bars in (b) are 200 nm.

Fig. 3. (a) Four NV centers with different axes in the [100]-oriented diamond are used to detect the light field. The corresponding coordinate system is set near NV₁. (b) Experimentally obtained fluorescence patterns in the focal plane with the excitation of a radially polarized beam; the fluorescence is recorded with the NV centers in (a). (c) Theoretical estimated fluorescence patterns of NV centers in the focal plane; the fluorescence intensities are normalized by the maximum value in each image. Scale bars in (b) and (c) are 200 nm.

Fig. 4. Reconstructed intensity and phase distributions for the three field components of the radially polarized beam in the focal plane. The intensity distribution results are normalized by total intensity. Scale bars are 150 nm.