Fig. 1. Excitation diagram of a nanoantenna. The spiral represents the light field structure. As the light field propagates, the spiral changes from right-handed to left-handed, indicating a change in the polarization state of the excitation light field. When a spherical nanoantenna is placed in the light field, the polarization transformation of the light field is transferred to the scattered field, as shown in the circled subfigure. This property can be used to achieve the positioning of the nanoantenna.

Fig. 2. Experimental results of excitation light field for the transformation along the z-axis. (a) and (b) are the intensity distributions of the right- (R) and left-handed (L) circular polarization light in the x–z plane. The red dashed line is marked as the optical axis. (c) and (d) are the intensity distributions of the right- (R) and left-handed (L) circular polarization light in the optical axis for γ=0.5λ and λ. The solid lines in (c) and (d) are theoretical values.

Fig. 3. Results of the field sweeping experiment and FDTD simulation by using the spherical nanoantennas for γ=0.5λ. (a)–(c) are the simulated intensity distributions of the left- and right-handed circular polarization components of the scattered light field at the far field. (d) and (e) are the experimentally measured dependence of the component factor of the scattered field on the position of the spherical nanoantennas with step sizes of 5 nm and 1 nm, respectively. The solid line is the result of a linear fit. e represents the standard error. R2 represents the correlation coefficient of linear fit, whose value close to 1 indicates a high correlation.

Fig. 4. Location of spherical nanoantennas in the x-direction. (a) and (b) are the simulative 3D distributions of the intensity and ellipse degree with the factors α=0.36λ, β=0, and γ=0, respectively. (c) and (d) are the experimentally measured dependence of the component factor of the scattered field on the position of the spherical nanoantennas with step sizes of 5 nm and 1 nm, respectively. The solid line is the result of a linear fit. e represents the standard error.

Fig. 5. Generation of the excitation light field. (a)–(c) show the generation principle. L: left-handed circular polarization; R: right-handed circular polarization. The desired excitation light field can be obtained by superimposing the two light fields in space. (d) and (e) are the 3D distributions of the intensity and ellipse degree with the factors α=0, β=0, γ=λ, i.e., the transformation along the z-axis. (f) presents the curve of the ellipse degree along the z-axis with different γ.

Fig. 6. Spatial coordinate diagram before and after focus.

Fig. 7. Experimental setup and intensity distribution captured on camera. (a) Schematic diagram of the setup, where L represents the lens, P is the polarizer, LC is the liquid crystal device, BS stands for the beam-splitting cube, MO denotes the micro-objective (NA = 0.95), OT is the objective table, PG is the polarization grating, and CCD is the camera. (b) Phase distribution of the LC.

Fig. 8. Experimental demonstration of the excitation light field whose left- and right-handed circular polarization components separate in the x-direction with α=0.2λ and 0.36λ, respectively.

Fig. 9. Intensity distribution captured by the CCD camera when the nanoantenna is in different positions. L represents left-handed circularly polarized light; R represents right-handed circularly polarized light. zsp represents the position of the nanoantenna. The parameters corresponding to this figure are α=β=0, γ=λ.

Fig. 10. Schematic of the FDTD model. (a) The overall view, (b)–(d) the three view drawing.

Fig. 11. Scattering field of spherical gold nanoantennas. (a)–(c) are the intensity distributions of the scattering field with the nanoantennas position at z=−λ, where (a) is the right-handed component, (b) is the left-handed component, and (c) is the total field. (d)–(f) are the results with the nanoantennas position at z=λ. (g) and (h) are the component factors of the scattering field with the scanning of the spherical gold nanoantennas. The scanning accuracies of the two images are 5 nm and 1 nm, respectively. (g) and (h) are normalized uniformly. R2 is the correlation coefficient, close to 1, indicating high linearity.

Fig. 12. (a) The dependence of the slope (reflecting measurement sensitivity) of the displacement measurement curve on the nanoantennas size. (b) The dependence of relative energy on the nanoantennas size. Relative energy is defined as the peak scattering energy flux of the nanoantennas relative to the total energy of the light source.

Fig. 13. The dependence of the extrema distance on the transformation factor. R2 is the correlation coefficient, close to 1, indicating high linearity.

Fig. 14. Structure of elliptical polarization. (x, y) is the Cartesian coordinates of the original space. Ex and Ey are the projection of light in the x- and y-directions, respectively. (x1, y1) is the Cartesian coordinate system with the major and minor axes (2A1 and 2A2) of the polarization ellipse as the axis. γ is the angle between the two coordinate systems. ε is the ellipse degree which describes the continuous change from circular polarization to linear polarization.