Bifocal devices can generate two focal points in the vertical or transverse direction, have the advantages of improving the depth and resolution of imaging as well as the transmission efficiency and quality of optical signals, and have a wide range of applications in optical communications, optical imaging, microscopy technology, and optical sensors. Traditional bifocal devices are limited by the Abbe diffraction limit, but recently optical super-oscillation provides a new technology for far-field super-resolution focusing, which can make the focused focal spot break through the diffraction limit. However, the existing bifocal super-oscillatory lenses rely on complex optimization algorithms, the device processing is difficult, and the device size is limited. Based on the principle of optical super-oscillation, combined with the binary particle swarm optimization (BPSO) algorithm and the angular spectrum diffraction theory, two single-focal focused binary phase super-oscillation masks with different focal lengths are designed, and the bifocal focused binary phase super-oscillation masks can be obtained by using the Boolean logic “AND” operation. A bifocal super-oscillation mask is loaded into a spatial light modulator (SLM) to generate a super-resolution bifocal focusing device. This method has the advantages of easy implementation and controllable design focal length, and has significant application potential in optical communication, biomedical imaging and other fields.

This paper consists of three core steps: first, for circularly polarized light (wavelength λ=632.8 nm), two binary phase super-oscillation masks (S-SOM₁ and S-SOM₂) are designed and optimized by using the BPSO algorithm and the angular spectrum diffraction theory with the corresponding focal lengths of f₁=280000λ (177184 μm) and f₂=300000λ (189840 μm), respectively. Second, a Boolean “AND” operation is performed on the phase distributions of the two masks to synthesize a bifocal super-oscillation mask (B-SOM), and the bifocal synchronous modulation is achieved by preserving the overlapping region of the phases. Finally, a far-field super-resolution bifocal focusing and measurement platform based on a spatial light modulator is designed and constructed, the B-SOM is loaded into the SLM in the form of a grayscale map, the scanning shot of the optical field with a step size of 0.05 mm is taken through the electrically-controlled displacement stage to obtain the distribution of the optical field, and the key parameters are extracted to verify the performance.

The Boolean “AND” operation is performed on the phase distributions of the single-focal super-oscillation masks S-SOM₁ and S-SOM₂ obtained from the optimized design to obtain the phase distributions of the bifocal super-oscillation masks (Fig. 3). From the theoretical results, it can be seen that the transverse full widths at half maximum (FWHMs) of the two focal spots are 21.846 μm and 21.114 μm, respectively, which are lower than the diffraction limits of 22.277 μm and 23.495 μm, and super-resolution focusing has been realized in theoretical calculations (Fig. 5). The experimental results show that the designed bifocal device successfully realizes far-field super-resolution focusing. The longitudinal FWHMs of the bifocal are 4.523 mm and 4.198 mm, respectively (Fig. 7), and the transverse FWHMs are 20.333 μm and 23.353 μm, respectively (Fig. 8), which are lower than the Abbe diffraction limits of 22.225 μm and 23.650 μm. In addition, the bifocal sidelobe ratios are as low as 5.1% and 12.7%, respectively (Table 1), which effectively suppress the optical field crosstalk. The experimental focal spot positions (z=177.784 mm and z=189.184 mm) are in good agreement with the theoretical calculations, and the small deviations are due to the partial loss of the modulation phase after the logic “AND” operation.

In this paper, we propose a far-field super-resolution bifocal focusing method based on spatial light modulator, which is based on the principle of super-oscillation, and utilize the binary particle swarm optimization algorithm and the angular spectrum diffraction theory to design a single-focal binary-phase super-oscillation mask, and adopt the Boolean logic “AND” operation to generate a bifocal super-oscillation mask from two binary-phase super-oscillation masks with different focal lengths. Based on this method, the bifocal super-oscillation masks with working wavelength of 632.8 nm and focal lengths of 280000λ (177184 μm) and 300000λ (189840 μm) are designed and optimized, respectively. By loading the super-oscillation mask into a spatial light modulator without precision processing, far-field super-resolution bifocal focusing is experimentally demonstrated, with the peak intensity positions of the two focal spots located at 177784 μm and 189184 μm, respectively. The average FWHMs are 20.333 μm and 23.353 μm, respectively, which are lower than the Abbe diffraction limit. The low sidelobes are also maintained with ratios of 5.1% and 12.7%, respectively. The results significantly improve the control accuracy and resolution of far-field super-resolution bifocal imaging, which can be applied to the visible wavelength band and extended to other optical bands.