Fig. 1. (a) Schematic of polarization-multiplexed optical analog computing systems. The different inputs of TE and TM polarization will output different operation results; (b) The values of the individual optimization target on the complex amplitude plane; (c) The flowchart of the adjoint optimization

Fig. 2. (a)-(e) The topological optimization process of metasurfaces for normal incidence. The final metasurface structure is completely binary after topological optimization. The colorbars represent the dielectric constant distribution of the metasurfaces; (f) The topological optimization results for TM polarization at normal incidence with a single-point target of 0+0i

Fig. 3. (a) The selected target points of multi-objective optimization for TM polarization; (b) Optimization results on the complex amplitude plane for TM polarization at points 1, 2, and 3; (c) Optimization process for TM polarization at points 1, 2, and 3; (d) Optimization process for TE polarization at points 1, 2, and 3; (e) The dielectric constant distribution of the metasurface after topological optimization

Fig. 4. Simulation results for the polarization-multiplexed optical differentiation operations. The colorbars represent the distribution of the normalized input and the output intensity

Fig. 5. (a) Schematic of polarization-controlled differentiation direction. The different input light of TE and TM polarization will achieve differentiation operations in orthogonal polarization direction, respectively; (b) The amplitude transfer function for TE polarization; (c) The amplitude transfer function for TM polarization; (d) The polarization-multiplexed metasurface structure after topological optimization. The colorbar represents the dielectric constant distribution of the metasurface