Fig. 1. Real-time diffraction efficiency, evaluation function values and optimization structure parameters. (a) TE, TM, and average diffraction efficiency at random wavelength points during optimization; (b) the change of evaluation function value during optimization iterations; (c) real-time particle position during optimization

Fig. 2. Polarization-independent combined beam grating with single-layer trapezoidal structure

Fig. 3. Theoretical diffraction efficiency of a single-layer trapezoidal grating at the center wavelength reflected -1 order autocollimation incident

Fig. 4. Effect of slot depth and duty cycle on the average diffraction efficiency of TE and TM for single-layer trapezoidal grating

Fig. 5. Polarization-independent combined beam grating with double-layer trapezoidal structure

Fig. 6. Theoretical diffraction efficiency of the double-layer trapezoidal grating at center wavelength reflection -1 auto-collimation incident

Fig. 7. Effect of groove depth and duty cycle on the average diffraction efficiency of TE and TM for double-layer trapezoidal grating

Fig. 8. The influence of sidewall angle variation on the average diffraction efficiency of TE and TM polarizations across the entire spectral range for gratings, as well as the width-to-period ratio and groove depth tolerances of gratings at different sidewall angles. (a) The average diffraction efficiency across the entire spectral range for different sidewall angles; (b) 76°etch depth and specific width tolerance; (c) 78°etch depth and specific width tolerance; (d) 82°etch depth and specific width tolerance.

Fig. 9. Near-field calculation model of grating

Fig. 10. Amplitude value of E_y component of grating with single-layer trapezoidal structure. (a) TM；(b) TE

Fig. 11. Amplitude value of E_y component of grating with double-layer trapezoidal structure. (a) TM；(b) TE