Fig. 1. Schematic of a four-layer slanted grating

Fig. 2. Flowchart of simulated annealing algorithm

Fig. 3. Diffraction efficiencies and polarization dependent loss of optimized grating versus incident wavelength under normal incidence

Fig. 4. Analysis of incident wavelength and angular bandwidth of the polarization-independent four-layer slanted grating with optimized grating parameters. (a) Diffraction efficiency contour versus incident wavelength and angle for TE polarization; (b) diffraction efficiency contour versus incident wavelength and angle for TM polarization; (c) corresponding -1st diffraction angle; (d) average diffraction efficiency map under TE and TM polarizations

Fig. 5. Tolerance analysis of grating duty cycle. (a) Diffraction efficiency contour versus incident wavelength and grating duty cycle for TE polarization; (b) diffraction efficiency contour versus incident wavelength and angle for TM polarization; (c) corresponding PDL contour versus incident wavelength and grating duty cycle

Table 1. Comparison of efficiencies calculated by Campbell’s procedure and RCWAo procedure in this article

Table 2. Dependence of grating performance on fabrication tolerances of the grating depths