This paper presents scalar and vector analyses of sawtooth gratings with a period of 2.0 µm in terms of Fourier transformation and rigorous coupled wave analysis (RCWA) and its fabrication on a slanted silicon substrate by a newly proposed fast atom beam (FAB) etching method. First, the optical and geometrical properties of sawtooth gratings were investigated and optimized under the phase-matching requirement, and the 1st diffraction efficiency for TM polarization and the scalar approximation, 73.0% and 100%, were estimated, respectively. Second, sawtooth gratings optimized by two diffraction analysis methods were successfully fabricated by the FAB etching method. Last, by a hot-embossing process suitable for mass production, 100 µm thick poly-methyl methacrylate (PMMA) material was replicated from a sawtooth-patterned silicon substrate, and its 1st diffraction efficiency for TM polarization, 63.0%, was measured from optical testing.
We present the design of retrodiffraction gratings that utilize total internal reflection (TIR) in a lamellar configuration to achieve high performance for both TE and TM polarized light and polarization-sensitive performance for gratings behaving as polarizer filters; the design was based on rigorous coupled wave analysis (RCWA) and the Taguchi method. The components can thus be fabricated from a single dielectric material and do not have to be coated with a metallic or dielectric film layer to enhance the reflectance. The effects of the structural and optical parameters of lamellar gratings were investigated, and the TIR gratings in a lamellar configuration were structurally and optically optimized in terms of the signal-to-noise ratio (S/N) and a statistical analysis of variance (ANOVA) of the refractive index, grating period, filling factor, and grating depth as control factors and the estimated efficiency by RCWA as a noise factor. For more accurate robustness, a two-step optimization process was used for each purpose. For TIR gratings designed to perform similarly for TE and TM incident polarization, the -1st-order efficiencies were estimated to be up to 92.0% and 88.5% for TE and TM polarization, respectively. Also, for the TIR gratings designed to achieve polarization-sensitive performance when behaving as a polarizer filters, the -1st-order diffraction efficiencies for TE and TM polarization were estimated to be up to 95.5% and 2.7%, respectively. From these analysis results, it was confirmed that the Taguchi method shows feasibility for an optimization approach to a technique for designing optical devices.
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