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System schematic with field and structure parameters defined. The structure includes the grating period (Λ), height (t), width (w), defined as where FF is the fill factor, and the distance between the substrate and grating (h). The incident light is transverse magnetic (magnetic field directed in the z-direction) polarized, and the incident angle from normal (θ) is in the xy-plane.
Simulated response of the optimized suspended silicon grating with μm, FF = 72%, t = 3 μm, and h = 4 μm with (a) a contour plot of transmittance as a function of increasing angle from normal, θ, and (b) respective line plots at normal incidence and , with transmitted bands designated (i) and (ii). (c) Magnetic field profiles, Hz , on each resonance showing the supported modes at .
(a)-(c) Scanning electron micrographs of a representative grating with (a) a plan view, (b) a transverse cross-sectional view, and (c) a sidewall profile. (d), (e) Comparison between finite element simulations and experimental response for a grating with dimensions: μm, FF = 72%, t = 2.85 μm, and h = 4.05 μm exhibiting (d) broadband reflectance at normal incidence and (e) transmission filtering at . The numerical results have been reduced by 30% to account for the substrate bottom silicon/air interface. 30
Experimental and simulated transmittance of suspended silicon gratings with FF = 72%, t = 2.85 μm, and h = 4.05 μm, and with (a) vertically offset experimental data and (b) simulated contour plot at with experimental peak locations overlaid (*).
Dispersion relations for even (blue) and odd (green) TM guided modes in (a) a nearly uniform slab with , t = 3 μm, and ; (b) a dielectric/air grating with the same parameters and FF = 72%. Intersections with the red line (circles), within the gray light cone, show the phase-matching condition for light incident at , with (i) and (ii) indicating the observed transmission resonances. represents a third resonance condition corresponding to second order diffraction. (c) Electric (Ex ) and magnetic (Hz ) field profiles near zone center (k x = 0) for mode (ii)+ and mode (ii)− responsible for the broadband reflectance and narrowband filtering, respectively.
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