Silica meta-optics: When high-performance does not need a high-index

Abstract

Metasurfaces -- planar arrays of subwavelength nanostructures -- are typically realized with high-index dielectrics, while low-index platforms are often dismissed for their weaker contrast. Here, we identify and experimentally verify regimes where a low-index platform (SiO$_2$) surpasses a high-index counterpart (TiO$_2$). We demonstrate that a low index suppresses higher-order Bloch modes, enabling the design of efficient devices with relaxed feature sizes. Low-index metasurfaces also offer two intrinsic advantages: a broad, well-behaved chromatic response without the need for explicit dispersion engineering, and strong tolerance to fabrication errors. We validate these features experimentally with silica metagratings, metalenses, and structured-light phase plates at $λ=632\ nm$. The metagratings reach $\geq$50% absolute diffraction efficiency over a $200\ nm$ bandwidth, the metalenses deliver 75% absolute diffraction efficiency with diffraction-limited performance, and the vortex phase plates achieve 80% conversion efficiency at the design wavelength and 60% with $100\ nm$ wavelength detuning. These results delineate conditions where low-index metasurfaces outperform high-index designs, suggesting a route to scalable, broadband, fabrication error-resilient flat optics.

Figures (5)

• Figure 1: Key advantages of low refractive index contrast metasurfaces.(a) Single-mode and multi-mode Bloch representation in low-index and high-index contrast material nanopillars. When the unit cell is comparable in size to the operating wavelength, low-index pillars support fewer Bloch modes than high-index pillars, suppressing intermodal beating and preserving target phase gradients. (b) Broadband behavior of a low-index vs. high-index contrast material metasurface. Low material dispersion and modal dispersion of Bloch modes in low-index media pillars preserve a well-defined phase response over a wide spectral range. (c) Robustness of optical functionality to fabrication error $\delta r$ in high-index vs low-index contrast materials. With lateral size errors $\delta r$ (shaded), high-index contrast metasurfaces lose the intended phase gradient, resulting in aberrated wavefronts, while low‑index contrast designs largely preserve the phase profile and functionality.
• Figure 2: Guided‑mode distribution and efficiency of high‑ vs. low‑index contrast metagratings.(a) Transmission maps for TiO$_2$ and SiO$_2$ square pillars versus normalized pitch $U/\lambda$ and height $H/\lambda$; for each $U$, the pillar occupies 75% of the unit‑cell area. (b) Onset of the first higher‑order Bloch mode versus $U/\lambda$ and fill factor (blue: SiO$_2$; magenta: TiO$_2$). Designs below the curve are single‑mode; above, multi-mode. Vertical dashed lines mark the structural cut‑off (the largest $U/\lambda$ for which all fill factors remain single‑mode), highlighting the wider single‑mode window of SiO$_2$. (c) Absolute diffraction efficiency $\eta$ (power in the target order divided by incident power on the metasurface) versus $U/\lambda$ and numerical aperture ($\text{NA}=\sin\theta$, with $\theta$ the deflection angle) for TiO$_2$ and SiO$_2$ gratings. The efficiency difference map $(\eta_{\text{TiO}_2}-\eta_{\text{SiO}_2})$ indicates regions where TiO$_2$ (red) or SiO$_2$ (blue) is superior. Insets schematically depict guided‑mode content and inter‑pillar coupling in each quadrant.
• Figure 3: Analysis of the dispersion behavior and fabrication tolerance of low-index contrast metasurfaces.(a) Schematics and effective‑index ($n_\text{eff}$) dispersion of the fundamental Bloch mode for SiO$_2$ and TiO$_2$ pillar libraries when single-mode and multi-mode. For single-mode operation, we used pitches $U = 400\ nm$ for SiO$_2$ and $U = 280\ nm$ for TiO$_2$. For multi-mode behavior, we used $U = 550\ nm$ for SiO$_2$ and $U = 440\ nm$ for TiO$_2$. Blue, green, and red markers denote $\lambda=400$, $600$, and $800\ nm$, respectively. (b) Absolute diffraction efficiencies of simulated gratings when drawn from a single-mode library or a multi-mode library. The gray dashed line marks the design wavelength $\lambda_d=632\ nm$. Legend applies to both plots. (c) Schematic of a uniform lateral radius error $\delta r$ in the fabricated pillars. (d) Absolute diffraction efficiency of simulated gratings with $U=550\ nm$ and $U=280\ nm$ versus $\delta r$. Legend applies to both plots.
• Figure 4: Broadband measurements of silica metasurfaces.(a) Measured absolute diffraction efficiency and Scanning Electron Microscopy (SEM) image of the metagrating. The scatter points represent experimental data, while the solid lines indicate simulated results. The grating consists of 16 nanopillars arranged in a $550\ nm$ unit cell, which produces a deflection angle of 4 degrees (NA = $\sin\theta$ = 0.07). The scale bar in both the SEM image and the inset corresponds to 1 $\mu m$. (b) Cut of the raw data Point Spread Function (PSF) of the metalens designed for NA = 0.1 at $\lambda_d=632\ nm$ and measured at various wavelengths. From top to bottom: $\lambda =658$, $632$, $532$, $488\ nm$. The lens shows diffraction-limited focusing for the measured wavelengths with Strehl ratios $\geq 0.8$. The effective-NA varies from 0.104 to 0.077 from $\lambda=658$ to $488$ nm, respectively. (c) Reconstructed phase of a measured orbital angular momentum (OAM) beam with a topological charge of $\ell = 5$ at $\lambda_d=632\ nm$ (upper plot) and modal decomposition spectrum on the azimuthal ($\ell$) modes of a Laguerre–Gaussian basis (lower plot). (d) Same as (c) but at a detuned wavelength of $515\ nm$.
• Figure 5: Effect of fabrication error on metasurface performance.(a) Scanning Electron Microscopy image of the metasurface with fabrication imperfection (scale bar 1 $\mu m$). The inset highlights the zoomed-in fabrication error. (b) Focusing profile for two silica lenses of NA = 0.1 (top) and NA = 0.5 (bottom) with fabrication imperfections. (c) Point spread function at design wavelength $\lambda_d = 632$ nm. Both the high NA lens and low NA lens are diffraction-limited and focused light with an absolute diffraction efficiency of 71% and 43%, despite the fabrication errors.