Off-axis metasurfaces for folded flat optics

Miniaturizing optical systems requires reducing both component size and the open space between components. Traditional metasurface approaches excel at replacing bulky optics but struggle to compact the free-space path without nonlocal, momentum-dependent transfer functions. An alternative is to fuse flat optics and folded optics, folding the path with metasurfaces while operating under highly off-axis illumination to improve contrast by separating the zeroth order. Achieving efficient reflection at large incident and diffracted angles remains challenging due to reduced diffraction efficiency stemming from angular scattering and limited numbers of scatterers per period at large angles. Conventional gradient-phase metasurfaces based on local phase control and generalized Snell’s law demand high-index, high-aspect-ratio, deep-subwavelength elements and careful impedance matching to avoid spurious reflections—requirements that become more difficult at grazing incidence and large redirection angles crucial for folded optics. This work addresses these challenges by demonstrating a passive, low-index, low-aspect-ratio metagrating architecture that efficiently redirects and focuses visible light under extreme off-axis conditions, enabling compact folded flat optics.

Metasurfaces traditionally rely on local control of transmission/reflection phase and amplitude to map desired phase profiles, emulating curved optics via generalized Snell’s law. High-performance elements (e.g., metalenses, freeform reflectors, retroreflectors) often require densely spaced, high-index, high-aspect-ratio nanostructures and careful impedance matching to suppress spurious reflections. Prior studies highlighted that phase-gradient engineering alone is insufficient for efficient large-angle beam steering and that impedance matching and, in some cases, nonlocal or auxiliary-field approaches are necessary to achieve perfect anomalous reflection. Metagratings have been proposed to surpass the limits of graded metasurfaces by channeling energy into desired diffraction orders and suppressing others, including strategies to mitigate Wood’s anomalies and higher-order scattering. However, efficient operation at visible wavelengths, high NA, and grazing incidence, using low-index, scalable-fabrication-friendly materials, has remained difficult. The present work builds upon high-efficiency passive planar metagratings to realize folded flat optics with large angles of view.

Design concept: A low-refractive-index (n≈1.5) surface-relief metagrating layer is placed on a reflective substrate (e.g., metal mirror or spectrally/polarization-selective reflector). Operating at grazing incidence boosts Fresnel reflectivity and facilitates destructive interference to cancel the specular (zeroth order) reflection. By balancing amplitude and phase between the mirror and the surface-relief reflection pathways, the zeroth order is suppressed, forcing power into desired anomalous diffraction orders. Multi-element per period metagratings are used to suppress higher-order spurious diffraction (e.g., m = −2), mitigating Rayleigh–Wood anomalies and enabling high efficiency at large redirection angles. The approach targets s-polarized light at λ = 532 nm, incident at θi = 80°. Optimization: Rigorous coupled-wave analysis (RCWA) with a multi-start gradient-descent (MATLAB fmincon) optimizer is used to maximize first-order diffraction efficiency. The metagrating parameters (element widths, spacings, number of elements per quasi-repeating period) are optimized for each required local diffraction angle across the device aperture. For a focusing reflector with 1 cm focal distance over a 2 × 2 cm² area (approximately 90° × 90° field, 110° diagonal, NA ≈ 0.82), RCWA optimizations are performed at 400 × 400 discrete points. The structure within each supercell at a given location is chosen from the nearest optimized point, effectively creating 50 × 50 µm pixels with locally constant duty cycles, scaled by the local pitch such that element widths vary smoothly. The grating orientations and pitches are derived by superimposing the fields of an off-axis plane wave and a spherical wave centered at the focal point, extracting the local grating lines. Metagrating design variants: One- to four-element unit cells are explored. The optimal number of elements depends on the desired diffraction angle. For some angles (e.g., −30°), an optimized one-element grating outperforms multi-element designs under a minimum duty cycle constraint; at others (e.g., +30°), multi-element designs are superior. A two-element unit cell is shown to suppress the m = −2 order, avoiding efficiency drops near Rayleigh–Wood anomalies. Fabrication: Structures are patterned by electron beam lithography directly in ZEP520A (n = 1.57) resist spun to a uniform height of 120 nm on a polished Si wafer coated with 100 nm Ag (n = 0.0424 + 3.10j) and capped with 10 nm SiO2 (n = 1.465) to prevent oxidation. The largest fabricated metasurface is 2 × 2 cm². GDS layout resolution is 1 nm. Prototype test coupons (0.5 × 0.5 mm²) are also fabricated to validate unit-cell designs across exit angles. Characterization: Diffraction efficiencies are measured using a fiber-coupled tunable supercontinuum source spectrally filtered to 5 nm bandwidth at 532 nm, with s-polarized illumination at 80° incidence. RCWA predictions are compared to measured efficiencies for one- and two-element metagratings; the Rayleigh–Wood anomaly suppression in the two-element case is verified experimentally. A flat-field image of the full 2 × 2 cm² device is captured using a laser collimator (expanded, collimated, s-polarized 532 nm), focusing at 1 cm; a screen at 5 cm records the projected luminance map. Uniformity is compared to simulation via normalized RMSE. Imaging sharpness is quantified with a projected rectangular checkerboard reticle; MTF is estimated using the edge-gradient method for vertical and horizontal directions. Multiplexed RGB demonstration: A multiplexed reflector combining metasurface strips optimized for λ ≈ 632.8 nm (R), 532 nm (G), and 450 nm (B) is fabricated. Curved pixel strips (~40 µm wide) are interleaved parallel to grating lines; an aperture at the focal point is proposed to mitigate cross-talk.

• High-efficiency off-axis focusing metasurface reflector realized using low-index (n ≈ 1.5), low-aspect-ratio (~2:1, 120 nm height) dielectric ridges on a reflective substrate.
• Operation at λ = 532 nm, s-polarization, with 80° incident angle; focus at 1 cm; angle-of-view ~90° × 90° (110° diagonal), NA ≈ 0.82.
• Two-element metagrating suppresses higher-order diffraction (e.g., m = −2), eliminating Rayleigh–Wood anomaly-induced efficiency drops; achieves 88% diffraction efficiency at the optimized angle/wavelength (80° incidence, ~5° exit at 532 nm) in tests.
• Full-aperture device simulations predict first-order efficiency mean 95%, max 98%, min 83% across the metasurface.
• Experimental flat-field luminance image matches simulation with 3.4% normalized RMSE, confirming high uniformity and efficiency.
• Prototype samples across diffracted angles (−45°, −30°, −15°, +1°, +10°, +20°, +30°, +45°) show measured diffraction efficiencies that closely follow RCWA predictions within ±4%.
• Imaging MTF: vertical MTF ≥ 0.5 at ~1 cycles/degree; horizontal MTF < 0.5 at ~0.4 cycles/degree due to layout alignment discretization and pixel boundary effects.
• Multiplexed RGB metasurface reflects three colors with similar uniformity; brightness reduced by ~3× due to spatial multiplexing; suggests potential for full-color projection with focal-plane aperture to suppress cross-talk.
• The architecture supports scalable fabrication (compatible with nano-imprint lithography) due to low aspect ratio and low-index materials.

The presented off-axis metasurface architecture addresses the core challenge of efficient large-angle anomalous reflection under highly oblique incidence—key to folded optical systems. By canceling the specular (zeroth-order) path via engineered interference between the mirror and a low-index surface-relief layer, and by using multi-element unit cells to suppress spurious higher orders and Rayleigh–Wood anomalies, optical power is funneled efficiently into the desired first order across a wide range of deflection angles. Curving the ridges according to the desired off-axis focusing geometry enables two-dimensional focusing in a compact folded path. Simulations and experiments confirm near-unity mean efficiency (≈95%) across a very large numerical aperture, and a centimeter-scale 2 × 2 cm² device demonstrates uniform luminance consistent with predictions. The ability to implement these functions with low-index, low-aspect-ratio dielectric features on reflective substrates makes the approach compatible with scalable, low-cost fabrication, positioning it for applications in compact imaging, large-angle reflectors, beam expanders, grating couplers, and folded AR/VR systems. While current demonstrations are monochromatic and s-polarized, the observed performance and RGB multiplexing proof-of-concept indicate a promising path toward practical, color-capable folded flat optics.

This work demonstrates a passive, low-index, low-aspect-ratio metagrating-based metasurface that efficiently redirects and focuses visible light at extreme off-axis incidence, enabling compact folded flat optics. By suppressing the zeroth order through interference and mitigating higher-order diffraction via multi-element unit cells, the device achieves a simulated mean first-order efficiency of ~95% (max 98%, min 83%) over a 90° × 90° field and is validated experimentally with close agreement (3.4% NRMSE in flat-field). A two-element metagrating overcomes Rayleigh–Wood anomalies and achieves high efficiency (≈88%) at the design angle/wavelength, and a multiplexed RGB demonstration suggests a route to color projection. Future work could: (i) improve image sharpness by applying Lohmann detour phase corrections and increasing spatial sampling density in the layout; (ii) interleave elements at the nanoscale or use stacked wavelength-selective layers for higher-efficiency full-color operation; (iii) broaden bandwidth and polarization tolerance; (iv) integrate with scanning laser sources or dynamic metasurfaces for compact, high-performance projection and imaging systems; and (v) transition to nano-imprint lithography for mass production.

• Demonstrated performance is at a single design wavelength (λ = 532 nm) with s-polarization; bandwidth and polarization insensitivity are limited in the current implementation.
• Operation relies on grazing incidence (≈80°) to leverage Fresnel reflectivity and interference, which may constrain system layouts.
• Horizontal MTF is degraded (~0.5 at ~0.4 cycles/degree) due to discretization in grating alignment and phase sampling; 50 × 50 µm pixelation boundaries introduce artifacts affecting image quality.
• Fabrication for the prototype uses e-beam lithography with a uniform 120 nm height; while compatible with nano-imprint lithography in principle, large-area mass manufacturing is not shown here.
• Multiplexed RGB approach reduces brightness by ~3× and requires a focal-plane aperture to mitigate cross-talk; color channels are not optimized for simultaneous high efficiency.
• Tolerance to incident angle and wavelength variations is characterized at specific points; broader operational robustness remains to be comprehensively validated.