Inverse design enables large-scale high-performance meta-optics reshaping virtual reality

Meta-optics, utilizing artificial subwavelength components or meta-atoms, has significantly advanced electromagnetic wave engineering. While forward design methods have proven effective for simpler functions like single-wavelength wave bending or focusing, they struggle with the complexity of large-scale meta-optics needed for multiple custom functions across wavelengths, polarizations, spins, and incident angles. The limitations of forward design necessitate a shift towards inverse design, a methodology that optimizes design geometries from desired functions using computational algorithms. Inverse design has demonstrated success in various fields, including optimizing photonic crystals, on-chip nanophotonics, and metasurfaces. However, applying inverse design to aperiodic large-scale meta-optics presents significant computational challenges due to the multiscale nature of the problem (nanoscale meta-atoms and macroscale meta-optics). Simulations become computationally intractable with increasing design dimensions; techniques like finite-difference time-domain (FDTD) or finite element analysis are computationally expensive for large-scale devices, while ray-tracing simulations lack the accuracy needed to capture the full wave nature of optical fields at the nanoscale. This research aims to address these computational hurdles and demonstrate a scalable inverse design method for creating large-scale, high-performance meta-optics with applications in virtual reality (VR).

The literature highlights significant progress in meta-optics, with various applications demonstrated such as polarization/light-field/depth imaging cameras, metasurface-driven OLEDs, and VR/AR systems. Existing design methodologies predominantly rely on forward design approaches, which are limited in their ability to handle the complexity and scale of multi-functional devices. Inverse design offers a potential solution, but existing inverse design techniques for photonics are often limited by computational cost, especially when dealing with aperiodic, large-scale 3D structures. While topological optimization and machine-learning techniques have been explored, these methods face challenges in efficiently handling the scale and complexity of meta-optics. The current state-of-the-art for inverse-designed 3D metasurfaces is limited to diameters of around 100 µm for visible light. This paper builds upon previous work that focused on inverse design for two-dimensional metasurfaces, seeking to overcome the challenges inherent in scaling up to large-scale three-dimensional devices.

This research introduces a novel inverse-design framework for aperiodic large-scale three-dimensional meta-optics. The framework addresses the computational challenges of large-scale inverse design by employing several key strategies. Firstly, a three-dimensional fast approximate solver, based on the convolution of local fields and Green’s function, significantly speeds up the simulation process. Accurate local fields above a training set of meta-atoms are pre-computed using rigorous coupled wave analysis (RCWA), and a surrogate model based on Chebyshev interpolation rapidly predicts the local field of arbitrary meta-atoms. This surrogate model offers a six-order-of-magnitude speed improvement compared to direct RCWA simulation. Secondly, to efficiently compute gradients during optimization, an adjoint method is used. This method allows the computation of gradients for all design parameters with only two simulations, a significant improvement over traditional brute-force methods which require many more simulations. Thirdly, the design framework incorporates fabrication constraints through a surrogate model, avoiding the need to add these constraints during the optimization process itself. The inverse design process involves iterative optimization loops, using a forward simulator and an adjoint simulator, until the device performance converges and satisfies design criteria. The optimization algorithm used is a local gradient-based method called a “conservative convex separable approximation”. The designed meta-optics are fabricated using electron beam lithography (EBL) and atomic layer deposition, creating TiO2 nanofin structures with spatially varying geometries. The performance of the fabricated meta-optics is characterized experimentally, measuring focal intensity distribution, focusing efficiency, and imaging performance. The polarization conversion capabilities of the meta-atoms are also considered using Jones matrices to ensure polarization-insensitive focusing.

The researchers successfully demonstrated several key findings: 1. **High-performance, large-scale meta-optics:** The inverse-design framework enabled the creation of large-diameter meta-optics, including a 2-mm diameter RGB-achromatic polarization-insensitive metalens (NA = 0.7) and a 1-cm diameter RGB-achromatic metalens (NA = 0.3), the largest reported to date. These devices consist of approximately 10^9 meta-atoms. The 2mm metalens exhibited achromatic focusing with negligible focal shifts (<50 nm) across RGB wavelengths and a focusing efficiency of ~15%, independent of incident polarization. High resolution imaging of a USAF resolution target was demonstrated, resolving features as small as 2.2 µm. A six-wavelength achromatic metalens (NA = 0.3 and 0.7) was also demonstrated, confirming the versatility of the method. The measured full-width-half-maximums (FWHMs) of focal spots were consistent with theoretical Airy function profiles. The 1cm metalens demonstrated achromatic focusing across RGB wavelengths, with a maximum focal shift of ~4.5 µm, and a focusing efficiency of ~15%. High-resolution imaging was also shown with this cm-scale metalens. 2. **Superiority over forward design:** The researchers compared the performance of their inverse-designed metalenses with those designed using conventional forward design methods. The results clearly indicated that the inverse-designed metalenses exhibited significantly better focusing efficiencies and uniformity across RGB wavelengths compared to their forward-designed counterparts. This highlights the superiority of the proposed inverse design approach in handling the complexities of large-scale multi-objective optimization problems. 3. **Virtual Reality Application:** The large-scale meta-optics were successfully integrated into a virtual reality (VR) imaging system, using a centimeter-scale RGB-achromatic meta-eyepiece and a laser-illuminated micro-LCD. The system demonstrated high-resolution binary and grayscale VR imaging across RGB wavelengths, even producing a video of a running cat. The system improved significantly upon previously reported meta-optics based VR systems by achieving increased aperture size, polarization-insensitive focusing, simpler meta-atom geometries, and the ability to display dynamic content.

The results demonstrate the successful development and experimental validation of a novel inverse-design framework for creating large-scale, high-performance meta-optics. The framework overcomes the computational limitations of existing methods, enabling the design and fabrication of previously unachievable meta-optical devices. The superiority of the inverse-design approach over conventional forward design is clearly demonstrated by the enhanced performance of the fabricated metalenses. The integration of the meta-optics into a VR system showcases the potential of this technology to significantly improve the performance and functionality of VR and AR devices, addressing current limitations in size, weight, aberration correction, and efficiency. The high resolution and polarization insensitivity demonstrated are key advances, paving the way for more realistic and immersive VR experiences.

This paper presents a significant advancement in meta-optics design by introducing a computationally efficient inverse-design framework capable of handling large-scale, three-dimensional devices. The successful fabrication and experimental demonstration of centimeter-scale high-performance metalenses, along with the integration into a functional VR system, validate the effectiveness of this approach. Future research directions include further improvements in focusing efficiency, exploration of more complex meta-atom designs, and the optimization of other optical components within VR/AR systems using the developed framework. The integration of more advanced computational methods and the exploration of multi-physics phenomena in photonic platforms are also promising avenues for future investigation.

While the presented inverse-design framework achieved significant progress, some limitations exist. The focusing efficiency of the meta-lenses, while improved compared to previous work, could be further enhanced. Fabrication errors, such as stitching errors in the large-area EBL process, contributed to a reduction in experimental focusing efficiency compared to simulation results. The current design primarily focuses on correcting chromatic and monochromatic aberrations under normal incidence, leaving room for future improvement in the correction of higher-order aberrations like coma and field curvature. The surrogate model used relies on a large dataset, and future work could explore more data-efficient surrogate models based on neural networks to further enhance the scalability of the design framework.