Inverse design of metasurfaces with non-local interactions

Optical metasurfaces, which manipulate wavefronts by spatially arranging sub-wavelength phase-shifter elements, typically rely on independent meta-atoms. This independence necessitates high-index-contrast materials and high-aspect-ratio structures for tight light localization, hindering mass production and integration. The demand for thinner, simpler metasurfaces with high efficiency motivates the use of ultrathin dielectric nanoresonators, which, however, exhibit strong electromagnetic coupling between neighbors due to their extended evanescent fields. This coupling makes conventional design approaches, based on libraries of independent meta-atoms, unsuitable. The limited availability of high-index materials in the visible spectrum further restricts the design of high-efficiency ultrathin dielectric metasurfaces. Existing thin resonator-based metasurfaces are limited to slow or uniform phase changes or longer wavelengths. This paper introduces a global evolutionary optimization approach to overcome these challenges, exploiting the strong interactions between nanoresonators rather than avoiding them.

The existing literature extensively covers conventional metasurface designs using independent meta-atoms, requiring high-aspect-ratio structures for efficient wavefront manipulation. Studies demonstrate the challenges in achieving high efficiency with thinner-than-wavelength metasurfaces due to inter-element coupling. Attempts using ultrathin dielectric nanoresonators have been limited to specific applications due to this coupling. Previous work highlights the need for global optimization techniques to account for non-local interactions in these ultrathin metasurfaces. The paper references several examples of computational inverse design approaches used in nanophotonics and metasurfaces, providing context for the proposed evolutionary optimization method.

This research employs an inverse design strategy based on evolutionary optimization (EO) using a genetic algorithm (GA) to determine the optimal spatial arrangement of TiO2 nanoresonators. The GA mimics natural selection, iteratively improving designs based on their performance. The workflow involves generating a population of metasurface structures, evaluating their performance using finite-difference time-domain (FDTD) simulations, and applying genetic operations (mutation, crossover, inversion, replacement) to evolve the population toward higher focusing efficiency. The objective function is defined to maximize focusing efficiency, calculated from the intensity profile at the focal spot. The algorithm utilizes a clustering approach, classifying populations based on performance to enhance diversity and explore different regions of the design space. The process continues until convergence, typically requiring tens of GA runs with different random initial populations. The optimized designs are then fabricated using atomic layer deposition (ALD) for thickness control and e-beam lithography and reactive ion etching for in-plane patterning. The resulting metalenses are characterized using scanning electron microscopy (SEM) and a custom optical setup to measure focusing efficiency and focal spot size.

The study demonstrates that metalenses designed using the evolutionary optimization approach exhibit significantly higher focusing efficiencies compared to those designed using conventional library search methods, particularly at larger numerical apertures (NAs). This improvement is attributed to the effective use of non-local interactions between the nanoresonators. The EO-designed lenses show focusing efficiencies far exceeding those of conventionally designed lenses across a range of NAs (0.17, 0.51, 0.77, 0.87, and 0.92). Experimental results validated the simulation findings, showing good agreement between simulated and measured efficiencies. Interestingly, the EO designs exhibit lower filling factors than the conventional designs, counter-intuitively leading to higher efficiency. This is explained by groups of closely spaced nanoresonators, along with surrounding empty space, acting as collective elements that create complex optical modes, enhancing light focusing. The aperiodic layouts of the EO-designed lenses, particularly for larger NAs, show a larger size variation and more empty spaces than periodic conventional designs. Diffraction-limited focal spots were observed in both conventionally and EO-designed metalenses.

The significantly improved focusing efficiencies of the EO-designed metalenses directly address the limitations of conventional methods in handling non-local interactions in ultrathin metasurfaces. The results highlight the potential of leveraging these interactions to achieve enhanced optical performance. The lower filling factors in EO designs represent a departure from the conventional approach, offering design flexibility and potential for improved performance. The successful experimental validation of the simulated designs confirms the robustness and effectiveness of the proposed inverse design methodology. The study demonstrates the potential to design high-performance ultrathin optical components for applications such as imaging and sensing. Future research could explore other optimization algorithms, such as topology optimization, to further improve efficiency and explore different metasurface geometries.

This work presents a novel inverse design method for creating highly efficient, ultrathin metasurfaces for visible light. By using evolutionary optimization to account for non-local interactions between nanoresonators, the researchers achieved significantly higher focusing efficiency compared to conventional design methods. The resulting metalenses show lower filling factors, which counter-intuitively lead to better performance. This approach opens new avenues for designing high-performance, compact optical components with potential applications in various fields. Future studies could explore the application of other machine learning algorithms, such as deep learning, and consider the design of spherical lenses.

While the study demonstrates significant performance improvements, there is still potential for further optimization, especially at high NAs. The computational cost of the evolutionary optimization increases with the size of the metasurface. The current study focused on cylindrical metalenses; the methodology’s applicability to other geometries requires further investigation. The fabrication process, while precise, might be challenging to scale up for mass production.