Eye accommodation-inspired neuro-metasurface focusing

Light focusing has been a long-standing research topic, with optical lenses ubiquitous in daily life and laboratories. Conventional lenses are bulky and rely on polished surfaces to impart gradual phase changes. Metasurfaces, composed of sub-wavelength scatterers, enable compact, customizable optical responses and have led to metalenses capable of focusing with reduced dimensions. Over the past decade, extensive studies pursued broadband, achromatic, and efficient metalenses. A key limitation is that most metalenses operate only in predefined environments, making adaptability to changing scenarios and incident waves challenging. AI-enabled adaptive optics on metasurfaces has shown promise, but deep learning typically depends heavily on the quantity/quality of training data and prior environmental information, and may fail in rapidly changing environments due to model bias, environmental dynamics, and device uncertainties. Motivated by the human eye’s accommodation—which adjusts lens shape to maintain focus across varying conditions—the authors propose a practical approach that avoids time-consuming searches and provides self-adaptability: a supervised evolving learning (SEL) algorithm driving an adaptive focusing neuro-metasurface (SELAF) that iteratively adjusts metasurface voltages to approach the focal point without prior knowledge of the EM environment.

The paper situates its contribution within metasurface and metalens research targeting broadband, achromatic, and high-efficiency operation. Prior works have demonstrated various metasurface functionalities and achromatic metalenses, yet typically for fixed conditions. Adaptive optics approaches leveraging deep learning have enabled intelligent imaging, reprogrammable metasurface imaging, and self-adaptive cloaking. However, these methods require large, high-quality training datasets and prior environment information, and can be brittle under rapid environmental changes and device uncertainties (e.g., diode characteristics). This motivates the need for an adaptive, data-evolving strategy that can robustly handle unknown and dynamic scenarios without extensive prior training tailored to specific environments.

System concept and architecture: The proposed supervised evolving learning (SEL) framework comprises two intertwined cycles: an operation cycle and an evolving cycle. In the operation cycle, an actor (the reconfigurable neuro-metasurface) modulates the EM environment; a perception module (an array probe) measures the environment and forms an internal representation (1D electric field energy matrix); a steering network (focus steering network, FSN) predicts supervised parameters (phase compensation); a semi-supervised controller combines predicted values with local knowledge to generate execution decisions (metasurface voltages); and a motor (multichannel power supply) applies the voltages to update the metasurface state. The evolving cycle includes data storage (accumulating simulated and experimental data), network training (periodic retraining of the FSN to improve adaptation and accelerate convergence), and knowledge updating (providing guidance to the controller). This supervised, iterative trial-and-error strategy drives rapid adaptation without prior environmental knowledge. Hardware and metasurface design: A prototype SELAF system employs a transmissive neuro-metasurface of size 100 × 372 × 2.2 mm³ configured as 5 × 31 unit cells. Each column (31 along y) shares the same bias voltage. Unit cells are stacked double-layer F4B structures with two PIN diodes enabling a 180° phase reversal per element. The transmission coefficient exceeds -0.8 dB over 5.78–6.03 GHz with average transmittance >95%, and performance is robust for incidence angles from -50° to 50°. Despite 2 phase states per meta-atom, the 31-cell column provides sufficient degrees of freedom for effective focusing and supports other frequencies. A transmitting antenna illuminates from random directions; a 1D array probe samples electric field data at 31 positions on the focal plane, feeding the SEL system. Focusing principle: For a focal point at (x, F) behind the metasurface, the required phase at unit cell i is φ^(i)(λ) = 2π/λ(√((x − x_i)^2 + F^2) − F) + φ_shift(λ), where φ_shift(λ) = a/λ + b is an additional wideband phase term with parameters a and b determined by the wavelength band [λ_min, λ_max]. This ensures constructive interference at the focus across the band. Focus Steering Network (FSN): The FSN maps the measured 1D electric fields e to per-element phase compensation Δφ = f_θ(e), using a CNN architecture inspired by visual processing (convolutions, pooling, fully connected layers, ReLU). Input is 1D electric field data (31 samples). Offline pretraining uses a dataset of 2,000,000 samples with electric fields generated with random phases. Data are shuffled and normalized; split into 80% training and 20% test sets. Loss is mean absolute error (MAE) between predicted and target phase compensations. After training, MAE on both sets is near 0, and network-predicted fields match theoretical computations at the focus. SEL-based focus controller: Given target phase compensation, voltages for each unit are computed using the phase–voltage response curve. To handle variations due to fabrication and environment (temperature, humidity), voltages are updated via the Adam adaptive gradient descent algorithm using the gradient of phase with respect to voltage (obtained via curve fitting or numerical differentiation). Voltage update: u_{i+1} = u_i − α m_i / (√(v_i) + ε) with bias-corrected moments (per Adam). To increase robustness, a fuzzy gradient is used by sampling g ~ N(g, σ^2). The controller stores (u_i, u_{i+1}) and the last successful focusing voltage u′. Initial voltage is selected by nearest-neighbor from historical episodes with closest focal position. Iteration termination uses three criteria: effective correlation coefficient, main lobe energy, and side lobe energy. Discrete 2-state scenario: With 2-state PIN diodes (180° phase flip), voltage adjustment is interval-based; diodes are flipped with probability p(x) = 1 / (1 + e^{−δx}), where x relates to the phase compensation Δφ and δ depends on FSN accuracy (larger δ for higher accuracy). δ is updated during FSN retraining. Experimental procedure: In experiments, only 1D electric field data at 31 probe positions are used online for adaptation. For evaluation, 2D fields at the focal plane are re-measured at initial and final iterations. Multiple EM environments are tested: single-source illumination from arbitrary angles, dual-source incidence, and presence of a scattering obstacle. Iterative focusing is demonstrated, showing energy concentration at the desired focal position over successive voltage updates.

- The SEL-driven neuro-metasurface (SELAF) adaptively focuses incident waves to user-defined positions without prior environmental knowledge, effectively handling multiple sources, arbitrary incidence angles, and scattering obstacles. - High transmission and angle-robust unit cells enable efficient focusing with only 2 phase states per element; the metasurface exhibits transmission better than -0.8 dB across 5.78–6.03 GHz with >95% average transmittance and stability for incidence from -50° to 50°. - FSN training (2 million samples; 80/20 split) achieves near-zero MAE on training and test sets; predicted phase compensations closely match theoretical expectations, as verified by electric field distributions at the focal plane. - Experimental focusing efficiencies for three representative scenarios are 45% (single source), 39% (dual sources), and 42% (with scattering obstacle). Required iterations were 25, 102, and 72, respectively. - Effective correlation coefficients at the focal position after adaptation are 90.15% (single source), 86.17% (dual sources), and 90.2% (with obstacle). Final 2D field maps show well-focused energy at specified positions. - Using only 1D probe inputs can yield multiple focal points; nevertheless, the main lobe energy remains dominant with side-lobe energy proportion < 0.3. The multi-focus issue can be eliminated by using 2D field data as FSN input.

The study addresses the key challenge of real-time adaptability in metasurface-based focusing by emulating eye accommodation with a supervised evolving learning framework. By iteratively adjusting voltages based on sensed fields and a continuously evolving steering network, the SELAF system overcomes limitations of conventional deep learning approaches that require extensive prior data and fixed environments. The results demonstrate robust, rapid adaptation across diverse and complex EM scenarios while using only 1D sensing, confirming that supervised iterative control with on-site learning can reliably reach desired focal states. This approach integrates classical EM focusing principles with machine learning to improve resilience to environmental dynamics and device uncertainties. The architecture generalizes beyond focusing and is potentially applicable to achromatic control, beam shaping, 6G channel enhancement, wireless power transfer, and intelligent EM imaging, where fast, closed-loop, environment-aware wave control is critical.

Inspired by the human eye’s accommodation, the authors introduced supervised evolving learning (SEL) and realized an adaptive focusing system (SELAF) based on a high-transmittance neuro-metasurface. Guided by an evolving focus steering network and a semi-supervised controller, the system rapidly focuses incident waves to target positions in unknown, dynamically changing environments using only 1D measurements, without human intervention. Experiments validate high adaptability across single- and dual-source illuminations and in the presence of scattering obstacles, with strong correlation to theoretical focusing and efficient convergence. The SEL framework provides a generalizable, fast, and robust architecture for EM wave manipulation, with promising implications for achromatic operation, beam shaping, 6G communications, wireless charging, and intelligent imaging. Future work could extend sensing to 2D to suppress multi-focus artifacts, expand device phase states for finer control, and broaden frequency ranges and environmental conditions via continued data-driven evolution.

- Input sensing is limited to 1D electric field data during operation, which can lead to multiple focal points; although main lobe energy remains dominant (side-lobe proportion < 0.3), full 2D sensing would mitigate this issue. - Metasurface elements provide only two discrete phase states (180° flip), constraining granularity of control; finer multi-level phase tuning could improve efficiency and focal quality. - The phase–voltage response can vary with fabrication and environmental conditions (temperature, humidity), requiring adaptive control (fuzzy gradients) and periodic retraining; residual uncertainties may affect convergence speed and accuracy. - Iterative adaptation requires multiple steps (up to 102 iterations in tested cases), which, while practical, could be further reduced with enhanced models, priors, or sensing. - The FSN relies initially on simulated training data and benefits from periodic retraining with experimental data; model bias may persist until sufficient on-site data accumulate.