Wavelength-Multiplexed 2D Beam Steering via a Passive Diffractive Network

The evolution of beam steering technologies reflects a progression from bulky mechanical systems to more compact, electronic solutions. Mechanical scanners, such as gimbal-based mirrors, offer high precision but suffer from inertia and slow response times, limiting their use in high-speed applications. Liquid crystal devices and micro-electromechanical systems (MEMS) provide faster modulation but are constrained by limited angular range and complexity. Optical phased arrays (OPAs) have emerged as promising active solutions, enabling electronic beam steering with rapid response, yet they often require dense phase shifters and complex fabrication, increasing cost and size.

Recent breakthroughs involve the use of diffractive optics and deep learning for inverse design. Multi-layer diffractive processors, such as those developed by Shen et al. and others, can manipulate wavefronts passively, offering a compact and energy-efficient alternative. These systems leverage neural network-based optimization algorithms to tailor the spatial features of dielectric layers, achieving functionalities like phase conjugation, super-resolution imaging, and wavefront shaping. However, extending these approaches to wideband, multi-channel 2D beam steering remains challenging due to spectral crosstalk, fabrication tolerances, and the complexity of nonlocal wavefront transformations. The current state-of-the-art includes single-layer gratings and multilayer diffractive elements, but none fully exploit deep learning to achieve arbitrary, high-density, multi-wavelength control across 2D fields.

The core challenge addressed in this work is achieving high-density, multi-wavelength, arbitrary 2D beam steering in a passive, compact, and scalable manner. Traditional dispersive elements like gratings are limited to linear wavelength-to-angle mappings, restricting the flexibility of beam routing. Active solutions such as phased arrays, while versatile, are complex, power-consuming, and difficult to miniaturize. The fundamental bottleneck lies in designing passive optical components that can perform complex wavefront transformations across a broad spectral range without active tuning or mechanical movement. Overcoming spectral crosstalk, fabrication imperfections, and alignment sensitivities to realize high-fidelity, multi-channel steering remains a significant technical hurdle.

This research introduces a multilayer passive diffractive network optimized via deep learning, capable of arbitrary wavelength-to-angle mappings in 2D. Key innovations include:

1) Cascaded dielectric layers with spatially optimized phase and thickness profiles, enabling complex, nonlocal wavefront transformations beyond linear dispersion.

2) Joint training of all layers using error backpropagation to minimize the mean squared error between simulated outputs and target beam positions across multiple wavelengths.

3) Exploiting the scale-invariance of diffractive optics, allowing adaptation to different spectral bands by proportional scaling of features, without re-engineering.

4) Demonstrating high-density control of 625 channels in simulations and validating in experiments across terahertz and visible regimes.

This approach significantly advances passive optical beam steering, combining the flexibility of active systems with the simplicity and energy efficiency of passive devices.

• �� Construct a multilayer diffractive structure with thousands of subwavelength features per layer, each capable of phase modulation.
• �� Use deep learning algorithms—specifically error backpropagation and stochastic gradient descent—to optimize the phase and thickness parameters of each layer, minimizing the MSE between the output fields and target beam positions.
• �� Simulate wavefront propagation between layers using Rayleigh–Sommerfeld scalar diffraction theory, modeling each layer as a complex transmission function.
• �� Assign each wavelength within the 400-750nm range to a specific target position in the output plane, creating a training dataset of 625 pairs.
• �� During training, iteratively update the multilayer parameters to improve wavelength-specific beam steering accuracy.
• �� Validate the trained model through numerical simulations, assessing positional accuracy, angular deviation, and generalization to intermediate wavelengths.
• �� Fabricate the optimized multilayer structure via 3D printing or lithography, and experimentally test in terahertz and visible regimes using appropriate sources and detectors.
• �� Fine-tune the system with in-situ learning to compensate for fabrication imperfections and alignment errors, especially in the visible-light experiments.

• �� Numerical simulations involved designing 625 channels across 400-750nm, with target beam positions covering a 25×25 grid, achieving subwavelength accuracy and high PSNR.
• �� Terahertz experiments used two 3D-printed dielectric layers, illuminated by tunable terahertz sources at five wavelengths, successfully steering beams with deviations below 0.06°.
• �� Visible experiments employed phase-only spatial light modulators to implement the designed phase profiles, with nine wavelengths (470-710nm), achieving angular steering resolution of ~0.06°.
• �� Calibration procedures included in-situ learning to mitigate fabrication and alignment errors, improving the fidelity of experimental results.
• �� The experimental setups incorporated high-precision alignment stages, spectral filters, and detectors to accurately measure the output beam positions and angles.
• �� Data collection involved capturing the output intensity distributions at various wavelengths, comparing them to numerical predictions, and iteratively refining the device parameters.

• �� The numerical model achieved 625 independent channels with positional errors below 0.2λ, and the system maintained PSNR over 33dB, demonstrating robust performance and generalization to intermediate wavelengths.
• �� Terahertz experiments confirmed the ability to steer beams at five wavelengths with angular deviations less than 0.06°, matching simulation results.
• �� Visible-light experiments demonstrated multi-wavelength control with nine channels, achieving angular steering resolutions of ~0.06°, validating the design's scalability and robustness.
• �� The system's angular resolution (~0.11° in simulations and ~0.06° in experiments) surpasses traditional grating-based devices, enabling precise, high-density beam control.
• �� The results collectively showcase the potential for passive, wavelength-multiplexed 2D beam steering across broad spectral regimes with high fidelity and efficiency.

• �� The technology can be integrated into high-speed optical communication systems for dynamic, multi-channel data routing without mechanical parts.
• �� In autonomous vehicles, it enables compact, fast LiDAR systems capable of high-resolution 3D scanning with minimal power consumption.
• �� In imaging and sensing, it allows rapid multi-angle illumination or detection, improving resolution and acquisition speed.
• �� The broad spectral adaptability supports applications in quantum optics, biomedical imaging, and free-space optical links.
• �� Future integration with phase and polarization multiplexing could further enhance capacity and functionality, enabling multifunctional photonic chips.

• �� Precise fabrication and alignment of multilayer structures are critical; misalignments can significantly degrade performance, requiring advanced manufacturing techniques.
• �� Phase quantization constraints in high-frequency regimes may reduce diffraction efficiency and increase sidelobes, necessitating quantization-aware training.
• �� The spectral resolution depends on the source linewidth; broader sources cause spatial blurring, limiting channel density and speed.
• �� Environmental factors such as temperature fluctuations and mechanical vibrations could impact system stability, requiring robust calibration and compensation strategies.