Designing surfaces that precisely control how light behaves at the nanoscale is tricky. Optical Fourier surfaces, which are nanostructured gratings that redistribute light into specific directions and wavelengths, hold enormous potential for compact spectrometers, augmented-reality displays, and advanced sensors. However, their standard design process relies on computer simulations that assume idealised conditions such as single-angle illumination and the absence of fabrication imperfections—a far cry from reality.
The gap between what simulations predict and what fabricated devices actually do has long frustrated researchers. It widens further when designers try to exploit one of the most powerful but underused design parameters: the angle of incoming light. Changing the incident angle can activate or suppress optical modes without any physical modification to the structure, effectively enabling multiple functions on a single device.
“This effectively introduces an additional degree of freedom beyond geometry, expanding the design space significantly,” said Associate Professor Dong Zhaogang from the Singapore University of Technology and Design (SUTD). “But its practical use has been limited because simulations at oblique incidence are often computationally unstable and costly, while real experimental systems involve angular distributions rather than single-incident angles.”
To address this, Assoc Prof Dong collaborated with Professor Zhu Jinfeng from Xiamen University, Dr Wei Chen from Hefei University of Technology, and other researchers from Singapore and China to develop a deep-learning framework that sidesteps simulation entirely. In their research paper “ Reality-infused deep learning for angle-resolved quasi-optical Fourier surfaces ”, the team trained an AI model, a transformer-based neural network dubbed ExpForm, directly on experimental measurements collected from fabricated nanostructures.
The approach centres on a high-throughput, angle-resolved spectroscopy system that captures broadband reflectance spectra across a wide range of incident and azimuthal angles. Each measurement takes roughly six minutes, and the team collected over 25,000 spectral instances from four quasi-optical Fourier surface samples fabricated using nanoimprint lithography. These real-world spectra, complete with fabrication-induced roughness, structural asymmetry, and measurement noise, became the training data for the neural network.
“Conventional optical simulations often diverge from experimental reality because they rely on idealised assumptions, such as perfectly smooth geometries without surface roughness or disorder,” Assoc Prof Dong said. “Simulations also fail to capture many real-world factors, including fabrication tolerances, intrinsic material imperfections, and measurement noise.”
The framework operates in two directions. A forward network takes structural and angular parameters as input, and predicts the resulting optical spectrum in real-time. An inverse network does the opposite. Given a desired spectral response, it works backwards to identify the structural dimensions and illumination angles needed to produce it. Together, the two networks form an end-to-end design tool that replaces the traditional cycle of simulate, fabricate, measure, and repeat.
Compared to conventional finite-difference time-domain simulations, the ExpForm model achieved 99.79 percent consistency with experimental measurements while delivering an approximately 900-fold improvement in spectral evaluation speed. A randomly selected test case showed that conventional simulation failed to capture key spectral features (wavelength positions, resonance shapes, and quality factors) under oblique and azimuthal incidence conditions.
“For a researcher or engineer, this means design cycles can be reduced from hours or days to seconds, enabling rapid, iterative development,” shared Assoc Prof Dong. “Reliance on costly trial-and-error fabrication is significantly reduced.”
The inverse design capability proved equally capable. The team demonstrated on-demand generation of narrowband resonances at specific wavelengths, high-reflectance profiles, and dual-band resonances—all achieved by adjusting incident angles rather than refabricating new structures.
“It enables the solution of previously inaccessible problems, including the design of complex spectral responses, rapid prototyping without repeated fabrication cycles, and the development of angle-programmable devices where a single structure can support multiple functions,” Assoc Prof Dong noted.
The team has made the full experimental training dataset publicly available, a decision Assoc Prof Dong said was driven by a desire to lower barriers for other research groups and encourage fair benchmarking of different neural network models. Existing experiment-driven approaches in this field have largely been confined to microwave frequencies, so this work extends the paradigm into the visible and near-infrared range.
Moving forward, the researchers see the reality-infused approach extending to high-Q resonators, nonlinear optical platforms, and three-dimensional metastructures. They have already demonstrated its applicability to dielectric devices driven by bound states in the continuum, as well as structures with both in-plane and out-of-plane geometric degrees of freedom.
“This work represents a shift from purely first-principles-driven design toward a data-informed, experimentally grounded paradigm, where AI functions as a co-designer rather than merely a computational tool,” Assoc Prof Dong shared. “Beyond photonics, the same paradigm is applicable to fields such as materials science, electronics, and quantum devices.”
PhotoniX