J. Eur. Opt. Society-Rapid Publ. 22, 20( 2026) 187
in areas such as multi-wavelength imaging, adaptive optics, broadband antennas, and telecommunication systems [ 26 – 29 ]. Moreover, they deliver more stable performance in applications involving variable operating frequencies, including radar stealth and medical imaging.
Over the past few decades, inverse design techniques and topology optimization have become increasingly prominent in the field of photonics [ 30 – 40 ]. Compared with alternative optimization approaches [ 41 – 43 ], topological optimization enables superior performance within restricted device dimensions by analyzing relatively large input parameter window. Surpassing the performance of the conventional design, enhanced digital configuration capabilities improve achievements on photonic device performance [ 44 ].
Regression and gradient-based methodology has begun to be utilized as the basis for topology optimization in a wide range of metamaterial applications [ 45 – 51 ]. As for the topic of electromagnetic metamaterials, S. Nanda et al. use an inverse artificial neural network on split ring resonator structural and target parameter dataset [ 47 ]. Another inverse design focused on spectral prediction of multi-layered graphene based photonic metamaterials [ 48 ]. E. Harper et al. [ 49 ] presented a research on all-dielectric meta-surface. In this regard, meta-atom geometry engineering by dielectric materials show that they play a fundamental role on broadband metamaterial based devices. Nevertheless, no data-driven model has been studied to broaden the negative index spectrum of photonic crystals.
This study presents an original artificial-intelligenceassisted methodology for the design of broadband negative-refractive-index photonic media, encompassing both design and computational modeling processes. Optimization techniques aimed at driving the effective refractive index and group velocity into the negative regime are supported by deep neural networks( DNNs) [ 52 ], building upon artificial neural network frameworks. The numerical analysis is conducted using a block-iterative frequency-domain method based on the plane-wave approximation. Furthermore, as conventional photonic design workflows are inherently complex, iterative, and time-consuming, machine learning is employed to significantly reduce the trial-anderror process involved in material selection and photonic crystal geometry determination. The proposed approach is expected to facilitate the discovery of strong negativerefractive-index behaviors that are difficult to achieve using classical methods, thereby not only accelerating the design process but also enabling more realistic implementations of broadband superlenses and other advanced optical devices.
2 Methods of calculation
A variety of well-established analytical and computational design methods based on electromagnetic theory are available for the analysis and design of photonic media, allowing researchers to easily construct geometries and perform calculations on structures with complex configurations. Among the most widely used tools are MIT Photonic Bands( MPB) and MIT Electromagnetic Equation Propagation( MEEP), which have proven reliability in photonic simulations [ 53, 54 ]. The design approaches employed in this context can generally be categorized as combinations of basic and advanced electromagnetic theory, finite-difference time-domain( FDTD) simulations, frequency-domain simulations, topological design strategies, optimization methods, and hybrid frameworks integrating these techniques [ 55, 56 ].
Phenomena such as wave propagation in space, the calculation of transmission and reflection coefficients, and the analysis of wavefronts and field patterns can be accurately evaluated using time-domain simulations. FDTD-based simulation tools, which are widely available in the literature [ 57 ], are particularly suited for this purpose. These tools are commonly used to solve electromagnetic problems associated with periodic structures such as photonic crystals. By solving Maxwell’ s equations under periodic boundary conditions, photonic band structures can be obtained. This enables the determination of group and phase velocities, photonic band gaps, light – matter interactions, and other key optical, photonic, and electromagnetic properties in periodic media.
Metamaterials can be analyzed using frequency-domain simulations, focusing on their unit-cell properties, as well as time-domain simulations that capture their dynamical behavior. While metamaterial designs typically rely on metallic unit cells with inherently resonant frequency responses, it will be shown in the following sections that broadband unit cells can exhibit similar characteristic behavior.
In this context, machine learning tools will be developed and employed to maximize the operational bandwidth within the project. Using MATLAB [ 58 ] together with its deep learning and artificial neural network modules, the relevant algorithms will be trained on datasets containing material properties to achieve a negative refractive index over a broad bandwidth by designing the size, arrangement, and geometric structure of meta-atoms in photonic crystals. This approach enables accurate prediction of refractive index values and other key parameters without the need for extensive preliminary testing. The process is planned to proceed through the following steps:
2.1 Target definition and data collection
The primary objective of the study is defined as achieving a negative refractive index over a wide bandgap. Large datasets incorporating meta-atoms with varying sizes, arrangements, and geometrical configurations will be generated. At this stage, simulation tools such as MEEP and MPB will be used to compute the relevant optical properties in line with the optimization goal.
2.2 Identification of input and output features
Geometrical parameters, including size, arrangement, and structural features, will be defined as input variables, while the targeted optical properties and performance metrics will serve as outputs. To improve model learning, data scaling( ensuring that all features lie within a specific range) and normalization( rescaling data to a common distribution or magnitude) will be applied.