J. Eur. Opt. Society-Rapid Publ. 2026, 22, 20 Ó The Author( s), published by EDP Sciences, 2026 https:// doi. org / 10.1051 / jeos / 2026018 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Negative-refractive-index behavior in a periodic photonic metamaterial: unit-cell topology tailoring for broadband response
Cevat Açıkel 1, Ecem Helvacı 1, Bilgehan B. Öner 2, and Irem O. Alp 1,* 1 Department of Physics, Faculty of Sciences, Gazi University, Ankara, Türkiye 2 Department of Physics, Graduate School of Natural and Applied Sciences, Gazi University, Ankara, Türkiye
Received 21 January 2026 / Accepted 24 February 2026
Abstract. This paper examines how systematic control of unit-cell topology governs dispersion characteristics and bandwidth stability in configured periodic structures with numerical simulations. Distinct from the existing literature, the study targets a negative refractive index over a broad frequency range, while neural network – based optimization is used as a supporting tool to efficiently guide for bandwidth maximization. Comprehensive analysis is employed to optimize bandwidth effectively and validate the applicability of the resulting low-dispersion periodic structures. For the optimized unit cell, the third photonic band spans a wavelength range 1388 – 1631 nm( after model enhancement 1429 – 1578 nm) covering the S, C, and L optical communication bands, demonstrating broadband and stable dispersive behavior beyond a narrow resonance regime. The obtained results are thus expected to enhance the performance of negative-index based photonic components used in optical and photonic communication systems, compact antenna architectures, and advanced material engineering.
Keywords: Metamaterials, Photonic crystals, Negative refractive index, Neural network, Machine learning.
1 Introduction
The literature indicates that artificial intelligence has increasingly been applied to photonic design over the past decades [ 1 – 6 ]; however, an approach that optimizes the operational bandwidth of the negative refractive index has not yet been established. In conventional studies, metamaterials have typically been investigated at a single frequency, namely the resonance point. Pendry demonstrated the super-resolution potential of a negative refractive index at the resonance frequency [ 7 ], while Shelby and co-workers reported the first experimental verification of this behavior [ 8 ]. In the years that followed, various application-oriented designs have been presented in the literature [ 9 – 12 ]. Artificial neural networks( ANNs) constitute an effective tool for meeting the requirement of guiding light within specific frequency ranges in photonic crystals. In this study, networks trained on diverse material properties are employed to rapidly and accurately predict the effective refractive index and related parameters, thereby enabling calculations that would otherwise require weeks using conventional methods to be completed within a significantly shorter time frame.
* Corresponding author. iremoner @ gazi. edu. tr
The metamaterials considered in this study have gained a prominent position in the field of photonics since the early 2000s and have exhibited extraordinary phenomena such as invisibility, super-resolution, and advanced focusing, enabled by electromagnetic properties not found in nature [ 13 – 15 ]. These structures, formed by periodic arrangements of meta-atoms at the micro- or macro-scale, can control their interaction with electromagnetic waves through geometric tuning. As no natural material possesses such characteristics, the first experimental demonstration of metamaterials was realized in 2000 by Smith and co-workers using periodic arrays of split-ring resonators and metallic subwavelength structures, following approximately four decades of theoretical development [ 5 ]. Subsequent variations of this approach [ 16 – 18 ] have established metamaterial design as a broad and active research area.
The concept of a negative refractive index was first introduced by Veselago in 1967 [ 19 ]. Materials exhibiting a negative refractive index underpin a wide range of applications, including superlenses, optical camouflage( cloaking) devices, advanced filters, and compact antennas [ 20 – 25 ]. Nevertheless, existing studies have predominantly focused on narrow frequency ranges, largely based on metallic materials. In contrast, broadband metamaterials offer a significantly wider range of applications compared to single-frequency designs, providing substantial advantages
This is an Open Access article distributed under the terms of the Creative Commons Attribution License( https:// creativecommons. org / licenses / by / 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.