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J. Eur. Opt. Society-Rapid Publ. 22, 20( 2026)
Figure
11. Spatial distribution of the real part of the Poynting vector( top row) and the corresponding in-plane Poynting vector field( bottom row) for the optimized 4 4 symmetric geometry. The colormap illustrates the magnitude and sign of the power flow, while the arrow plots indicate the local energy propagation direction across the unit cell. The results highlight the symmetry-induced field distribution and energy transport characteristics of the structure. ðk ��M ¼ 125 10 �3; band: 1; k ��M ¼ 5:00 10 �3; band: 3; k ��M ¼ 125 10 �3; band: 3Þ
[ 66 – 71 ]. Nguyen et al. [ 66 ] aimed to achieve broadband negative permittivity by combining fishnet dimer-type geometries with copper layers. For the fishnet dimer configuration, they experimentally demonstrated an operational bandwidth of approximately 10 %. In [ 67 ], the authors experimentally fabricated a curved fishnet metamaterial integrated into a rolled-up tube( RUT) structure, consisting of eight alternating layers of gold( Au) and silicon dioxide( SiO 2). They showed that the negative-index region can be precisely tailored by adjusting the dimensions of the perforated holes defining the metamaterial geometry.
Islam et al. [ 68 ] reported a negative real refractive index peak exceeding 3 GHz across the C- to X-band frequency range. In another study [ 69 ], thermo-sensitive VO 2 films were employed to investigate temperature-tunable splitring-resonator-based metamaterials operating in the THz regime. For low-loss performance, the ratio of the real part of the refractive index to its imaginary part was adopted as a key figure of merit( FOM). A similar performance criterion was also considered in the THz study presented in [ 70 ], where the design was based on asymmetrically aligned paired cut metal wires positioned on the front and back sides of a dielectric substrate. Rasad et al. [ 71 ], on the other hand, demonstrated a single-layer periodic circular silver structure fabricated on a PET substrate, achieving a negative refractive index peak value as low as �57 within the 2.00 – 3.55 GHz frequency range.
In contrast to these previous studies, which primarily aimed at achieving or enhancing negative refractive index behavior without explicitly stabilizing it at a fixed negative value, the present work focuses on maintaining the negative refractive index as constant as possible over an extended bandwidth. Moreover, since most conventional approaches rely on metallic layers, the performance metric is typically defined by the ratio between the negative real part and the imaginary part of the refractive index to ensure low-loss operation. However, the designs considered in this study are based entirely on dielectric materials – such as Si, GaP, and( in the microwave regime) Al 2 O 3 – which exhibit near-zero absorption within their respective operational wavelength ranges. Consequently, the proposed structures inherently satisfy the low-loss criterion at the highest level without requiring additional optimization of the real-to-imaginary index ratio.
4 Conclusions
The numerical results demonstrate that the proposed AIassisted framework can successfully identify photonic geometries exhibiting a negative effective refractive index over a broad and practically relevant frequency interval. For the optimized unit cell, the third photonic band exhibits a normalized frequency range from 0.480 to 0.564, corresponding to a wavelength interval of approximately 1388 – 1631 nm( after model enhancement 1429 – 1578 nm). This range fully covers the S, C, and L optical communication bands, indicating that the designed structure operates well beyond a narrow resonance regime and maintains stable dispersive behavior across a wide bandwidth.
The dispersion analysis further confirms that the targeted band remains well isolated from adjacent bands,