Hybrid ANN-Z Method for Modeling Carbon Nanotube-Based Reconfigurable Intelligent Surfaces for Terahertz Beam Steering.

Optical reconfigurable intelligent surfaces based on single-walled carbon nanotubes offer promising solutions for terahertz beam steering and photonic wave manipulation in future 6G wireless systems. However, accurate modeling of these structures remains challenging due to quantum transport effects, kinetic inductance, and multi-resonant excitonic behavior across broad frequency ranges. This protocol describes a hybrid computational framework that integrates quantum conductivity modeling using the Kubo formalism, polynomial regression-based data smoothing, and Z-domain transfer function analysis for accurate characterization of single-walled carbon nanotube optical reconfigurable intelligent surface unit cells. The method begins with design of crossed single-walled carbon nanotube nano-strip resonators on a quartz substrate with (10,5) chirality (diameter 0.60 nm, bandgap 1.762 eV), followed by full-wave electromagnetic simulation in CST Microwave Studio across the 0.5-30 THz band. A polynomial regression model of order 8 processes the extracted S-parameters to remove numerical fluctuations and predict smoothed electromagnetic responses. A discrete transfer function H(z) with numerator order 6 and denominator order 7 is then fitted using least-squares optimization with QR decomposition, enabling pole-zero stability analysis and passivity verification. The protocol further incorporates quantum conductivity tuning via chemical potential modulation for beam steering optimization. Representative results demonstrate reflection phase tunability exceeding 310°, absorption enhancement up to 92.3%, beam steering range of ±45° with side lobe levels below -12 dB, and computational acceleration of 180× compared to conventional full-wave optimization methods. The polynomial regression achieved test root mean square error of 0.0688 with R2 coefficient of 0.994, while H(z) fitting achieved root mean square error of 0.89 dB. Stability analysis confirmed all poles within unit circle. This protocol provides an efficient, reproducible pathway for designing programmable photonic metasurfaces and intelligent terahertz communication systems for 6G and beyond.