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

Summary

This protocol presents a hybrid artificial neural network and Z-transform method for accurate electromagnetic modeling of single-walled carbon nanotube-based optical reconfigurable intelligent surfaces operating in the terahertz band (0.5-30 THz) for 6G wireless communication applications, achieving 180× computational acceleration with reflection phase tunability exceeding 310° and beam steering range of ±45°.

Abstract

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.

Introduction

The rapid evolution toward sixth-generation (6G) wireless systems has accelerated exploration of terahertz (THz) and optical frequency bands to achieve ultra-high data rates exceeding 1 Tbps, intelligent sensing, holographic beamforming, and adaptive wavefront engineering^1,2,3. The terahertz band (0.1-30 THz) offers abundant bandwidth but suffers from severe free-space attenuation (approximately 20 dB·km^-1 at 1 THz), atmospheric molecular absorption from water vapor at 557 GHz, 752 GHz, 988 GHz, and 1.13 THz, and extreme sensitivity to blockage from atmospheri....

Protocol

1. SWCNT Optical RIS Unit Cell Design

1. Selection of SWCNT Chirality
   1. Select SWCNT chirality (10,5) based on quantum conductivity analysis.
   2. Calculate the nanotube diameter using below mentioned formula
      
      where a_cc=0.142 nm is the carbon-carbon bond length. The (10,5) chirality yields diameter of 0.60 nm and bandgap of 1.762 eV, optimal for terahertz operation.
   <....

Results

Selection of SWCNT Chirality
The protocol described was implemented for a (10,5) SWCNT optical RIS unit cell operating across the 0.5-30 THz band. Representative results demonstrate the effectiveness of the hybrid polynomial-Z modeling approach for accurate electromagnetic characterization and beam steering optimization.

Quantum Conductivity Analysis
Kubo formalism revealed that the (10,5) SWCNT exhibits complex surface conductivity dominated by imagin.......

Discussion

Critical steps in the protocol require careful attention to ensure successful implementation. First, accurate selection of SWCNT chiral indices is essential because the bandgap and optical response are highly chirality-dependent. The (10,5) chirality specified in this protocol provides optimal bandgap of 1.762 eV for terahertz operation, but users targeting different frequency bands should calculate the corresponding chirality using the bandgap formula E_g = 2ħv_F/d = (2 × 1.0546×10⁻³⁴

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
CST Microwave Studio	Dassault Systèmes	N/A	Version 2024, Frequency domain solver
MATLAB	MathWorks	N/A	Version R2014a or later
Quartz substrate	University Wafer	4526	500 nm thickness, ε_r = 3.8
SWCNT (10,5) chirality	NanoIntegris	SWCNT-105	0.60 nm diameter, >90% semiconducting
Personal Computer	N/A	N/A	32 GB RAM, 8 CPU cores minimum