Plackett–Burmann Design and Machine Learning Models for Optimization and Prediction of Confinement Loss in PCF Sensor

This study focuses on the optimization and performance assessment of a dual-core photonic crystal fiber (PCF)-based surface plasmon resonance (SPR) sensor for advanced biosensing applications. The Plackett-Burman Design (PBD) was employed to optimize key structural parameters, including air hole diameters (d<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub>, d<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>, d<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub>, d<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub>) and gold layer thickness (t<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gold</sub>). Finite Element Method (FEM) simulations were utilized to analyze the sensor’s optical properties, while PBD helped identify the most influential parameters affecting confinement loss (C<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Loss</sub>). Regression analysis was used to model the relationship between the sensor’s geometric parameters and confinement loss, revealing that d<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> and t<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gold</sub> have the most statistically significant effects. The optimized PCF-SPR sensor demonstrated outstanding performance, achieving a maximum wavelength sensitivity of 8000 nm/RIU, a resolution of 1.25 × 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> RIU, and an amplitude sensitivity of 573.436 RIU-1, underscoring its high potential for refractive index-based detection. To enhance predictive modeling, we applied an extensive range of machine learning regression models to estimate confinement loss. A comparative evaluation of these models identified the Extra Tree Regressor (ETR) as the most effective in accurately predicting sensor performance. These findings highlight the synergy between FEM simulations, design of experiments (DOE), and machine learning for optimizing PCF-SPR sensors, paving the way for highly sensitive, real-time biosensing applications.