Modeling an SPR Sensor for Carcinoma-Related Refractive-Index Detection: The Case of CaF₂/Au/Si₃N₄/BP Multilayer System.

A thin-film surface plasmon resonance (SPR) sensor is presented using a prism-coupled Kretschmann configuration and an optimized multilayer architecture incorporating black phosphorus (BP) as an ultrathin overlayer. The response is modeled at 633 nm under TM polarization using the transfer-matrix method. Low-concentration sensing conditions in the 1-5 ng/mL range are represented through small effective-refractive-index perturbations of the aqueous sensing medium, providing a preliminary optical framework for evaluating refractive-index response in biosensing-related scenarios. The coupling prism, Au film thickness, and Si₃N₄ spacer thickness are optimized to control resonance depth, linewidth, and angular shift. The optimized CaF₂/Au/Si₃N₄/BP configuration exhibits systematic condition-dependent displacement of the SPR minimum and an evanescent-field distribution that remains strongly localized at the sensing interface while extending into the sensing medium, enabling refractive-index interrogation. High angular sensitivity is obtained at low levels, reaching 517.62°/RIU at 2 ng/mL and 482.82°/RIU at 1 ng/mL, with quality factors above 120 RIU^-1 in the same regime. Composite indicators (figure of merit and contrast signal factor) peak at intermediate levels, whereas resonance broadening at higher levels reduces the quality factor and increases the inferred limit of detection, evidencing a sensitivity-resolution trade-off. Benchmarking against reported SPR platforms indicates that BP-assisted interface engineering provides a competitive low-level operating window within a preliminary refractive-index-sensing framework that is relevant to future biosensor design. These results motivate further experimental validation, including BP stabilization, surface biofunctionalization, and practical implementation under liquid-phase sensing conditions.