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Mathematical Modeling of a Plasmonic Palladium-Based Hydrogen Sensor

The presented plasmonic palladium-based perfect absorber hydrogen sensor is used to detect hydrogen via measured reflectance spectra. The perfect absorber geometry enables a highly sensitive, cost-effective, miniatuarizable, and purely optical detection system. Through fiber optics, this scheme allows for a clear separation of the detector and all electronic components rendering it inherently safe, even in explosive environments. The sensor has a complex transient behavior, which exhibits temperature-dependence, nonlinearities, and hysteresis. This transient behavior is mathematically represented by a physically motivated model. The derived model is a distributed parameter system, which considers the dispersed hydrogen diffusion in the palladium and describes the nonlinear input and linear output characteristics. Experimental measurements are conducted at 25 °C, 30 °C, and 40 °C to identify the model parameters and to show the model accuracy.