Multi-layer reflectivity calculation based meta-modeling of the phase mapping function for highly reproducible surface plasmon resonance biosensing

Phase-sensitive surface plasmon resonance biosensors are known for their high sensitivity. One of the technology bottle-necks of such sensors is that the phase sensorgram, when measured at fixed angle set-up, can lead to low reproducibility as the signal conveys multiple data. Leveraging the sensitivity, while securing satisfying reproducibility, is therefore is an underdiscussed key issue. One potential solution is to map the phase sensorgram into refractive index unit by the use of sensor calibration data, via a simple non-linear fit. However, basic fitting functions poorly portray the asymmetric phase curve. On the other hand, multi-layer reflectivity calculation based on the Fresnel coefficient can be employed for a precise mapping function. This numerical approach however lacks the explicit mathematical formulation to be used in an optimization process. To this end, we aim to provide a first methodology for the issue, where mapping functions are constructed from Bayesian optimized multi-layer model of the experimental data. The challenge of using multi-layer model as optimization trial function is addressed by meta-modeling via segmented polynomial approximation. A visualization approach is proposed for assessment of the goodness-of-the-fit on the optimized model. Using metastatic cancer exosome sensing, we demonstrate how the present work paves the way toward better plasmonic sensors.