Exploring phase sensitivity and limit of detection near the critical coupling of metasurfaces and its phase singularity

It is commonly accepted that phase singularities in refractive index sensors can provide highly sensitive detection. To address this issue, we studied the phase sensitivity and the limit of detection of Tamm photonic crystals used as temperature sensors, taken here as a model system by exploring critical coupling and its associated phase singularity. To finely tune the optical Tamm mode to critical coupling, the top metal layer is periodically nanostructured and controlled, enabling the investigation of optical Tamm resonances around phase singularities. We use a highly stable common-path interferometry setup based on digital holography, which allows us to measure extremely high phase sensitivity even at very low light intensities, while also providing information about reflectivity in the complex domain. We experimentally validate an analytical model based on Temporal Coupled Mode Theory, which fully explains the phase sensitivity response and the limit of detection of such resonant photonic sensors. We demonstrate that, although approaching a phase singularity drastically enhances phase sensitivity, no improvement of the limit of detection is expected. Furthermore, phase singularity has no effect on the limit of detection, and therefore on the efficiency of such sensors for practical applications. This work provides a comprehensive description of phase sensors operating at critical coupling, and challenges the commonly accepted assumption regarding the role of phase singularities in sensing.