Fig. 2
From: Exceptional point engineered glass slide for microscopic thermal mapping
Optical characterization of enhanced thermal sensitivity enabled by exceptional point. a Calculated spectra of half the scattering eigenvalue splitting, i.e., the generalized reflection (\(\Delta \upsilon {\mathrm{/}}2 = \left| {\sqrt {r_{\mathrm{f}}r_{\mathrm{b}}} } \right|\), green curve) and the forward reflection coefficient (|rf|, red curve) from the exceptional point (EP) engineered glass slide, which are in stark contrast with the reflection spectrum of the diabolic point (DP) structure with a 1904-nm-thick PMMA anti-reflection film on a glass slide (|r|, blue curve). The EP degeneracy featured by zero scattering eigenvalue splitting is designed at 632.8 nm by optimizing the respective thicknesses of Au and PMMA layers. The abrupt EP phase transition can be fully characterized by the quasi-linear response of forward reflection with almost negligible differences. b Experimentally measured spectra of the generalized reflection and the forward reflection from the fabricated EP glass slide, and the reflection from the DP structure. The minimum forward reflection at the EP wavelength slightly deviates from the ideal reflectionless condition, and is measured at 0.14 (corresponding to a reflectance of ~2%) due to fabrication imperfection. However, the sharp EP phase transition is still observed. c Theoretical temperature responses of scattering eigenvalue splitting and the forward reflection at 632.8 nm, compared with the reflection from the DP structure. Near the EP degeneracy, the scattering eigenvalue splitting evolves with a square-root relation with the temperature increase, providing more than 1 order of magnitude sensitivity enhancement. d Calibration of the thermal sensitivity in terms of the generalized reflection as well as the forward reflection. Because of the initial deviation from an ideal EP condition observed in b, the slopes of the measured \(\left| {\sqrt {r_{\mathrm{f}}r_{\mathrm{b}}} } \right|\) and |rf| spectra are similar, indicating similar thermal sensitivities for the two cases. Compared with the barely detectable thermal response from the DP control sample, the EP glass slide provides significantly improved thermal sensitivity. Each error bar records the data of five separate measurements and indicates the standard deviation. The curves are the best fits of the medians of these measurements. In the calculation of the thermal response c, the empirical thermal expansion of PMMA is taken as αL=8.2 × 10−5 °C−1 as a result of experimental data fitted with the theory, where the thermal-induced thickness change is related to temperature variation by ΔL=αL×L×ΔT
