Fig. 4: Effects of disorder in the non-resonant exceptional point degeneracy sensing protocols based on stationary points in the Bloch dispersion relation.
From: Non-resonant exceptional points as enablers of noise-resilient sensors
a Logarithmic plot of the differential reflectance ΔR (gray dots) as a function of the detuning \(\nu\) from the frequency ωSP for 104 disorder realizations of the resonant frequencies of the Coupled Mode Theory model. The disorder strength is taken to be \(W = 0.01\). The average value 〈ΔR〉 (blue line) follows the predicted dependence Eq. (11) \(\langle {\Delta} R\rangle\sim\left|\nu\right|^{0.66}\) indicated by the black dashed line. Inset: The sensitivity bound \({\nu }_{{{{{{\rm{c}}}}}}}\) for three different disorder strengths (blue dots). The black dashed line indicates the best fit \({\nu }_{{{{{{\rm{c}}}}}}}\sim W\). b Detuning error \({\sigma }_{\nu }\) as a function of detuning \(\nu\) for three different disorder strengths in case of a regular-band-edge-based sensing scheme (red lines) and of a stationary-inflection-point-based sensing scheme (blue lines). The red highlighted area represents the domain \(\sigma_\nu\; > \;\nu\) where the signal cannot be resolved. The resolution limit for each sensing protocol is defined by the point where the σν line crosses the line \(\sigma_\nu = \,\nu,\) shown by the black dashed line.
