Fig. 3: Differential reflectance near SIP frequency obtained from two-chain CMT model.
From: Non-resonant exceptional points as enablers of noise-resilient sensors
a Logarithmic plot of the differential reflectance \(\Delta R\) (blue line) as a function of the frequency detuning \(\nu\) from the stationary inflection point (SIP) frequency \({\omega }_{{{{{{\rm{SP}}}}}}}\). The black dashed line indicates a variation of the differential reflectance which is \(\Delta R\propto {\left|\nu \right|}^{0.66}\). The inset shows the dispersion relation of the Coupled Mode Theory (CMT) model. The SIP frequency \({\omega }_{{{{{{\rm{SP}}}}}}}\) is indicated by a horizontal dashed line. b Logarithmic plot of the differential reflectance \(\Delta R\) (blue line) as a function of the Peirels’ phase detuning \(\nu =\Delta \phi\) from the critical phase \({\phi }_{{{{{{\rm{SP}}}}}}}\). The black dashed line indicates a variation of the differential reflectance which is \(\Delta R\propto {\left|\nu \right|}^{0.66}\). In the background we show a schematic of the CMT model Eq. (12). c Logarithmic plot of the differential reflectance \(\Delta R\) (color lines) as a function of the frequency detuning \(\nu\) from the SIP frequency \({\omega }_{{{{{{\rm{SP}}}}}}}\) in case of a finite-size system for various number of unit-cells \(L\). The black dashed line indicates a variation of the differential reflectance which is \(\Delta R\propto {\left|\nu \right|}^{0.66}\). In order to optimize the scaling performance, we have used a ramped loss \(\gamma \left(n\right)={\gamma }_{{{\max }}}{\left(\frac{n-1}{L-1}\right)}^{2}\), where \({\gamma }_{{{\max }}}\) is the amount of loss in the last unit cell and \(n\) is the number of the unit cell.
