Fig. 2

PT symmetry features of the dual coupled microresonator. a Evolution of the normalized real (mode splitting) and imaginary (loss) components of the eigenvalues of the passive PT symmetry system as a function of \({\gamma }_{c}\) (normalized by \({\gamma }_{c}\) at the EP, i.e.,\({\gamma }_{c}^{{\text{EP}}}\)). Purple solid lines plot the relative frequencies at which the normalized transmission becomes 1/2 at a given\({\gamma }_{c}\). The blue-shaded area represents the preferred operating region of the signal and idler light. b Transmission spectra of the systems. The blue solid lines represent the measured transmission spectra, while the red dashed lines represent their curve fittings for devices operating at different coupling conditions. Panel (i) to (v) correspond to the blue data points shown in a from left to right. The ripples observed in the spectra are typical Fabry–Perot resonances resulting from the end facet reflections. Note that the transmission spectrum in each panel yields a total of four data points in (a)—mode splitting and loss corresponding to \({\omega }_{\pm }\), at different\({\gamma }_{c}\). A three-dimensional plot showing the evolution of the transmission spectrum is provided in Additional file 1: S3. For comparison, panel (vi) shows the transmission spectrum near pump resonance where the horizontal axis means relative frequency with respect to \({\omega }_{p}\). Analysis of the pump operation from PT aspect as well as TMM are given in Additional file 1: S3. The simulations (red dashed lines) for the curve fitting are carried out based on the transfer matrix model (Additional file 1: S2). More details for data extraction are given in Methods