Generalized temporal coupled-mode theory for a PT-symmetric optical resonator and Fano resonance in a PT-symmetric photonic heterostructure

We have proposed generalized temporal coupled-mode theory for PT-symmetric optical resonator, and on this basis we have explained the Fano resonance in PT-symmetric photonic heterostructure. Our theoretical predictions agree very well with the simulated results obtained by transfer matrix method, which confirms the correctness of our theory. Compared with conventional Fano resonance in optical resonator with time-reversal symmetry, in this Fano resonance the amplitudes of scattering coefficients can be tuned in much larger range, which can be much larger than one, and tend to infinity at singular scattering point, where the rates of dissipation and accumulation are equal to each other and the difference of the phases of the coupling coefficients between output fields and resonant mode is equal to +/-pi/2. Not only that, the quality factor Q here can be negative out of accumulation, and approaches infinity at this singular scattering point. The phases of reflections jump pi in the vicinity of the minima of corresponding amplitudes. We believe that we open a new door to study Fano resonance in non-Hermitian optics and inspire relevant study in other non-Hermitian wave systems. (c) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Automated summary

We have introduced generalized temporal coupled-mode theory for PT-symmetric optical resonator, and used it to explain the Fano resonance in PT-symmetric photonic heterostructures. Our theory's predictions match well with the simulated results from the transfer matrix method, confirming its accuracy. In contrast to conventional Fano resonance in optical resonators with time-reversal symmetry, this Fano resonance allows for a much larger range of tunable scattering coefficient amplitudes, which can exceed one and approach infinity at a singular scattering point.