Quasinormal Modes, Local Density of States, and Classical Purcell Factors for Coupled Loss-Gain Resonators

We first present a quasinormal mode (QNM) theory for coupled loss-gain resonators working near an exceptional point. Assuming linear media, which can be fully quantified using the complex pole properties of QNMs, we show how QNMs yield quantitatively good model to full dipole spontaneous emission response in Maxwell's equations at various spatial positions and frequencies (linear response). also develop highly accurate intuitive QNM coupled-mode theory, used rigorously such systems only bare resonators, where hybrid complete system are automatically obtained. Near lossy point, analytically Lorentzian-like Lorentzian-squared-like lineshape, consistent with other works. However, rigorous analytical numerical solutions microdisk demonstrate that general lineshapes far richer than what has been previously predicted. Indeed, classical picture take on wide range positive negative Purcell factors from modes system. These unphysical signal clear breakdown though local density states is correct. rich spectral features Green function propagators, physical observables. Second, approach index modulated ring point unusual chiral power flow linearly polarized emitters, agreement recent experiments, explained without invoking interpretation missing dimension (the Jordan vector) decoupling cavity eigenmodes.