Bifurcation of avoided crossing at an exceptional point in the Lorentz oscillator model

Physical phenomena associated with exceptional points of non-Hermitian operators are subject of active research in photonics and other fields. I will show that an exceptional point occurs already in the classic Lorentz oscillator model of optical dispersion. The reason that this feature of the Lorentz dispersion equation has remained unnoticed is that normally the wavevector is regarded as a complex function of the real frequency, in which case the exceptional point is not encountered. However, if the frequency is treated as a complex function of the real wavevector, the Lorentz dispersion equation describes the transition between the strong and weak coupling regimes through the bifurcation of an avoided crossing at the exceptional point. These two situations correspond to two classes of experiments: while transmission measurements imply a real frequency, scattering experiments impose a real wavevector. In the latter class of experiments, exceptional points will be encountered in many physical systems generally described by Lorentz-oscillator-type models.