Fixed points on band structures of non-Hermitian models: Extended states in the bandgap and ideal superluminal tunneling

Space-time reflection symmetry (PT symmetry) in non-Hermitian electronic models has drawn much attention over the past decade mainly because it guarantees that the band structures calculated under open boundary conditions be the same as those calculated under periodic boundary conditions. PT symmetry in electromagnetic (EM) models, which are usually borrowed from electronic models, has also been of immense interest, mainly because it leads to exceptional parameter values below which non-Hermitian operators have real eigenvalues, although PT symmetry is not the sole symmetry that allows such exceptional parameter values. In this work, we examine one-dimensional PT-symmetric non-Hermitian EM models to introduce novel concepts and phenomena. We introduce the band-structure concept of fixed points, which leads to bidirectional reflection zeros in the corresponding finite structures, contrary to a common belief about the EM structures with PT symmetry (and without parity inversion and time-reversal symmetries). Some of the fixed points manifest themselves as, what we name, extended states in the bandgap on the band structure while some other fixed points are the turning points of the band structure. The extended states in the bandgap are in fact the dual of the well-known bound states in the continuum, while the turning points allow us to observe ideal superluminal tunneling in the corresponding finite structures. By ideal superluminal tunneling, we mean the case where not only the transmission coefficient has an almost uniform phase over a broad bandwidth, but also the magnitudes of the transmission and reflection coefficients are almost equal to unity and zero, respectively, over the bandwidth.

Automated summary

PT symmetry has attracted much attention in both non-Hermitian electronic and electromagnetic models. In this study, we explore one-dimensional PT-symmetric non-Hermitian electromagnetic models and introduce the concept of fixed points in the band structure. These fixed points lead to bidirectional reflection zeros and allow for the observation of extended states in the bandgap and ideal superluminal tunneling. The results of this work provide novel insights into the behavior of PT-symmetric electromagnetic models.