Exceptional points of Bloch eigenmodes on a dielectric slab with a periodic array of cylinders

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Original languageEnglish
Article number095507
Journal / PublicationPhysica Scripta
Issue number9
Online published24 Aug 2020
Publication statusPublished - Sept 2020


Eigenvalue problems for electromagnetic resonant states on open dielectric structures are non-Hermitian and may have exceptional points (EPs) at which two or more eigenfrequencies and the corresponding eigenfunctions coalesce. EPs of resonant states for photonic structures give rise to a number of unusual wave phenomena and have potentially important applications. It is relatively easy to find a few EPs for a structure with parameters, but isolated EPs provide no information about their formation and variation in parameter space, and it is always difficult to ensure that all EPs in a domain of the parameter space are found. In this paper, we analyze EPs for a dielectric slab containing a periodic array of circular cylinders. By tuning the periodic structure towards a uniform slab and following the EPs continuously, we are able to obtain a precise condition about the limiting uniform slab, and thereby order and classify EPs as tracks with their endpoints determined analytically. It is found that along each track, a second-order EP of resonant states (with a complex frequency) is transformed to a special kind of third-order EP with a real frequency via a special fourth-order EP. Our study gives a clear and complete picture for EPs in parameter space, and can provide useful guidance to their practical applications.

Research Area(s)

  • Diffraction and Scattering, Gratings, Photonic crystal slabs, PARITY-TIME SYMMETRY, FREQUENCY