Exceptional points and their coalescence ofPT-symmetric interface states in photonic crystals

Abstract

The existence of surface electromagnetic waves in the dielectric-metal interface is due to the sign change of real parts of permittivity across the interface. In this work, we demonstrate that the interface constructed by two semi-infinite photonic crystals with different signs of the imaginary parts of permittivity also supports surface electromagnetic eigenmodes with real eigenfrequencies, protected by P T symmetry of such loss-gain interface. Using a multiple scattering method and full wave numerical methods, we show that the dispersion of such interface states exhibit unusual features such as zig-zag trajectories or closed-loops. To quantify the dispersion, we establish a non-Hermitian Hamiltonian model that can account for the zig-zag and closed-loop behaviour for arbitrary Bloch momentums. The properties of the interface states near the Brillouin zone center can also be explained within the framework of effective medium theory. It is shown that turning points of the dispersion are exceptional points (EPs), which are characteristic features of non-Hermitian systems. When the permittivity of photonic crystal changes, these EPs can coalesce into higher order EPs or anisotropic EPs. These interface modes hence exhibit and exemplify many complex phenomena related to exceptional point physics.

Plasmon Localization Assisted by Conformal Symmetry

“…In order to improve the visibility of the bands, in this section we choose a small value for the electron scattering rate γ e = 2 meV, which, however does not affect the validity of our argument. The optical response is obtained via semi-analytical solutions calculated by transforming the full set of Maxwell's equations via transformation optics, and finding the poles of the reflection coefficient, as detailed in [34,35]. In addition, we verify our semi-analytical calculations by plotting the corresponding spectra obtained via finiteelement simulations performed with COMSOL Multiphysics.…”

Purcell effect in PT-symmetric waveguides

“…A PT-symmetric photonic crystal can be also designed as a group of gain cylinders paired with a group of lossy cylinders. Then surface electromagnetic waves emerge at the gain-loss interface, while exceptional points can be tuned to coalesce forming higher-order exceptional points [32].…”

Classification of multiple arbitrary-order non-Hermitian singularities

“…Here, the topological notion of homotopy with fixed endpoints explains the equivalence among encircled loops [17]. To date, there have been many studies on the encircling of a few EPs in single-particle systems [18][19][20][21][22] as well as on that of a large number of EPs in many-body systems [23].…”