Abstract
We analyze the scattering properties of a parity-time ($\mathcal{PT}$)-symmetric structure made of a waveguide and a finite chain of side-coupled resonators. Typical one-dimensional $\mathcal{PT}$ structures exhibit unidirectional invisibility (also called anisotropic transmission resonances), meaning unity transmission and zero reflection for incidence from one direction. The side-coupled nature of our structure provides these features as well, but with different characteristics than the traditional tight-binding chain. We explore these properties in detail with numerical and analytical approaches for various chain lengths and geometries. As an interesting feature, we can achieve a broadband unidirectional invisibility with only two resonators. Furthermore, we observe rich dispersions for these anisotropic transmission resonances with four resonators, which can be carefully tuned.
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