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We describe the formation of bulk and edge arcs in the dispersion relation oftwo-dimensional coupled-resonator arrays that are topologically trivial in thehermitian limit. Each resonator provides two asymmetrically coupled internalmodes, as realized in noncircular open geometries, which enables the system toexhibit non-hermitian physics. Neighboring resonators are coupled chirally toinduce non-hermitian symmetries. The bulk dispersion displays Fermi arcsconnecting spectral singularities known as exceptional points, and can be tunedto display purely real and imaginary branches. At an interface betweenresonators of different shape, one-dimensional edge states form that spectrallyalign along complex arcs connecting different parts of the bulk bands. We alsodescribe conditions under which the edge-state arcs are free standing. Thesefeatures can be controlled via anisotropy in the resonator couplings.

Bulk and edge-state arcs in non-hermitian coupled-resonator arrays