Coupled-resonator optical waveguides (CROWs) are known to have interesting
and useful dispersion properties. Here, we study the transport in these
waveguides in the general case where each resonator is open and asymmetric,
i.e., is leaky and possesses no mirror-reflection symmetry. Each individual
resonator then exhibits asymmetric backscattering between clockwise and
counterclockwise propagating waves, which in combination with the losses
induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling
between the resonators induces an additional source of non-hermiticity, and a
complex band structure arises. We show that in this situation the group
velocity of wave packets differs from the velocity associated with the
probability density flux, with the difference arising from a non-hermitian
correction to the Hellmann-Feynman theorem. Exploring these features
numerically in a realistic scenario, we find that the complex band structure
comprises almost-real branches and complex branches, which are joined by
exceptional points, i.e., nonhermitian degeneracies at which not only the
frequencies and decay rates coalesce but also the eigenmodes themselves. The
non-hermitian corrections to the group velocity are largest in the regions
around the exceptional points.Comment: 11 pages, 9 figure
