TY - JOUR

T1 - Non-Hermitian-transport effects in coupled-resonator optical waveguide

AU - Schomerus, Henning

AU - Wiersig, Jan

PY - 2014/11/10

Y1 - 2014/11/10

N2 - Coupled-resonator optical waveguides 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 nonorthogonal 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., non-Hermitian degeneracies at which not only the frequencies and decay rates but also the eigenmodes themselves coalesce. The non-Hermitian corrections to the group velocity are largest in the regions around the exceptional points.

AB - Coupled-resonator optical waveguides 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 nonorthogonal 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., non-Hermitian degeneracies at which not only the frequencies and decay rates but also the eigenmodes themselves coalesce. The non-Hermitian corrections to the group velocity are largest in the regions around the exceptional points.

U2 - 10.1103/PhysRevA.90.053819

DO - 10.1103/PhysRevA.90.053819

M3 - Journal article

VL - 90

JO - Physical review a

JF - Physical review a

SN - 1050-2947

IS - 5

M1 - 053819

ER -