Anti-parity-time topologically undefined state

TL;DR

This paper introduces an anti-parity-time-symmetric photonic lattice that exhibits a novel topologically undefined state with equal light distribution, offering new insights into topological photonics and potential applications in optical circuits.

Contribution

The study demonstrates the creation of a topologically undefined state in an anti-PT-symmetric lattice, expanding the understanding of topological phases in photonic systems.

Findings

Topological state appears when <.

A state with undefined winding numbers occurs at =.

Edge states are enhanced by defects in the non-trivial case but not in the undefined state.

Abstract

We constructed an anti-parity-time-symmetric photonic lattice by using perturbations. The results show the topological state will appear when the waveguide coupling constants $\kappa_1<\kappa_2$; Interestingly, a state with undefined winding numbers occurs when $\kappa_1=\kappa_2$, in which the light distributes only in the wide waveguides with equal magnitude distribution. Further studies show that the edge state will be strengthened by introducing defect for the topologically non-trivial case, while it will not affect the equal intensity transmission for the topologically undefined state. Our work provides a new way to realize the topological state and equally divided light transmission and might be applicable in optical circuits and optical interconnect.