Square-root non-Bloch topological insulators in non-Hermitian ring resonators

Area of Science:

• Topological physics
• Non-Hermitian systems
• Photonics and optical devices

Background:

• The Su-Schrieffer-Heeger (SSH) model describes topological insulators with unique edge states.
• Non-Hermitian systems introduce gain and loss, leading to complex topological phenomena like the skin effect.
• Ring resonators offer a tunable platform for simulating complex physical models.

Purpose of the Study:

• To investigate the topological skin effect in a novel square-root topological insulator model.
• To explore the properties of non-Hermitian asymmetric coupling in a ring resonator array.
• To demonstrate the potential of ring resonators for simulating and understanding topological phenomena.

Main Methods:

• Mapping the ring resonator array to a square-root of the SSH model with non-Hermitian asymmetric coupling.
• Implementing gain and loss in the ring perimeters to create asymmetric coupling.
• Utilizing theoretical analysis with a tight-binding model and full-wave simulations.

Main Results:

• The square-root topological insulator exhibits non-Bloch features and shares phase transition points with the parent Hamiltonian.
• Band closing points differ between open and periodic chains due to the skin effect.
• Multiple topological edge modes are supported, doubling the band gaps compared to the original SSH model.

Conclusions:

• Ring resonators provide a viable platform for investigating the topological skin effect.
• The square-root topological insulator model demonstrates unique topological properties and enhanced edge mode support.
• This research opens avenues for applications in optical devices like light traps, lasers, and filters.