Topological Floquet bound states in the continuum

Area of Science:

• Photonics
• Condensed Matter Physics
• Waveguide Optics

Background:

• Bound states in the continuum (BICs) are unique wave phenomena with potential applications in optics and photonics.
• Topological edge states offer enhanced robustness and localization properties.
• Honeycomb photonic structures provide a versatile platform for exploring exotic wave phenomena.

Purpose of the Study:

• To investigate the existence and properties of Floquet bound states in the continuum (BICs) in a honeycomb array of helical waveguides.
• To explore the role of refractive index gradient and edge geometry in supporting and localizing these states.
• To examine the robustness of topological edge states against defects.

Main Methods:

• Theoretical analysis of a honeycomb array of helical waveguides with zigzag-zigzag edges.
• Introduction of a refractive index gradient orthogonal to the waveguide edges.
• Analysis of the Floquet-Bloch spectrum and band structure.
• Investigation of state localization and defect robustness.

Main Results:

• A refractive index gradient induces strong asymmetry in the Floquet-Bloch spectrum, enabling the formation of Floquet BICs.
• The spectrum splits into bulk and edge states, with topological edge states exhibiting significantly stronger localization.
• Localized Wannier-Stark-like bulk modes coexist with the localized Floquet BICs.
• Edge Floquet states demonstrate robustness by passing through a missing waveguide defect.

Conclusions:

• Honeycomb waveguide arrays with refractive index gradients can support strongly localized topological edge states, a form of Floquet BICs.
• These engineered Floquet BICs exhibit remarkable robustness against structural defects.
• The findings open avenues for novel photonic devices with enhanced wave localization and transport properties.