Interface States in Space-Time Photonic Crystals: Topological Origin, Propagation, and Amplification

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Spacetime Physics

Background:

• Characterizing topology in spatiotemporal media is challenging due to broken symmetries.
• Traveling-wave modulations in crystals can break or preserve symmetries, impacting their topological properties.

Purpose of the Study:

• To demonstrate persistent space-time symmetries in traveling-wave modulated crystals.
• To enable topological characterization and predict spatiotemporal interface states.
• To provide a unified framework for understanding topological properties in various modulation regimes.

Main Methods:

• Utilized Lorentz transformations to simplify spatiotemporal modulation analysis.
• Identified conserved joint parity-time-reversal symmetry in transformed variables.
• Quantized a spatiotemporal Zak phase to establish a Z2 topological invariant.

Main Results:

• Discovered that space-time symmetries persist in both subluminal and superluminal modulated crystals.
• Predicted unique spatiotemporal interface states with selective directional amplification.
• Observed frequency- and momentum-converted replicas and broadband amplification without momentum gaps.

Conclusions:

• The developed framework unifies the topological description of spatiotemporal media, including photonic time crystals.
• The findings clarify the topological origin of exotic phenomena in modulated systems.
• This work opens new avenues for exploring topological physics in time-varying materials.