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Probing Band Topology Using Modulational Instability.

Daniel Leykam1,2, Ekaterina Smolina3, Aleksandra Maluckov1,4

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Modulational instability in topological photonic lattices reveals sensitivity to topological band inversions. This phenomenon can probe bulk topological invariants and generate complex wave fields.

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Area of Science:

  • Photonics
  • Topological physics
  • Nonlinear optics

Background:

  • Topological photonic lattices exhibit unique properties governed by band topology.
  • Nonlinear Bloch waves are crucial for advanced optical functionalities.
  • Modulational instability is a key phenomenon in nonlinear wave dynamics.

Purpose of the Study:

  • To investigate the modulational instability of nonlinear Bloch waves in topological photonic lattices.
  • To explore the connection between instability dynamics and topological band inversions.
  • To establish modulational instability as a tool for probing topological invariants and creating novel wave fields.

Main Methods:

  • Linear stability analysis to capture initial instability development.
  • Numerical simulations to observe long-timescale dynamics.
  • Analysis of nonlinear wave mixing and energy spreading.
  • Characterization of spontaneous wave polarization singularities.

Main Results:

  • Long-wavelength instabilities and bifurcations are sensitive to topological band inversions.
  • Nonlinear wave mixing leads to energy spreading across the entire band.
  • Spontaneous creation of wave polarization singularities is observed.
  • The band Chern number determines the nature of these singularities.

Conclusions:

  • Modulational instability serves as a sensitive probe for bulk topological invariants in photonic lattices.
  • This instability can be utilized to engineer and create topologically nontrivial wave fields.
  • The findings bridge nonlinear dynamics and topological photonics, opening new avenues for research.