Topological Phenomena in Classical Optical Networks

Abstract

We propose a scheme to realize a topological insulator with optical-passive elements, and analyze the effects of Kerr-nonlinearities in its topological behavior. In the linear regime, our design gives rise to an optical spectrum with topological features and where the bandwidths and bandgaps are dramatically broadened. The resulting edge modes cover a very wide frequency range. We relate this behavior to the fact that the effective Hamiltonian describing the system's amplitudes is long-range. We also develop a method to analyze the scheme in the presence of a Kerr medium. We assess robustness and stability of the topological features, and predict the presence of chiral squeezed fluctuations at the edges in some parameter regimes.

18 pages, 9 figures

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• Tutorial: Computing topological invariants in two-dimensional photonic crystals
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• Active topolectrical circuits
• Nonlinear one-way edge-mode interactions for frequency mixing in topological photonic crystals
• Photonic Anomalous Quantum Hall Effect
• Two-Dimensional Photonic Crystals for Engineering Atom-Light Interactions
• Stability of topological edge states under strong nonlinear effects
• Topology-Enhanced Nonreciprocal Scattering and Photon Absorption in a Waveguide
• Topological edge states for disordered bosonic systems
• Fractional Quantum Zeno Effect Emerging from Non-Hermitian Physics
• Edge Solitons in a Nonlinear Mechanical Topological Insulator
• Nonlinear compact localized modes in flux-dressed octagonal-diamond photonic lattice