Topological Photonic Lattice

Topological Photonics

Propagation speed 1.0×

Defect strength 1.0×

Chern number ν

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Edge transmission

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Bulk transmission

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Backscatter events

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How it works

Each site of the honeycomb lattice is a coupled optical resonator or waveguide; light hopping between neighbours plays the role of an electron hopping between atoms in a real topological insulator. The lattice's band structure carries a topological invariant, the Chern number ν, computed from the Berry curvature Ω(k) of the occupied band over the Brillouin zone:

ν = (1/2π) ∬_BZ Ω(k) d²k

Bulk–boundary correspondence guarantees that whenever ν changes across an interface — here, the lattice edge against vacuum — exactly |Δν| protected one-way edge modes must exist there, propagating without any state to backscatter into. That is why the amber beam glides past the red defect on the boundary almost undisturbed: it has nowhere to reflect to.

Phase toggle — flips the lattice between a topological (ν=1) and a trivial (ν=0) phase by reversing the sign of the effective coupling. In the trivial phase the protected edge mode disappears, so the same "edge" beam now backscatters off the defect exactly like the bulk wave.
Bulk wave — shows or hides a second beam launched straight through the interior of the lattice, which has no topological protection and Rayleigh-scatters off any defect it meets.
Propagation speed — how fast both beams advance along their paths.
Defect strength — size of the red obstacle site; a bigger defect deflects the bulk beam harder, but barely touches the topological edge beam's transmission.

Real-world relevance: this one-way, defect-immune channel is exactly what photonic-topological-insulator devices exploit for robust delay lines, isolators and low-loss on-chip interconnects that keep working despite fabrication disorder.

Edge state (protected) Bulk wave (unprotected) Defect / impurity site Bulk lattice site

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