Research results

Dynamics of Topological Photonics

Curated results from NRSSH and Diamond lattice simulations, emphasizing phase structure, final-state convergence, chaotic lasing regimes, and stable topological edge behavior.

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2 Lattice families studied: NRSSH and Diamond.

4 Diamond dimerization regimes compared.

100s Gain/loss parameter combinations scanned.

v0.1.0 Packaged simulation code with tests and examples.

Lattice systems

Model Structures

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NRSSH lattice structure — **Non-reciprocal SSH lattice** A two-site unit cell with asymmetric intra-cell hopping and inter-cell coupling.

Diamond lattice structure — **Diamond lattice** A three-site unit cell where gain and loss occupy different sublattices.

Result family

NRSSH Results

The non-reciprocal SSH model reveals threshold behavior between lossy, gain-dominated, and chaotic phases when nonlinear saturation controls the onsite gain response.

NRSSH eigenenergy spectrum with isolated edge states — **Topological edge energies** Isolated edge states appear in the band gap for the NRSSH lattice.

NRSSH saturated phase diagram — **Saturated phase diagram** Convergence times map the transition from lossy behavior into gain-dominated lasing.

Unsaturated tight-binding NRSSH phase diagram — **Unsaturated limit** Without saturation, gain-dominated regions become unstable rather than settling.

NRSSH chaotic final-state intensity evolution — **Chaotic final moments** Selected chaotic points show irregular intensity evolution and sensitivity to initial conditions.

Result family

Diamond Results

Diamond lattices show richer gain/loss structure because gain is localized on A sites while B and C sites carry loss, producing nonlinear phase boundaries and stable edge-mode regimes.

Diamond lattice eigenenergy spectrum — **Hybridized eigenstates** Diamond bands host localized hybrid states near zero onsite energy.

Diamond equal hopping phase diagram — **Equal hopping baseline** Trivial hopping produces nonlinear phase boundaries due to asymmetric gain/loss placement.

Diamond facing dimerization phase diagram — **Facing dimerization** Stable topological phases emerge with longer convergence times and critical behavior.

Stable edge mode Final-state intensities localize at the edge and decay into the bulk.

Interpretation

Key Findings

The simulations connect phase diagrams to physical laser behavior: stable emission, loss-dominated decay, chaotic lasing, and topologically protected edge localization.

Thresholds are geometry-dependent

NRSSH thresholds follow the saturation-controlled gain/loss balance, while Diamond lattices bend the transition curve because gain and loss occupy different sublattices.

Saturation controls stability

Unsaturated gain produces runaway intensities; saturated gain can produce stable final states or chaotic oscillation depending on hopping.

Facing dimerization stands out

Face-dimerized Diamond lattices support stable topological phases, longer convergence times, and visible critical transition behavior.

Documentation

Read the notes or inspect the package

The result figures, documentation pages, package metadata, and source repository remain linked from the deployed site.

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