LLE-512 · KERR MICROCOMB BENCH

LUGIATO–LEFEVER · SPLIT-STEP ψ(θ,τ) · 512 MODES
BOOTING
∂ψ/∂τ = −(1 + iζ)ψ + id₂ ∂²ψ/∂θ² + i|ψ|²ψ + f τ = 0  ·  ⟨|ψ|²⟩ = 0  ·  ζ_max = π²f²/8 =
INTRACAVITY |ψ(θ)|²pk –
COMB SPECTRUM · dB vs μ
SPACE–TIME θ × τnewest ↓
⟨|ψ|²⟩ vs ζ · BISTABILITY + SCAN TRACE
FIELD GUIDE — WHAT AM I LOOKING AT

LASER SCAN ▷ replays the classic experiment: tune the pump from blue to red across the resonance. You'll see primary Turing rolls (MI picks μ ≈ √((2⟨|ψ|²⟩ − ζ)/d₂)), then chaotic MI, then the intracavity power collapses onto discrete soliton steps — count the survivors on the LED. The trace lands on the lower branch of the gray bistability curve, riding it until ζ_max = π²f²/8 (dashed line), where solitons decay. No thermal nonlinearity in here, so backward tuning is free — drag ζ down and the solitons just follow.

Spectrum: stationary solitons → smooth sech²-ish comb; breathers → comb lines pulsing; chaos → grass. Waterfall: tilted stripes mean drifting structures, vertical stripes mean trapped ones, pulsing blobs are breathers. The dashed line on the right screen is the homogeneous (cw) solution ρ(1 + (ζ − ρ)²) = f²; MI lives above |ψ|² = 1.