The Network — CROW, Polariton Hopping and the Spectral Relay Mesh

Act 12 of the NexusOS physics sequence. First disclosed 2026-07-19. AGPL-3.0. Founder: Te Rata Pou.

Coupled Resonator Optical Waveguides (CROW)

Yariv et al. (1999) showed that a chain of identical high-Q resonators, coupled through evanescent-field overlap, forms a photonic waveguide. The photon hops — one cavity at a time — through quantum-mechanical tunnelling. The Hamiltonian is: H = Σᵢ ω₀ aᵢ†aᵢ − J Σᵢ (aᵢ†aᵢ₊₁ + h.c.).

Tight-Binding Dispersion

ω(k) = ω₀ − 2J·cos(k·a), where ω₀ is the single-cavity resonance, J is the photon hopping rate, a is the cavity spacing, and k ∈ (−π/a, π/a] is the Bloch wavevector. Group velocity: v_g = 2Ja·sin(ka). Bandwidth: W = 4J.

Slow Light

At the Brillouin zone edges (ka → 0, ±π), v_g → 0 and the group delay τ_g = N·a/v_g → ∞. Notomi et al. (2001) measured slow-light factors S > 90 in photonic crystal CROW structures.

Bose-Hubbard Model

With on-site photon-photon repulsion U: H = −J Σ aᵢ†aᵢ₊₁ + U/2 Σ nᵢ(nᵢ−1) − μ Σ nᵢ. Superfluid (J≫U, delocalized photons) vs Mott insulator (U≫J, one photon per cavity) quantum phase transition. Predicted by Greentree et al. and Hartmann et al. simultaneously in 2006.

WNSP Connection

Each pair of adjacent Ψ channels with overlapping evanescent fields forms a CROW unit. N coupled Ψ channels form an SRM segment. CROW → SRM design map: single resonator = Ψ channel (1 of 51,200); CROW chain = SRM segment; hopping J = inter-channel coupling κ_hop; band edge = buffer zone for temporal storage.