FWM gain matrix eigenvalue bound via Gershgorin discs: |lambda| <= |delta|+|g|

Layer 1 — Physicsin the nonlinear-photonics subtree

Four-wave-mixing gain matrix and Gershgorin eigenvalue bound. Setup: degenerate FWM in a Kerr fiber produces signal (omega_p + Omega) and idler (omega_p - Omega) sidebands coupled via chi^(3). In the phase-space basis (A_s, A_i^*), the…

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Gershgorin circle theorem
FWM matrix eigenvalues: lambda = +-sqrt(delta^2+|g|^2); Gershgorin bound |lambda|<=|delta|+|g|
FWM (Stolen 1974)

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