LED and Laser Rate Equations L1-494

Semiconductor PhysicsOptoelectronic devicesδ=3 · standardL_DAG = 3.3📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

d N / d t = I / (q V) - (A \cdot N + B \cdot N^{2} + C \cdot N^{3}) - v_{g} \cdot g (N) \cdot S; d S / d t = G amma \cdot v_{g} \cdot g (N) \cdot S + G amma \cdot b e t a \cdot B \cdot N^{2} - S / t a u_{p}

Coupled rate equations for carrier density N and photon density S: injection, spontaneous & stimulated recombination, photon generation and cavity loss; stimulated emission above threshold.

L-DAG

E.carrier_rate -> E.photon_rate -> D.time.implicit -> O.LI_modulation

E.carrier_rateE.photon_rateD.time.implicitO.LI_modulation

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 100

Well-posed for typical semiconductor lasers; threshold bifurcation well-resolved; multi-mode regimes need spatial extension.

Solvability C

Solver class:: Stiff ODE (BDF); inversion by LM fit or Bayesian MCMC
Convergence rate q:: 2
Complexity:: O(N_time)

Specs (0)

No L2 specs registered yet for this principle.