Strong Interactions in Multimode Random Lasers: Supporting Online Material
نویسندگان
چکیده
Derivation of the self-consistent multimode laser equations. The Green function which forms the kernel of the fundamental self-consistent equation Eq. 1 has a non-hermitian spectral representation of the form (S1) G(x, x ′ ; k) = ∞ m=1 ϕ m (x, k) ¯ ϕ * m (x ′ , k) 2 k a (k − k m (k)). (S1) where the CF states ϕ m (x, k) satisfy the equation − 1 ǫ(x) ∇ 2 ϕ m (x, k) = k 2 m (k) ϕ m (x, k) (S2) with the boundary condition that outside the gain region there are only outgoing waves with wavevector k. The biorthogonal partners ¯ ϕ m (x, k) satisfy the complex conjugate equation with incoming wave boundary conditions, hence ¯ ϕ m (x, k) = (ǫ(x)ϕ m (x, k)) *. The biorthogonality 1
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