A Hamiltonian formulation for coupled-wave equations

We construct a Hamiltonian formulation for coupled-wave equations that describes the envelope functions of the electric field in an almost-periodic distributed-feedback waveguide with gain or loss. From the Hamiltonian, we can derive that the determinant of the fundamental matrix of the waveguide is always unity. A perturbation formula for the eigenvalues of the coupled-wave equations is simply derived using the Hamiltonian formulation. The Hamiltonian also provides the basis for the numerical calculation of the eigenvalues using the variational method