The translation matrix formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional periodic stratified structure. This modal approach allows us to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to second-harmonic generation in the undepleted pump regime. © 2004 The American Physical Society.
Cherchi, M. (2004). Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 69(6), 8. https://doi.org/10.1103/PhysRevE.69.066602