Asymptotic case. (a) Plot of    in function of time (time derivation operator (TDO) formulation) for two different structures: the black curve stands for a 3-layer structure (Eq. (8)), and the red curve for a 4-layer structure (Eq. (17)) for which the height e of the first upper cladding tends to infinity. The other parameters are 2h _(t=0s) = 1 µm, , and (n ₁; n ₃; n ₄) = (2; 1.5; 1) for the 3-layer structure and (n ₁; n ₂; n ₃; n ₄) =(2; 1.5; 1; 1) for the 4-layer one. (b) Relative error between the two cases depicted in (a).