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Fig. 3


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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).

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