(a) Plot of with time derivation operator (TDO) formulation, against time for the first strongly guided mode of a 4-layer waveguide (Eq. (17)) for three different rates of variation of the height h of the core layer: . The other parameters are 2h _(t=0s) = 1 µm, 2e _fixed = 0.2 µm and (n ₁; n ₂; n ₃; n ₄) = (2 ; 1.8 ; 1 ;1.5) . For example, by TDO formulation, the slope at t = 3 s (or 2h = 0.4 µm) is 0.100 ≡ Δ n _eff. (b) The COMSOL simulations associated at the specific point 2h = 0.4 μm (or t = 3 s) of the previous (a) TDO formulation curves. With COMSOL, the slope is calculated by a simple rate of change Δn _eff, between two fixed structures or situations 2h = 0.4 μm (t = 3 s) and 2h = 0.2 μm (t = 4 s): Δ n _eff = 0.098.