(a) Plot of with time derivation operator (TDO) formulation, against time for (a) the first strongly guided mode and (b) the first weakly guided mode of a 4-layer structure in case of variation of the height e of the first upper cladding (Eq. (23)) and for different sets of indices (n ₁; n ₂; n ₃; n ₄) = (2; 1.5; 1; 1) ; (2; 1.8; 1; 1.5); (2; 1.8; 1.5; 1.5). The other parameters are 2h _fixed = 0.4 µm, 2e _(t=0s) = 1 µm, and   For example, by TDO formulation, the slope at t = 4 s (or 2e = 0.2 µm) is respectively Δ n _eff ≡ 0.007 and 0.048 for both cones of light. (c) and (d) Represent the COMSOL simulations associated at the specific point of the previous (a) and (b) TDO formulation curves. With COMSOL, the slope is calculated by a simple rate of change Δn _eff, between two fixed structures or situations 2e = 0.2 μm (t = 4 s) and 2e = 0.1 μm (t = 4.5 s): Δ n _eff  = 0.007 and 0.045 respectively for both cones of light.