Temporal derivation operator applied on the historic and school case of slab waveguides families eigenvalue equations: another method for computation of variational expressions | The European Physical Journal Applied Physics (EPJ AP)

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Table 1

Compared results of the variation of the eigenvalues Δn _eff with our variational method based on time derivation operator (TDO), that is, equation (17) and Figure 4, and COMSOL software. As an example, this opto-geometric guiding structure is chosen at fixed parameters: optical indices ( n ₁; n ₂; n ₃; n ₄) = (2; 1.8; 1; 1.5), wavelength λ = 0.8 μm and 2e _fixed = 0.2 μm, with 2h = 0.4 μm.

	TDO (Eq. (17) − Fig. 4a)	COMSOL (see Fig. 4b)
Variation of Eigenvalues Δn _eff	0.100 (directly by the data of coordinate)	0.098 (=1.903 − 1.805)

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