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 2

Compared results of the variation of the eigenvalues Δn _eff with our variational method based on time derivation operator (TDO), that is equation (23) and Figures 5a and 5b, and COMSOL software. As an example, the 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 2h _fixed = 0.4 μm, with dimension 2e = 0.2 μm.

	TDO (Eq. (23) − Figs. 5a and 5b)	COMSOL (see Figs. 5c and 5d)
Variation of Eigenvalues Δn _eff	0.007 (directly by the data of coordinate)	0.007 (=1.903 − 1.896)
Variation of Eigenvalues Δn _eff	0.048 (directly by the data of coordinate)	0.045 (=1.640 − 1.595)

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