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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 =0.4μm, with dimension 2e =0.2μm.

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)
0.048 (directly by the data of coordinate) 0.045 (=1.640 − 1.595)

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