J. D. Colladon, C.R. Acad. Sci, vol.15, p.800, 1842.

J. Hecht, City of Light: The Story of Fiber Optics, 1999.

M. J. Adams, Introduction to Optical Waveguides, 1981.

A. W. Snyder and J. D. Love, Optical Waveguide Theory, 2000.

A. Yariv, Quantum Electronics, 1957.

T. Tamir, Guided-Wave Optoelectronics, 1990.

D. Marcuse, Theory of Dielectric Optical Waveguides, 1974.

D. Marcuse, IEEE J. Quant. Electron, vol.28, p.459, 1992.

R. L. Gallawa, I. C. Goyal, Y. Tu, and K. Gharak, IEEE J. Quant. Electron, vol.27, p.518, 1991.

P. N. Robson and P. C. Kendall, Rib Waveguide Theory by the Spectral Index Method Research, 1990.

E. A. Marcatili, Bell Syst. Techn. J, vol.48, p.2071, 1969.

T. Begou, B. Bêche, N. Grossard, J. Zyss, A. Goullet et al., J. Opt. A: Pure Appl. Opt, vol.10, issue.1, 2008.

M. Koshiba, K. Hayata, and M. Suzuki, Electron. Lett, vol.18, p.411, 1982.

B. Bêche, J. F. Jouin, N. Grossard, E. Gaviot, and J. Zyss, Sens. Actuators Phys. A, vol.114, p.59, 2004.

P. Yeh, A. Yariv, and C. Hong, J. Opt. Soc. Am, vol.67, p.423, 1977.

K. H. Schlereth and M. Tacke, IEEE J. Quant. Electron, vol.26, p.627, 1990.

M. Heiblum and J. Harris, IEEE J. Quantum Electron, vol.11, p.75, 1975.

L. Garnier, C. Saavedra, R. Castro-beltran, M. J. Lucio, E. Gaviot et al., Optik, vol.142, p.536, 2017.

B. Bêche, E. Gaviot, A. Renault, J. Zyss, and F. Artzner, distribution, and reproduction in any medium, provided the original author(s) and source are credited, Optik, vol.121, 2010.

L. Garnier, A. Doliveira, F. Mahé, E. Gaviot, and B. Bêche, Temporal derivation operator applied on the historic and school case of slab waveguides families eigenvalue equations: another method for computation of variational expressions, Eur. Phys. J. Appl. Phys, vol.87, p.10501, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02183526

, Compared results of the variation of the eigenvalues Dn eff with our variational method based on time derivation operator (TDO), that is equation (23) and Figures 5a and 5b, and COMSOL software

. Tdo-(eq, 23) À Figs. 5a and 5b) COMSOL (see Figs. 5c and 5d)

L. Garnier, Eur. Phys. J. Appl. Phys, vol.87, p.9, 2019.