Abstract
To study the propagation of guided modes in an optical fiber under weak guidance assumptions, we usually use a scalar approximation of the Maxwell’s system which generally leads to the Helmholtz equations. Most of works in the literature treat optical fibers where the refractive index is constant in the core. In this work, we give more detailed calculations and expend the study to the case where the index of refraction is variable in the core of the fiber. The technique of calculation we propose is based on a formal asymptotic expansion that allows us to derive the equation and the transmission conditions of the scalar eigenvalue problem from Maxwell’s equations in the vectorial case. In the case where the refractive index is variable, which is the main contribution of this work, we carry out asymptotic expansions of lower order and higher order leading to a scalar eigenvalue problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bonnet, A.S., Gmati, N.: Spectral approximation of a boundary condition for an eigenvalue problem. SIAM J. Numer. Anal. 32(4), 1263–1279 (1995)
Choutri, A.: Etude mathématique et numérique des caractéristiques de la propagation des ondes guidées dans les fibres optiques. Thèse de doctorat en Mathématiques, USTHB, Alger (2012)
Choutri, A.: Etude de l’erreur de troncature du domaine pour un problème aux valeurs propres. C. R. Académie des Sci. 3, 231–235 (2008)
Choutri, A., Boureghda, A.: A numerical integral method for compute the guided modes in an optical half coupler in the scalar case. Rev. Roum. Math. Pures Appl. 54(4), 287–295 (2009)
Cao, Q., Chi, S.: Approximate analytical description for fundamental-mode fields of graded-index fibers: beyond the Gaussian approximation. J. Lightwave Technol. 19(1), 54–59 (2001)
Djellouli, R.: Contribution à l’analyse mathématique et au calcul numérique des modes guidés dans les fibres optiques. Thèse de Doctorat es Science. Université Paris Sud, Centre d’Orsay (1988)
Djellouli, R., Bekkey, C., Choutri, A., Rezgui, H.: A local boundary condition coupled to a finite element method to compute guided modes of optical fibers under weak guidance assumptions. Math. Methods Appl. Sci. 23, 1551–1583 (2000)
Ghatak, A., Thyagarajan, K.: Graded-index optical waveguides: a review. Prog. Opt. 18, 1–126 (1980)
Ikuno, H.: Vectorial wave analysis of graded-index fibers. Radio Sci. 17(1), 37–42 (1982)
Ikuno, H.: Asymptotic eigenvalues of vector wave equation for guided modes in graded-index fibre. Electron. Lett. 17(1), 8–9 (1981)
Ikuno, H.: Propagation constants of guided modes in graded-index fibre with polynomial-profile core. Electron. Lett. 15(23), 762–763 (1979)
Kawano, K., Kitoh, T.: Introduction to Optical Waveguide Analysis. Wiley-Interscience, Hoboken (2001)
Khijwania, S.K., Nair, V.M., Sarkar, S.: Propagation characteristics of single-mode graded-index elliptical core linear and nonlinear fiber using super-Gaussian approximation. Appl. Opt. 48(31), G156–G162 (2009)
Koshiba, M.: Optical Waveguide Theory By the Finite Element Method. Springer, Dordrecht (2012)
Marcuse, D.: Theory of Dielectric Optical Waveguides. Academic Press, New York (1974)
Mitschke, F.: Fiber Optics, Physics and Technology, 2nd edn. Springer, Berlin (2016)
Okamoto, K.: Fundamentals of Optical Waveguides, 2nd edn. Academic Press (Elsevier), Cambridge (2006)
Pocholle J.P., Caractéristiques de la propagation guidée dans les fibres optiques monomodes, Revue technique Tomson-CSF, Vol. 15, No. 4, Décembre (1983)
Patraa, P., Gangopadhyayb, S., Goswami, K.: A simple method for prediction of first-order modal field and cladding decay parameter in graded-index fiber. Elsevier Optik 119(5), 209–212 (2008)
Rezgui, H., Choutri, A.: An inverse eigenvalue problem. Application: graded-index optical fibers. Opt Quant Electron 49(10), 1–34 (2017)
Snyder, A.W., Love, J.D.: Optical Waveguide Theory. Chapman and Hall, London (1983)
Vassalo, C.: Optical Waveguide Concepts. Elsevier, Amsterdam (1991)
Vassalo, C.: Théorie des guides d’ondes électromagnétiques, Tomes 1 & 2. Edition Eyrolles et CNET-ENST, Paris (1985)
Yeh, C., Shimabukuro, F.I.: The Essence of Dielectric Waveguides. Springer, New York (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choutri, A., Boureghda, A. An asymptotic expansion approach for variable refractive index optical fibers (in weak guidance case). Opt Quant Electron 50, 74 (2018). https://doi.org/10.1007/s11082-017-1312-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-017-1312-0