Analytical Modal Solutions on Optical Inhomogeneous Fibers: the Frobenius-Taylor Method (FTM)

Authors

  • Isabel Ventim Neves CTS Universidade Nova de Lisboa
  • Manuel Guerreiro Neves

Keywords:

Inhomogeneous Optical Fibers, Modal Solutions, Dispersion, FTM

Abstract

Analytical solutions for wave propagation in a general inhomogeneous optical fiber profile are built using serial expansions about regular points of differential equations for radial variation of field components, called as Frobenius’ and Taylor’s, whose coefficients are evaluated recursively. Using both types of series expansion, a general and fast convergent algorithm for computing modal characteristics is presented: the Frobenius-Taylor Method (FTM), together with a set of alternative functions to the second-kind Bessel ones (used in the cladding), closely related but numerically more stables. The complete algorithm is presented and can be applied to both high and low values of the index difference, showing a fast convergence for frequencies just over, very near and far from cutoff.

 

Author Biography

Isabel Ventim Neves, CTS Universidade Nova de Lisboa

Professor

Department of Electrical Engineering

Faculty of Science and Technogy

Universidade Nova de Lisboa

References

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A.W. Snyder and J.D. Love, Optical Waveguides Theory, Chapman and Hall, London, 1983.

I.V. Neves and A.S.C. Fernandes, “Wave Propagation in a Radially Inhomogeneous Cylindrical Dielectric Structure:

A General Analytical Solutionâ€, Microwave Opt Technol Lett 5 (1992), 675-679.

C. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, Intern.

Series in Pure and Appl. Mathem., 1978.

Abramowitz and Stegun (ed.), Handbook of Mathematical Functions, Dover Publications, 1972.

I.V. Neves and A.S.C. Fernandes, “Modal Characteristics for A-Type and V-Type Dielectric Profile Fibersâ€,

Microwave Opt Technol Lett 16 (1997), 164-169.

I.V. Neves and A.S.C. Fernandes, “Modal Characteristics for W-Type and M-Type Dielectric Profile Fibersâ€,

Microwave Opt Technol Lett 22 (1999), 398-405.

I.V. Neves and A.S.C. Fernandes, “Modal Characteristics for Extended W-Type and M-Type Optical Fiber Profilesâ€,

Microwave Opt Technol Lett, 24 (2000), 112-117.

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Published

2014-04-14

How to Cite

Neves, I. V., & Neves, M. G. (2014). Analytical Modal Solutions on Optical Inhomogeneous Fibers: the Frobenius-Taylor Method (FTM). Asian Journal of Fuzzy and Applied Mathematics, 2(2). Retrieved from https://ajouronline.com/index.php/AJFAM/article/view/960

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