Guided–wave modes in graded–index optical fibers by two–point quasi–rational approximants
E. Castro*, P. Martín, J. Puerta, and C. Cereceda
Departamento de Física, Universidad Simón Bolívar, Apartado 89000, Caracas 1080A, Venezuela,
*e–mail: ecastro@usb.ve
Recibido el 8 de marzo de 2005 ]]> Aceptado el 7 de febrero de 2006
Abstract
Approximated analytic solutions for wave propagation in graded–index optical fiber have been found in the case of a parabolic profile. Approximants with high accuracy are presented that are much better than those found by other authors. A two–point quasi–rational method and two–point Pade approximants are used in this work. The approximants are explicitly determined for the azimuthal eigenvalues l = 0,1,2 and the mth mode numbers m = 0,1, 2, 3.
Keywords: Two–point quasi–rational approximants; graded–index fibres; waveguide propagation and eigenmode analysis.
Resumen
En el presente trabajo, se obtuvieron soluciones analíticas aproximadas para la propagación de ondas en fibras ópticas con indice gradual en el caso de perfil parabólico. Los aproximantes obtenidos resultaron ser mas precisos que aquellas aproximaciones halladas previamente por otros autores. En este trabajo se usaron los aproximantes cuasi–racionales a dos puntos y los aproximantes de Padé. Se determinaron explícitamente los determinantes para los autovalores azimutales l = 0,1, 2 y los modos m = 0,1, 2,3.
Descriptores: Aproximantes cuasi–racionales a dos puntos; fibras opticas de indice graduado; propagación en guías de ondas y analisis de los modos normales.
]]> PACS: 02.30 Mv,42.81.Qb,42.81.Ht
DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgments
We would like to thank the referee for several suggestions which improved our first manuscript.
References
1. P.K. Cheo, Fiber Optics and Optoelectronics (Prentice Hall Series In Solid Physical Electronics, Second Edition, 1990) Ch. 4. [ Links ]
2. M. Young, Optics and Lasers: Including Fibers and Optical Waveguides (Springer–Verlag, Berlin Heidelberg, Fourth Revised Edition, 1993) Ch. 10. [ Links ]
3. C.C. Davis, Lasers and Electro–Optics, Fundamentals and Engineering (Cambridge University Press, 1996) Ch. 17. [ Links ]
4. W. Streifer and C.N. Kurtz, J. Opt. Soc. Am. 57 (1967) 779. [ Links ]
5. S. Kawakami and Jun–Ichi Nishizawa, IEEE Trans. Microwave Theory Tech. MIT–16 (1968) 814. [ Links ]
6. E.G. Jhonson, J. Stack and C. Koehler, J. Lightwave technol. 19 (2001) 753. [ Links ]
7. F.C. Mc Neillie, J. Thomson, and I.S. Ruddock, Eur. J. Phys. 25 (2004) 479. [ Links ]
8. J.W. Rose and S.S. Mitra, Optics Letter 6 (1981) 446. [ Links ]
9. A.H. Hartog and M.J. Adams, Opt. Quant. Elec. 9 (1977) 223. [ Links ]
10. G.A. Jr. Baker and P.R. Graves–Morris, Pade Approximants, Part I: Basic Theory (Encyclopedia of Mathematics and its Applications Vol 14) (Cambridge: Cambridge University Press, 1981). [ Links ]
11. P. Martín , G. Donoso and J. Zamudio, J. Math. Phys. 21 (1980) 280. [ Links ]
12. E. Chalbaud and P. Martín, J. Math. Phys. 25 (1984) 1268. [ Links ]
13. E. Chalbaud and P. Martín, J. Math. Phys. 27 (1986) 699. [ Links ]
14. P. Martín and L. A. Guerrero, J. Math. Phys. 26 (1985) 705. [ Links ]
15. K. Visentin and P. Martín, J. Math. Phys. 28 (1987) 330. [ Links ]
16. A.L. Guerrero and P. Martín, J. Comput. Phys. 77 (1988) 276. [ Links ]
17. P. Martín and A.L. Guerrero, J. Comput. Phys. 85 (1989) 487. [ Links ]
18. P. Martín, and G. Baker, J. Math. Phys. 32 (1991) 1470. [ Links ]
19. E. Chalbaud and P. Martín, J. Math. Phys. 33 (1992) 2483. [ Links ]
20. P. Martín, R. Perez, and L.A. Guerrero, J. Comput. Phys. 99 (1992) 337. [ Links ]
21. L. Brualla and P. Martín, J. Phys. A: Math. Gen. 34 (2001) 9153. [ Links ]
22. P. Martín and J. Puerta, Eur. J. Phys. 12 (1991) 1992. [ Links ]
23. P. Martín, J.J. Rodriguez–Nuñez, and J.L. Márquez, Phys. Rev. B 45 (1992) 8359. [ Links ]
24. E. Castro and P. Martín, J. Phys. A: Math. Gen. 33 (2000) 5321. [ Links ]
25. C.L. Ladera and P. Martín, J. Comput. Phys. 73 (1987) 481. [ Links ]
26. L.C. Ladera and P. Martín, J. Phys. A: Math. Gen. 34 (2001) 4571. [ Links ]
27. S. Nakamura, Applied Numerical Method with Software (Englewood Cliffs, N J: Prentice Hall, 1992) Ch. 9. [ Links ] ]]>