Synthesis of nonuniform long-period optical gratings with a continuous refractive index profile
O.V. Kolokoltsev a,*, V.A. Svyryd b, I.F. Llamas b, and C.L. Ordóñez Romero a
a Universidad Nacional Autónoma de México (UNAM), CCADET, Apartado Postal 70-186, 04510, CD Universitaria, México, D.F.,
b UNAM, Facultad de Ingeniería, CD Universitaria, México, D.F. * Corresponding author: Oleg Kolokoltsev, e-mail: olegk@aleph.cinstrum.unam.mx Tel.: 56 22 86 02 Ext.1120, (UNAM), CCADET, Apartado Postal 70-186, 04510, CD Universitaria, México, D.F.
]]> Recibido el 11 de abril de 2005.
Abstract
In this work we present a new method for such a non-trivial problem as the synthesis of optical filters based on non-uniform Long-Period Fiber Gratings (LPGs). The method is based on a real-coded genetic algorithm (GA) with a new quasi-analytical procedure for solving the Zakharov-Shabat Inverse Problem. The method possesses an improved computational stability compared to classic numerical algorithms. The main peculiarity of the non-uniform LPG transmission gratings, compared to the Bragg gratings, is that their optical fields oscillate rapidly. However, the quasi-analytical approach proposed allows one to reduce to a minimum the number of sampling points, without, at the same time, losing accuracy in the solution, i.e. the method possesses an improved efficiency. The algorithm convergence was also improved by using the relations of the law of conservation of energy between the interacting waves. It has been shown that the algorithm works adequately even for the case of strongly over-coupled co-propagating lightwave modes, as we demonstrate in several examples of the synthesis of ultra-wide pass-band optical filters (FWHM of 100-200 nm).
Keywords: Long-period fiber gratings; synthesis; optical filters; genetic algorithm.
Resumen
En este trabajo presentamos un nuevo método para un problema no-trivial como la síntesis de filtros ópticos basados en rejillas de periodo largo (Long-Period Fiber Gratings o LPGs) no uniforme. El método esta basado en un código de algoritmo genético real (GA) con un nuevo procedimiento cuasi-analítico para la solución del problema inverso de Zakharov-Shabat. El método posee un estabilidad de computo mejorada compara con los algoritmos numéricos clásicos. La principal peculiaridad de la no uniformidad de las rejillas de transmisión LPG, comparado con las rejillas de Bragg, es que sus campos ópticos oscilan rápidamente. Sin embargo, la aproximación cuasi-analítica propuesta permite reducir al mínimo el número de puntos muestreados, pero, al mismo tiempo, no pierde la precisión en la solución, es decir, el método posee una eficiencia mejorada. La convergencia del algoritmo también fue mejorada usando las relaciones de la ley de conservación de la energía entre las ondas que interactúan. Esto ha mostrado que el algoritmo trabaja adecuadamente aun para los casos de modos de ondas luminosas de más fuerte co-propagación sobre acoplada, como se demuestra en varios ejemplos en la síntesis de filtros de banda de paso óptica ultra-ancha (FWHM de 100-200nm).
Descriptores: Rejillas en fibras de periodo largo; síntesis; filtros ópticos; algoritmo genético.
]]>PACS: 42.81.Qb
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References
1. Proceedings of VII Europ.Conf. on Integrated Optics. Netherlands, Delft. Apr. 3-6, (1995). [ Links ]
2. F. Casagrande et al., Applied Optics 41 (2002) 5238. [ Links ]
]]>3. Turan Erdoran, Journal of Light-wave Technology 15 (1997) 1277. [ Links ]
4. H. Ke, K.S. Chiang, and J.H. Peng, IEEE, Photonics Technology Letters. 10 (1998) 1596. [ Links ]
5. Qing Lui, Kin Seng Chiang, and Vipul Rastogi, IEEE, Journalof Light-wave Technology 21 (2003) 3399. [ Links ]
6. Gia-Wei Chern and L.A. Wang, J. Opt. Soc. Am. A 19 (2002) 772. [ Links ]
7. J.R. Qian and H.F. Chen, Electron Lett. 34 (1998) 1132. [ Links ]
]]>8. A.M. Vengsarka et al., Opt. Lett. 21 (1996) 336. [ Links ]
9. C.K. Madsen and J.H. Zhao, J. Wiley New York (1999). [ Links ]
10. K.A. Winick and J.E. Roman, IEEE QE 26 11. (1990) 1918. [ Links ]
11 . G.L. Lamb, Elements of Soliton Theory (New York: Willey, 1980). [ Links ]
12. V.E. Zakharov and A.B. Shabat, Sov. Phys. JETP. 34 (1972) 62. [ Links ]
]]>13. G.H. Song and S.Y. Shin, J. Opt. Soc. Am. 2 (1995) 1905. [ Links ]
14. C. Papachristos and P. Frangos, J. Opt. Soc. Am. A 19 (2002) 1005. [ Links ]
15. I. Kay, Comm. Pure Appl. Math. 13 (1960) 371. [ Links ]
16 . P.V. Frangos and D.L. Jaggard, IEEE, Trans. On Antennas and Propagation 40 (1992) 399. [ Links ]
17. E. Peral, J. Capmany, and J. Marti, IEEEJ. of QE 32 12. (1996) 2078. [ Links ]
]]>18. R. Feced, M.N. Zervas, and M.A. Muriel, IEEEJ. of QE 35 8 (1999) 1105. [ Links ]
19. R. Feced and M.N. Zervas, J. Opt. Soc. Am. (A) 17 (2000) 1573. [ Links ]
20. L. Poladian, Opt. Lett. 25 (2000) 787. [ Links ]
21. J. Skaar, L. Wang, and T. Erdogan, IEEEJ. of QE 37 (2001) 165. [ Links ]
22. J. Skaar and Knut Magne Risvik, J. of Lightwave Technology 16 (1998) 1928. [ Links ]
]]>23. G. Gormier and R. Boudreau, J. Opt. Soc. Am. B 18 (2001) 1771. [ Links ]
24. T. Bëck and H.P. Schefel, "Evolutionary Computation: An Overview", in Proc. IEEE International Conference on Evolutionary Computation (1996) 20. [ Links ]
25. O.V. Kolokoltsev, C. Sánchez Pérez, and R. Amezcua Correa, IEEEJ. of Selected Topics in Quantum Electronics 8 (2002) 1258. [ Links ]
26. A. Yariv, IEEEJ. of Quantum Electronics 9 (1973) 919. [ Links ]
27. H. Kogelnik, "Theory of Optical Waveguides", in Guided-Wave Optoelectronics, T. Tamir (Ed. New York: Springer-Verlag, 1990). [ Links ]
]]>