Comparison of Fundamental Space-Filling Mode Index, Effective Index and the Second and Third Order Dispersions of Photonic Crystals Fibers Calculated by Scalar Effective Index Method and Empirical Relations Methods
To design less costly and time consuming Photonic Crystal Fibers it is better to use Empirical Relations Method instead of Scalar Effective Index Method. If we compare both empirical relations method and scalar effective index method by accurate and powerful methods like Full-Vector Finite Element Method, we find that empirical relations method has less error than scalar effective index method in calculating PCF parameters such as nfsm, neff , and the second order dispersion. According to the investigations, we concluded, the inherent error of scalar effective index method approximately increases when pitch decreases. In large pitches the calculation of dispersion by scalar effective index method reveals less error in low wavelengths than high wavelengths and finally we calculated the third order dispersion which is important in some applications.
Ali PourkazemiMojtaba Mansourabadi
, "Comparison of Fundamental Space-Filling Mode Index, Effective Index and the Second and Third Order Dispersions of Photonic Crystals Fibers Calculated by Scalar Effective Index Method and Empirical Relations Methods," Progress In Electromagnetics Research M,
Vol. 1, 197-206, 2008. doi:10.2528/PIERM08021805 http://www.jpier.org/PIERM/pier.php?paper=08021805
1. Andalib, A., A. Rostami, and N. Granpayeh, "Analytical investigation and evaluation of pulse broadening factor propagating through nonlinear optical fibers (traditional and optimum dispersion compensated fibers)," Progress In Electromagnetics Research, Vol. 79, 119-136, 2008. doi:10.2528/PIER07092502
2. Guenneu, S., A. Nicolet, F. Zolla, and S. Lasquellec, "Numerical and theoretical study of photonic crystal fibers," Progress In Electromagnetics Research, Vol. 41, 271-305, 2003.
3. Kumar, D., P. K. Choudhury, and O. N. Singh II, "Towards the dispersion relations for dielectric optical fibers with helical windings under slow- and fast-wave considerations — A comparative analysis," Progress In Electromagnetics Research, Vol. 80, 409-420, 2008. doi:10.2528/PIER07120302
4. Saitoh, K. and M. Koshiba, "Empirical relations for simple design of photonic crystal fibers," Optical Society of America, Vol. 13, No. 1, 267-274, 2005.
5. Kim, J. I., Analysis and applications of microstructure and Holey optical fibers, Blacksburg, Virginia, Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University , September 10, 2003.
6. Li, Y., C. Wang, and M. Hu, "A fully vectorial effective index method for photonic crystal fibers: Application to dispersion calculation ," Optics Communications, Vol. 238, 29-33, 2004. doi:10.1016/j.optcom.2004.04.040
7. Li, Y., C. Wang, Y. Chen, M. Hu, B. Liu, and L. Chai, "Solution of the fundamental space-filling mode of photonic crystal fibers: numerical method versus analytical approaches," Applied Physics B, Vol. 85, 597-601, 2006. doi:10.1007/s00340-006-2246-6
8. Sinha, R. K. and S. K. Varshney, "Dispersion properties of photonic crystal fibers," Microwave and Optical Technology Letters, Vol. 37, No. 2, 129-132, 2003. doi:10.1002/mop.10845
9. Rostami, A. and A. Andalib, "A principal investigation of the group velocity dispersion (GVD) profile for optimum dispersion compensation in optical fibers: A theoretical study ," Progress In Electromagnetics Research, Vol. 75, 209-224, 2007. doi:10.2528/PIER07060402
10. Panajotovic, A., D. Milovic, and A. Biswas, "Influence of even order dispersion on soliton transmission quality with coherent intereference ," Progress In Electromagnetics Research B, Vol. 3, 63-72, 2008. doi:10.2528/PIERB07120404
11. Benson, T. M. and P. C. Kendall, "Variational techniques including effective and weighted index methods ," Progress In Electromagnetics Research, Vol. 10, 1-40, 1995.
12. Zhu, Z. M. and T. Brown, "Analysis of the space filling modes of photonic crystal fibers," Optics Express, Vol. 8, No. 10, 547-554, 2001.
13. Bjarklev, A., J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres, Kluwer Academic, Boston, 2003.
14. Birks, T. A., J. C. Knight, and P. S. J. Russell, "Endlessly singlemode crystal fiber," Optical Letters, Vol. 22, No. 13, 961-963, 1997. doi:10.1364/OL.22.000961
15. Husakou, A. V. and J. Herrmann, "Supercontinuum generation of higher order solitons by fission in photonic crystal fibers," Phys. Rev. Lett., Vol. 34, No. 10, 1064-1076, 2001.
16. Koshiba M. and K. Saitoh, "Applicability of classical optical fiber theories to holey fibers," Optics Letters, Vol. 29, No. 10, 1739-1741, 2004. doi:10.1364/OL.29.001739
17. Koshiba, M. and K. Saitoh, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron, Vol. 38, 927-933, 2002.