Mathematical Approximation for Modeling the Photonic Crystal Fibers

Mashaan Attalla mahmood


In this research a mathematical approximation for modeling a PCFs is derived. The effective refractive index neff of the clad region obtained by this relation will be used to study the properties of the PCFs such as normalized frequency, effective area, group velocity dispersion and the nonlinear coefficient. All these properties are studied when the holes of the PCFs are filled with air ,or with any material like chloroform.
The merit of our mathematical approximation is that, neff can be easily and directly calculated, then the dispersion profile can be controlled by fine manipulating the (d/Λ) of circular or elliptical air holes in PCF cladding. The results show good agreement with published works. The MATLAB 2010 program is used in this study, which is the most successful program to get appropriate diagrams and results


Photonic Crystal Fibers (PCF) , dispersion , refractive index

Full Text:



- Zhao, Y.; Deng, Z.-Q.; Li, J. Photonic crystal fiber based surface plasmon resonance chemical sensors.

Sens. Actuators B Chem. 2014, 202, 557–567.

- Silva, S.; Rozia, P.; Frazoa, O. Refractive index measurement of liquids based on microstructured optical

fibers. Photonics 2014, 1, 516–529.

- J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282(5393), 1476–1478 (1998).

- P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).

- T. A. Birks, J. C. Knight, and P. S. J. Russell, Endlessly single mode photonic crystal _bre,"

Opt. Lett. 22, 961 (1997).

G. Kakarantzas, T. A. Birks, and P. S. J. Russell, “Structural long-period gratings in photonic crystal

fibers,” Opt. Lett. 27, 1013-1015 (2002).

A. Diez, T. A. Birks, W. H. Reeves, B. J. Mangan, and P. S. J. Russell, “Excitation of cladding modes in

photonic crystal fibers by flexural acoustic waves,” Opt. Lett. 25, 1499-1501 (2000).

Anshu D. Varshney and Ravindra K Sinha

"Propagation Characteristics of Photonic Crystal

Fiber: Scalar Effective Index Method & Fully

Vectorial Effective Index Method" Adv. Studies Theor. Phys., Vol. 1, no. 2 .

Chen J. S. Y., (2006), “Optical parametric amplification in photonic crystal fibers”, M.Sc. Thesis, Department of Physics, University Of Auckland.

G. P. Agrawal. Nonlinear Fiber Optics. Academic Press, 3rd edition, 2001.



  • There are currently no refbacks.

Copyright (c) 2019 Al-Mustansiriyah Journal of Science

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2018 by Al-Mustansiriyah Journal of Science
ISSN: 1814-635X (Print), ISSN: 2521-3520 (online)