A Comparative Study of Multipole and Empirical Relations Methods for Effective Index and Dispersion Calculations of Silica-Based Photonic Crystal Fibers

Document Type : Research Paper

Authors

1 Department of Electrical Engineering,Faculty of engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Iran University of Science and Technology, Faculty of Electrical and Electronics Engineering, Tehran, Iran.

3 Department of Electrical Engineering, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.

Abstract

In this paper, we present a solid-core Silica-based photonic crystal fiber (PCF) composed of hexagonal lattice of air-holes and calculate the effective index and chromatic dispersion of PCF for different physical parameters using the empirical relations method (ERM). These results are compared with the data obtained from the conventional multipole method (MPM). Our simulation results reveal that the ERM is an accurate and fast method for dispersion analysis of PCFs with large pitch sizes. However, for small pitch sizes of PCFs, it is not as accurate as the MPM method. Therefore, ERM is a fast, simple and accurate method for modelling and analysis of Silica-based PCFs with large pitch sizes.

Keywords


[1]     A. Zahedi, F. Parandin, M. M. Karkhanehchi, H. Habibi Shams, and S. Rajamand “Design and Simulation of Optical 4-Channel Demultiplexer Using Photonic Crystals,” Journal of Optical Communications, vol.2, no.5, pp. 22-25, May 2013.
[2]     M. M. Karkhanehchi, F. Parandin, A. Zahedi, “Design of an all optical half-adder based on 2D photonic crystals,”  Photonic Network Communications, vol. 33, no. 2, pp. 159-165, April 2017.
[3]     F. Parandin, R. Malmir, M. Naseri, and A. Zahedi, "Reconfigurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals," Superlattices Microstruct., vol.113, no. 2018, pp. 737-744 , January 2018.
[4]     F. Parandin, M. Mehdi Karkhanehchi, M. Naseri, and A. Zahedi, "Design of a high bitrate optical decoder based on photonic crystals," Journal of Computational Electronics, vol. 17, no. 2, pp.830-836, March 2018.     
[5]     A. Ghanbari, A. Kashaninia, A. Sadr, and H. Saghaei, “Supercontinuum generation for optical coherence tomography using magnesium fluoride photonic crystal fiber,” Optik-International J. for Light. Electron Opt., vol. 140, pp. 545-554, July 2017.
[6]     H. Saghaei, and A. Ghanbari, “White light generation using photonic crystal fiber with sub-micron circular lattice,” J. Electrical Eng., vol. 68, no. 4, pp. 282-289, August 2017.
[7]     H. Saghaei, B. Seyfe, H. Bakhshi, and R. Bayat, “Novel approach to adjust the step size for closed-loop power control in wireless cellular code division multiple access systems under flat fading,” IET Commun., vol. 5, no. 11, pp. 1469-1483, July 2011.
[8]     H. Saghaei, and B. Seyfe, “New Approach to Closed-Loop Power Control in Cellular CDMA Systems under Multipath Fading,” Proc. IEEE Wicom’08 Conf., pp. 1-4, 2008,
[9]     H. Saghaei, “Supercontinuum source for dense wavelength division multiplexing in square photonic crystal fiber via fluidic infiltration approach,” Radioengineering, vol. 26, no. 1, pp. 16-22, March 2017.
[10]  M. Ebnali-Heidari, H. Saghaei, F. Koohi-Kamali, M. N. Moghadasi, and M. K. Moravvej-Farshi, “Proposal for supercontinuum generation by optofluidic infiltrated photonic crystal fibers,” IEEE J. Sel. Top. Quantum Electron., vol. 20, no. 5, pp. 582-589, March 2014.
[11]  H. Saghaei, V. Heidari, M. Ebnali-Heidari, and M. R. Yazdani, “A systematic study of linear and nonlinear properties of photonic crystal fibers,” Optik-International J. for Light. Electron Opt., vol. 127, no. 24, pp. 11938-11947, March 2016.
[12]  M. Ebnali-Heidari, F. Dehghan, H. Saghaei, F. Koohi-Kamali, and M. K. Moravvej-Farshi, “Dispersion engineering of photonic crystal fibers by means of fluidic infiltration,” J. Mod. Opt., vol. 59, no. 16, pp. 1384-1390, August 2012.
[13]  A. Ghanbari, A. Sadr, and H. Hesari, “Modeling photonic crystal fiber for efficient soliton-effect compression of femtosecond optical pulses at 850 nm,” Arab. J. Sci. Eng., vol. 39, no. 5, pp. 3917-3923, May 2014.
[14]  A. Ghanbari, A. Karimkhani nia, and A. Sadr, “Superlattice elliptical-core photonic crystal fiber soliton effect compressor at 1550nm,” Journal of  Communication Engineering., vol. 4, no.1, pp. 29-40, January-June  2015.
[15]  H. Saghaei, M. K. Moravvej-Farshi, M. Ebnali-Heidari, and M. N. Moghadasi, “Ultra-wide mid-infrared supercontinuum generation in As 40 Se 60 chalcogenide fibers: solid core PCF versus SIF,” IEEE J. Sel. Top. Quantum Electron., vol. 22, no. 2, pp. 279-286, September 2016.
[16]  B. Tan, X.-w. Chen, and S.-C. Li, “Total Internal Reflection Photonic Crystal Fiber,” J. Optoelectronics Laser, vol. 13, no. 5, pp. 491-495, July 2002.
[17]  H. Saghaei, A. Zahedi, R. Karimzadeh, and F. Parandin, “Line defects on As2Se3-Chalcogenide photonic crystals for the design of all-optical power splitters and digital logic gates,” Superlattices Microstruct., vol. 110, no.7, pp. 133-138, August 2017.
[18]  J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wadsworth, and P. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett., vol. 12, no. 7, pp. 807-809, August 2000.
[19]  M. Ebnali-Heidari, H. Saghaei, C. Monat, and C. Grillet, “Four-wave Mixing Based Mid-span Phase Conjugation using slow light engineered Chalcogenide and silicon photonic crystal waveguides,” The European Conference on Lasers and Electro-Optics, pp. CD4_3, May 2011.
[20]  J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express, vol. 13, no. 2, pp. 534-544, July 2005.
[21]  H. Saghaei and V. Van, “Broadband mid-infrared supercontinuum generation in dispersion-engineered silicon-on-insulator waveguide,” JOSA B, vol. 36, no. 2, pp. 193-202, February 2019.
[22]  M. Diouf, A. B. Salem, R. Cherif, H. Saghaei, and A. Wague, “Super-flat coherent supercontinuum source in As 38.8 Se 61.2 chalcogenide photonic crystal fiber with all-normal dispersion engineering at a very low input energy,” Appl. Opt., vol. 56, no. 2, pp. 163-169, January 2017.
[23]  H. Saghaei, “Dispersion-engineered microstructured optical fiber for mid-infrared supercontinuum generation,” Appl. Opt., vol. 57, no. 20, pp. 5591-5598, July 2018.
[24]  R. Raei, M. Ebnali-Heidari, and H. Saghaei, “Supercontinuum generation in organic liquid-liquid core-cladding photonic crystal fiber in visible and near-infrared regions,” JOSA B, vol. 35, no. 2, pp. 323-330, Febrarury 2018.
[25]  H. Saghaei, M. Ebnali-Heidari, and M. K. Moravvej-Farshi, “Midinfrared supercontinuum generation via As 2 Se 3 chalcogenide photonic crystal fibers,” Appl. Opt., vol. 54, no. 8, pp. 2072-2079, March 2015.
[26]  G. Qin, X. Yan, C. Kito, M. Liao, C. Chaudhari, T. Suzuki, and Y. Ohishi, “Ultrabroadband supercontinuum generation from ultraviolet to 6.28 μ m in a fluoride fiber,” Appl. Phys. Express, vol. 95, no. 16, pp. 161103, October 2009.
[27]  V. R. K. Kumar, A. George, J. Knight, and P. Russell, “Tellurite photonic crystal fiber,” Opt. Express, vol. 11, no. 20, pp. 2641-2645,  November 2003.
[28]  B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” JOSA B, vol. 19, no. 10, pp. 2331-2340, August 2002.
[29]  T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. M. De Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” JOSA B, vol. 19, no. 10, pp. 2322-2330, July 2002.
[30]  F. Bréchet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol., vol. 6, no. 2, pp. 181-191, April 2000.
[31]  S. Guo, F. Wu, S. Albin, H. Tai, and R. Rogowski, “Loss and dispersion analysis of microstructured fibers by finite-difference method,” Opt. Express, vol. 12, no. 15, pp. 3341-3352, July 2004.
[32]  Y. Cao, Z. Hou, and Y. Liu, “Convergence problem of plane-wave expansion method for phononic crystals,” Phys. Lett. A, vol. 327, no. 2, pp. 247-253, June 2004.
[33]  M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett., vol. 81, no. 7, pp. 1163-1165, June 2002.
[34]  R. Sinha, and A. Varshney, “Dispersion properties of photonic crystal fiber: comparison by scalar and fully vectorial effective index methods,” Opt. Quantum Electron., vol. 37, no. 8, pp. 711-722, June 2005.
[35]  K. Saitoh, and M. Koshiba, “Empirical relations for simple design of photonic crystal fibers,” Opt. Express, vol. 13, no. 1, pp. 267-274, January 2005.
[36]  M. D. Nielsen, N. A. Mortensen, M. Albertsen, J. R. Folkenberg, A. Bjarklev, and D. Bonacinni, “Predicting macrobending loss for large-mode area photonic crystal fibers,” Opt. Express, vol. 12, no. 8, pp. 1775-1779, May 2004.
[37]  S. Bandyopadhyay, P. Biswas, A. Pal, S. K. Bhadra, and K. Dasgupta, “Empirical relations for design of linear edge filters using apodized linearly chirped fiber Bragg grating,” J. Lightwave Technol., vol. 26, no. 24, pp. 3853-3859, Dec. 2008.