تحلیل مشخصات فیبر نوری حفره‌دار با استفاده از روش دیفرانسیل محدود در حوزه فرکانسی

نوع مقاله : مقاله پژوهشی

نویسنده

سازمان انرژی اتمی-پژوهشکده گداخت هسته ای

چکیده

روش دیفرانسیل و المان محدود در محاسبات مشخصات فیبرهای کریستال فوتونی نسبت به سایر روش­ها از دقت بالاتری برخوردار است. در این مقاله در ابتدا روش دیفرانسیل محدود در بازه فرکانسی برای تعیین مشخصات فیبرهای کریستال فوتونی تشریح شد. مشخصات انتشار در فیبر کریستال فوتونی در یک شبکه سه‌گوش با هشت لایه حفره هوایی محاسبه شد و مشخصات فیبر شامل، ضریب شکست مؤثر، پاشندگی موجبری تعیین شد، سپس با استفاده از قاعده مرکب سیمپسون در انتگرال دو بعدی، مقادیر سطح مقطع مؤثر و همچنین گشودگی عددی با استفاده از نتایج میدان­های الکتریکی حاصل، برای مقادیر مختلف اندازه حفره­ها و فاصله بین آن‌ها تعیین و نتایج آن با هم مقایسه شد. از آنجا که تعیین پاشندگی صفر در مخابرات و به­خصوص طراحی جبران­سازهای پاشش دارای اهمیت است با تعیین پاشندگی رنگی و طول­موج پاشندگی صفر در این نوع فیبرها، تأثیر مشخصات حفره­های هوا در نقطه صفر پاشندگی بررسی شد. در این مقاله برای اولین بار با استفاده از روش مذکور تأثیر مشخصات حفره­ها در مشخصات فیبر کریستال از جمله پاشندگی موجبر محاسبه و نشان داده شد با افزایش اندازه حفره­ها، در یک مقدار ثابت فاصله بین حفره­ها طول موج پاشندگی صفر کاهش می­یابد و برای مقدار ثابت اندازه حفره­ها با افزایش فاصله بین حفره­ها طول موج پاشندگی صفر در فیبر کریستال فوتونی افزایش می­یابد.

کلیدواژه‌ها

عنوان مقاله [English]

Analysis of Photonic Crystal fibers Using Finite Difference Frequency Domain Method

نویسنده [English]

  • maryam karimi
Nuclear Science and Technology Research Institute, Tehran, Iran
چکیده [English]

Finite difference and finite element methods have more accuracy in the calculation of photonic crystal fiber (PCF) characters than other methods. In the present paper the finite difference method in the frequency domain is used to describe and determine the characteristics of PCF. The propagation characteristics of photonic crystal fiber with eight-hole layer are calculated and the fiber characteristics, consisting of, effective refractive index and waveguide dispersion are determined. Then using the composite Simpson rule for double integral, the values of effective areas and numerical apertures are obtained using the results of fields for different values of the hole sizes and distances and the results are compared. Since the determination of zero dispersion region is important in telecommunication and especially for the design of compensators, by determining the color dispersion and zero dispersion wavelength in this kind of fibers, the effects of air hole characteristics in the zero point of dispersion is verified. In this paper for the first time, using the mentioned method, the effects of the hole size in PCF characteristics such as waveguide dispersion is calculated and it is shown that increasing the air hole size in the fixed hole distance, causes the zero dispersion wavelength to decrease and for the fixed air hole with increasing the hole distance, the zero dispersion wavelength increases in the PCF..

کلیدواژه‌ها [English]

  • Photonic crystal fiber
  • Effective refractive index
  • Dispersion
  • Effective area
  • Numerical aperture
  • Air hole characteristics

مراجع

[1] K. P. Hansen, “Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express, Vol. 11, pp. 1503–1509, 2003.
[2] T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G.R. Broderick, and D. J. Richardson, “Sensing with
microstructured optical fibres”, Meas. Sci. Technol., Vol. 12, pp. 854-858, 2001.
[3] J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A.
Petersson, and C. Jakobsen, “High-power air-clad largemode-area photonic crystal fiber laser”, Opt. Express, Vol.11, pp. 818-823, 2003.
[4] S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, “Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb”, Phys.Rev. Lett., Vol. 84, pp. 5102-5105, 2000.
[5] K. N. Park, T. Erdogan, K. S. Lee, “ Cladding mode coupling in long-period gratings formed in photonic crystal fibers”, Opt. Commun., Vol. 266, pp. 541–545, 2006.
[6] A. Shirakawa, J. Ota, M. Musha, K. Nakagawa, K. Ueda, Jacob R. Folkenberg and J. Broeng, "Large-mode-area erbium-ytterbium-doped photonic-crystal fiber amplifier for high-energy femtosecond pulses at 1.55 μm", Opt. Express, Vol. 13, pp. 1221-1227, 2005.
[7] F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber”, Science, Vol. 298, pp. 399-402, 2002.
[8] G. Genty, M. Lehtonen, H. Ludvigsen, J. Broeng, and M. Kaivola, "Spectral broadening of femtosecond pulses into continuum radiation in micro structured fibers", Opt. Express., Vol. 10, pp.1083-1098, 2002.
[9] J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, "Optical parametric oscillator based on four-wave mixing in microstructure fiber", Opt. Lett., Vol. 27, pp. 1675-1677, 2002.
[10] M. Karimi and F. E. Seraji, “Effects of geometry on amplification property of erbium doped holey fiber
amplifiers using scalar effective index method”, Progress In Electromagnetics Research B, Vol. 19, 385-403, 2010.
[11] M. Midrio, M. P. Singh, and C. G. Someda, "The Space Filling Mode of Holey Fibers: An Analytical Vectorial
Solution", IEEE J. Ligthwave. Technol., Vol. 18, pp. 1031-1037, 2000.
[12] A. Bjarklev, J. Broeng, and A. S. Bjarklev, "Photonic crystal fibers", Kluwer Academic Publishers, London, 2003.
[13] S. Kunimasa, K. Masanori, "Numerical Modeling of Photonic Crystal Fibers", IEEE J. Ligthwave. Technol., Vol. 23, pp. 3580-3590, 2005.
[14] F. Prudenzano, "Erbium-doped hole-assisted optical fiber amplifer: Design and optimization", IEEE J. Ligthwave Technol., Vol. 23, pp. 330-340, 2005.
[15] C. A. Defrancisco, B. V. Borges, and M. A. Romero, “A semi vectorial iterative finite-difference method to model photonic crystal fibers”, in SBMO/IEEEMTT-SIMOC, pp. 407–409, 2001.
[16] D. Mogilevtsev, T. A. Birks, P. S. J. Russell, "Localized function method for modeling defect modes in 2-D photonic crystals", J. Lightwave. Technol. Vol. 17, pp. 2078-2081, 1999.
[17] S. Guo, and S. Albin, “Simple plane wave implementation for photonic crystal calculations”, Opt. Express, Vol. 11, pp. 167–175, 2003.
[18] M. Karimi, “Optimization of Core size in Erbium Doped Holey Fiber Amplifiers”, Optik, Vol. 125, pp. 2780-2783, 2014.
[19] A. Cucinotta, F. Poli, S. Selleri, L. Vincetti, and M. Zoboli, "Amplification Properties of Er3+-Doped Photonic Crystal Fibers", IEEE J. Ligthwave. Technol., Vol. 21, pp. 782-788, 2003.
[20] F. Poli, A. Cucinotta, D. Passaro, S. Selleri, J. Lægsgaard, and J. Broeng, "Single-Mode Regime in Large-Mode-Area Rare-Earth-Doped Rod-Type PCFs", IEEE J. Select. Topic. Quant. Electron. Vol. 15, pp. 54-60, 2009.
[21] N. A. Mortensen, “Effective area of photonic crystal fibers”,Opt. Express. Vol. 10, pp. 341-348, 2002.
[22] M. Karimi, “Optimization of Erbium Doped Fiber Core size in Amplifier Systems”, Conference of Physics, yazd University, pp.593-596, August 2012, (In Persian).
[23] M. Karimi, " Refractive Index Calculation in Holey Fiber with Hexagonal Structure using Finite Element Method”Conference of Physics, Ferdowsi Mashhad University, August 2015, (In Persian).
[24] M. Karimi, "Small Signal Gain in Ytterbium Doped Fiber Laser with Honeycomb Structure", National Conference of Physics and its Applications, Malayer university, P. NCPAP65, 29, Jun, 2016, (In Persian).
[25] M. Karimi, "Small Signal Gain in Erbium Doped Fiber Laser with Hexagonal Structure", The Fourth National
Iranian Conference on Engineering Electromagnetics –ICEEM, NDJA university, Nowshahr, Mazandaran, A-10-
10-3, 11-13, April, 2016, (In Persian).
[26] M. Karimi, "Waveguide Dispersion Characteristic in Holey Optical fiber with Hexagonal Structure Using Fully vectorial Effective index and Finite Element Methods", the Iranian conference of optics & laser engineering, Malek-ashtar university of Technology, Oral presentation,
[27] M. Karimi, "Dispersion Characteristic in Photonic Crystal fiber Using Final Difference Frequency Domain Method", Sharif University of Technology, 2-3 Novamber, Tehran, Iran, 2016, (In Persian).
[28] Z. Zhu, and T. G. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers", Opt. Express. Vol. 10, pp. 853-864, 2002.
[29] F. Poli, A. Cucinotta, M. Fuochi, and S. Selleri, "Characterization of microstructured optical fibers for wideband dispersion compensation", J. Opt. Soc. Am. A, Vol. 20, pp. 1958-1962 , 2003.
[30] B. Dabas, R.K., "Dispersion characteristic of hexagonal and square lattice chalcogenide As2Se3 glass photonic crystal fiber", Optic. Commun. Vol. 283, pp. 1331–1337, 2010.
[31] T. A. Birks, D. Mogilevtsev, J. C. Knight, and P. St.J. Russell, "Dispersion Compensation Using Single-Material Fibers", IEEE Photon. Technol. Letter., Vol. 11, pp. 674-676, 1999.
[32] H. Demir, S. Ozsoy, "Large-solid-core square-lattice photonic crystal fibers", optical fiber technol. Vol. 17, pp. 594-600, 2011.
[33] R. K. Sinha, and A. Varshney, “Dispersion properties of photonic crystal fiber: comparison by scalar and fully vectorial effective index methods”, Optical and Quantum Electronics, Vol. 37, pp. 711–722, 2005.
[34] Y. F. Li, C. Y. Wang, M. L. Hu, "A fully vectorial effective index method for photonic crystal fibers: application to dispersion calculation", Optic. Commun. Vol. 238, pp. 29–33, 2004.
[35] K. Thyagarajan, A. Ghatak, “Fiber Optic Essentials”, A John Wiley & Sons, INC, 2007.
[36] R. H. Thaher, O. A. Shareef, S. D.Yousif, "Investigation into the Propagation Characteristics of Photonic Crystal Fiber, Iraq Academic Scientific Journals, ISSN: 19924453, pp. 285-300, 2012.
[37] K. Kurokawa, “Optical Fiber for High-Power Optical Communication”, Crystals Vol. 2, pp. 1382-1392, 2012.
[38] J. Arriaga, J.C. Knight, P.St.J. Russell, "Modeling the propagation of light in photonic crystal fibers", Physica D, Vol. 189, pp. 100–106, 2004.
[39] Blackie, “Blackie’s Dictionary of Physics”, 2016. [40] A. Ouchar, A. Sonne, and R. Aksas, “Chromatic Dispersion Of Micro structured Fiber Using Neural network”, IEEE Xplore, Conference Mediterranean Microwave Symposium (MMS-6068552, 2011. [41] Y. f. Li, C. y. Wang, Z. h. Wang, M. l.Hu, L. Chai, “Analytical solution of the fundamental space filling mode of photonic crystal fibers”, Opt. & Laser Technol. Vol. 39, pp.322–326, 2007.

فایل ها

سابقه مقاله

  • تاریخ دریافت: 24 مهر 1397
  • تاریخ بازنگری: 30 بهمن 1398
  • تاریخ پذیرش: 17 اردیبهشت 1398
  • تاریخ انتشار: 01 دی 1397

هم رسانی

ارجاع به این مقاله

آمار