Abstract
The power series formulation for modal field of single-mode graded index fibers by Chebyshev technique has worked excellently in predicting accurately different propagation characteristics in simple fashion. Here we develop a simple iterative method involving Chebyshev formalism to predict the modal field of single-mode graded index fiber in the presence of Kerr-type nonlinearity. Taking step and parabolic index fibers as typical examples, we show that our results match excellently with the available exact results obtained vigorously. Thus, the reported technique can be considered as an accurate alternative to the existing cumbersome techniques. Accordingly, this formalism will be beneficial to the technologies for evaluation of modal noise in single-mode Kerr-type nonlinear graded index fibers.
Acknowledgment
The authors are indebted to the anonymous reviewer for his constructive suggestions.
References
1. Tomlinson WJ, Stolen RH, Chank CV. Compression of optical pulses chirped by self-phase modulation in fibers. J Opt Soc Am. 1984;1:139–49.10.1364/CLEO.1984.TUE4Search in Google Scholar
2. Tai K, Tomita A, Jewell JL, Hasegawa A. Generation of subpicosecond soliton like optical pulses at 0.3 THz repetition rate by induced modulational instability. Appl Phys Lett. 1986;49:236–38.10.1063/1.97181Search in Google Scholar
3. Snyder AW, Chen Y, Poladian L, Mitchel DJ. Fundamental mode of highly nonlinear fibres. Electron Lett. 1990;26:643–44.10.1049/el:19900421Search in Google Scholar
4. Goncharenko IA. Influence of nonlinearity on mode parameters of anisotropic optical fibres. J Mod Opt. 1990;37:1673–84.10.1080/09500349014551831Search in Google Scholar
5. Sammut RA, Pask C. Variational approach to nonlinear waveguides-Gaussian approximations. Electron Lett. 1990;26:1131–32.10.1049/el:19900731Search in Google Scholar
6. Agrawal GP, Boyd RW. Contemporary nonlinear optics. Boston: Academic Press, 1992.Search in Google Scholar
7. Saitoh K, Fujisawa T, Kirihara T, Koshiba M. Approximate empirical relations for nonlinear photonic crystal fibers. Opt Express. 2006;14:6572–82.10.1364/OE.14.006572Search in Google Scholar
8. Agrawal GP. Nonlinear fiber optics. Cambridge, Massachusetts: Academic Press; 2013.10.1016/B978-0-12-397023-7.00011-5Search in Google Scholar
9. Liu X, Chraplyvy AR, Winzer PJ, Tkach RW, Chandrasekhar S. Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit. Nat Photonics. 2013. DOI:10.1038/nphoton.2013.109.Search in Google Scholar
10. Antonelli C, Golani O, Shtaif M, Mecozzi1 A. Nonlinear interference noise in space-division multiplexed transmission through optical fibers. Opt Express. 2017;25:13055–78.10.1364/OE.25.013055Search in Google Scholar PubMed
11. Lu X, Lee JY, Rogers S, Lin Q. Optical Kerr nonlinearity in a high-Q silicon carbide microresonator. Opt Express. 2014;22:30826–32.10.1364/OE.22.030826Search in Google Scholar PubMed
12. Yu YF, Ren M, Zhang JB, Bourouina T, Tan CS, Tsai JM, et al. Force-induced optical nonlinearity and Kerr-like coefficient in opto-mechanical ring resonators. Opt Express. 2012;20:18005–15.10.1364/OE.20.018005Search in Google Scholar PubMed
13. Hayata K, Koshiba M, Suzuki M. Finite-element solution of arbitrarily nonlinear, graded-index slab waveguides. Electron Lett. 1987;23:429–31.10.1049/el:19870311Search in Google Scholar
14. Seaton CT, Valera JD, Shoemaker RL, Stegeman GI, Chilwell JT, Smith D. Calculations of nonlinear TE waves guided by thin dielectric films bounded by nonlinear media. IEEE J Quantum Electron. 1985;21:774–83.10.1109/JQE.1985.1072762Search in Google Scholar
15. Okamoto K, Marcayili EAJ. Chromatic dispersion characteristics of fibers with optical Kerr-types nonlinearity. J Lightwave Technol. 1994;7(1989):1988–.Search in Google Scholar
16. Khijwania SK, Nair VM, Sarkar SN. Propagation characteristics of single-mode graded-index elliptical core linear and nonlinear fiber using super-Gaussian approximation. Appl Opt. 2009;48:G156–G162.10.1364/AO.48.00G156Search in Google Scholar PubMed
17. Diaz-Soriano A, Ortiz-Mora A, Dengra A. Comparative study of numerical methods used in modeling of photonic crystal fibers. Microwave Opt Technol Lett. 2013;55:1049–53.10.1002/mop.27504Search in Google Scholar
18. Gangopadhyay S, Sengupta M, Mondal SK, Das G, Sarkar SN. Novel method for studying single-mode fibers involving Chebyshev technique. J Opt Commun. 1997;18:75–78.10.1515/JOC.1997.18.2.75Search in Google Scholar
19. Patra P, Gangopadhyay S, Sarkar SN. A simple method for studying single-mode graded index fibers in the low V region. J Opt Commun. 2000;21:225–28.10.1515/JOC.2000.21.6.225Search in Google Scholar
20. Gangopadhyay S, Sarkar SN. Confinement and excitation of the fundamental mode in single-mode graded index fibers: Computation by a simple technique. Int J Opt Electron. 1997;11:285–89.Search in Google Scholar
21. Gangopadhyay S, Sarkar SN. Prediction of modal dispersion in single-mode graded index fibers by Chebyshev technique. J Opt Commun. 1998;19:145–48.10.1515/JOC.1998.19.4.145Search in Google Scholar
22. Gangopadhyay S, Sarkar SN. Evaluation of modal spot size in single-mode graded index fibers by a simple technique. J Opt Commun. 1998;19:173–75.10.1515/JOC.1998.19.5.173Search in Google Scholar
23. Patra P, Gangopadhyay S, Sarkar SN. Evaluation of Petermann I and II spot sizes and dispersion parameters of single-mode graded index fibers in the low V region by a simple technique. J Opt Commun. 2001;22:19–22.10.1515/JOC.2001.22.1.19Search in Google Scholar
24. Patra P, Gangopadhyay S, Sarkar SN. Confinement and excitation of fundamental mode in single-mode graded index fibers of low V number: Estimation by a simple technique. J Opt Commun. 2001;22:166–71.10.1515/JOC.2001.22.5.166Search in Google Scholar
25. Gangopadhyay S, Choudhury S, Sarkar SN. Evaluation of splice loss in single-mode graded index fibers by a simple technique. Opt Quant Electron. 1999;31:1247–56.10.1023/A:1007050402499Search in Google Scholar
26. Debnath R, Gangopadhyay S. A simple but accurate method for analytical estimation of splice loss in single-mode triangular index fibers for different V numbers including the low ones. J Opt Commun. 2016;37:321–28.10.1515/joc-2015-0062Search in Google Scholar
27. Hosain SI, Sharma A, Ghatak AK. Splice loss evaluation for single-mode graded index fibers. Appl Opt. 1982;21:2716–21.10.1364/AO.21.002716Search in Google Scholar
28. Roy D, Sarkar SN. Simple but accurate method to compute LP11 mode cut off frequency of nonlinear optical fibers by Chebyshev technique. Opt Commun. 2016;55:0841051–54.Search in Google Scholar
29. Sadhu A, Karak A, Sarkar SN. A simple and effective method to analyze the propagation characteristics of nonlinear single mode fiber using Chebyshev method. Microw Opt Technol Lett. 2013;56:787–90.10.1002/mop.28227Search in Google Scholar
30. Mondal SK, Sarkar SN. Effect of optical Kerr effect nonlinearity on LP11 mode cutoff frequency of single-mode dispersion shifted and dispersion flattened fibers. Opt Commun. 1996;127:25–30.10.1016/0030-4018(95)00706-7Search in Google Scholar
31. Shijun J. Simple explicit formula for calculating the LP11 mode cutoff frequency. Electron Lett. 1987;23:534–35.10.1049/el:19870385Search in Google Scholar
32. Chen PYP. Fast method for calculating cut-off frequencies in single-mode fibers with arbitrary index profile. Electron Lett. 1982;18:1048–49.10.1049/el:19820716Search in Google Scholar
33. Majumdar A, Das S, Gangopadhyay S. A simple method for prediction of effective core area and index of refraction of single mode graded index fiber in the low V region. J Opt Commun. 2014;35:269–74.10.1515/joc-2014-0020Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
