Splice loss in dual mode triangular index fibers: an analytic approach in the presence of nonlinearity for various V numbers

Bappa Ditya Biswas; Angshuman Majumdar; Adriza Dhar; Ramkrishna Rakshit

doi:10.1515/joc-2024-0168

Article

Splice loss in dual mode triangular index fibers: an analytic approach in the presence of nonlinearity for various V numbers

Bappa Ditya Biswas , Angshuman Majumdar , Adriza Dhar and Ramkrishna Rakshit

Published/Copyright: August 20, 2024

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From the journal Journal of Optical Communications

Abstract

We report mathematical techniques for determining the coefficient of transmission at the splice, where anomalies like transverse and angular are present. The investigation involves the first mode of higher order (LP₁₁) in Kerr pattern nonlinear fiber. In this case, the LP₁₁ mode for the triangular index (TI) profile is calculated using a standard power series. Chebyshev formalism is the source of the aforementioned term. When there is third-order nonlinearity (TON), the iteration approach is utilized on the analytical mathematical terms to obtain the characteristics listed above. It has been demonstrated that our findings closely match the simulated exact outcomes obtained with the complex finite element method (FEM). Consequently, the suggested straightforward and precise technique offers enormous promise for investigating alternative propagation characteristics in dual-mode fibers.

Keywords: triangular index fiber; Kerr nonlinearity; LP11 mode; splice loss; transverse and angular offsets

Corresponding author: Angshuman Majumdar, Department of Electronics and Communication Engineering, Brainware University, Barasat, Kolkata, 700125, West Bengal, India, E-mail: angshumankol2012@gmail.com

Research ethics: Research ethics are followed throughout the manuscript.
Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Competing interests: The authors state no conflict of interest.
Research funding: None declared.
Data availability: The data has been generated by MATLAB and can be obtained on request from the corresponding author.

References

1. Warm, S, Petermann, K. Splice loss requirements in multi-mode fiber mode-division-multiplex transmission links. Opt Express 2013;21:519–32. https://doi.org/10.1364/oe.21.000519.Search in Google Scholar

2. Tse, MLV, Tam, HY, Fu, LB, Thomas, BK, Dong, L, Lu, C, et al.. Fusion splicing holey fibers and single-mode fibers: a simple method to reduce loss and increase strength. IEEE Photon Technol Lett 2009;21:164–6. https://doi.org/10.1109/lpt.2008.2009467.Search in Google Scholar

3. Kristensen, JT, Houmann, A, Liu, X, Turchinovich, D. Low-loss polarization-maintaining fusion splicing of single-mode fibers and hollow-core photonic crystal fibers, relevant for monolithic fiber laser pulse compression. Opt Express 2008;16:9986–95. https://doi.org/10.1364/oe.16.009986.Search in Google Scholar PubMed

4. Saitoh, K, Yukihiro, T, Masanori, K. Bending-insensitive single-mode hole-assisted fibers with reduced splice loss. Opt Lett 2005;30:1779–81. https://doi.org/10.1364/ol.30.001779.Search in Google Scholar PubMed

5. Marcuse, D. Loss analysis of single mode fiber splices. Bell Syst Tech J 1977;56:703–18. https://doi.org/10.1002/j.1538-7305.1977.tb00534.x.Search in Google Scholar

6. Meunier, JP, Hossain, SI. An accurate splice loss analysis for single-mode graded-index fibers with mismatched parameters. J Lightwave Technol 1992;10:1521–6. https://doi.org/10.1109/50.184887.Search in Google Scholar

7. Aghaie, KZ, Digonnet, MJF, Fan, S. Optimization of the splice loss between photonic-bandgap fibers and conventional single-mode fibers. Opt Lett 2010;35:1938–40. https://doi.org/10.1364/ol.35.001938.Search in Google Scholar PubMed

8. Ghatak, A, Thyagarajan, K. Introduction to fiber optics. Cambridge, UK: Cambridge University Press; 1989.Search in Google Scholar

9. Hossain, SI, Sharma, A, Ghatak, AK. Splice loss evaluation for single-mode graded-index fibers. Appl Opt 1982;21:2716–20. https://doi.org/10.1364/ao.21.002716.Search in Google Scholar

10. Chakraborty, S, Majumdar, A, Gangopadhyay, S. A simple but accurate method for prediction of splice loss in single-mode dispersion shifted trapezoidal as well as dispersion flattened graded and step W fibers. Optik 2013;124:6752–6. https://doi.org/10.1016/j.ijleo.2013.05.083.Search in Google Scholar

11. 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;37:321–7. https://doi.org/10.1515/joc-2015-0062.Search in Google Scholar

12. Gangopadhyay, S, Choudhury, S, Sarkar, SN. Evaluation of splice loss in single-mode graded index fibres by a simple technique. Opt Quant Electron 1999;31:1247–56. https://doi.org/10.1023/a:1007050402499.10.1023/A:1007050402499Search in Google Scholar

13. Chen, PYP. Fast method for calculating cut-off frequencies in single-mode fibers with arbitrary index profile. Electron Lett 1982;18:1048–9. https://doi.org/10.1049/el:19820716.10.1049/el:19820716Search in Google Scholar

14. Shijun, J. Simple explicit formula for calculating LP11 mode cut-off frequency. Electron Lett 1987;23:534–6.10.1049/el:19870385Search in Google Scholar

15. Patra, P, Gangopadhyay, S, Goswami, K. A simple method for prediction of first-order modal field and cladding decay parameter in graded index fiber. Optik 2008;119:209–12. https://doi.org/10.1016/j.ijleo.2006.11.002.Search in Google Scholar

16. Agrawal, GP. Nonlinear fiber optics. Cambridge: Academic Press; 2013.10.1016/B978-0-12-397023-7.00011-5Search in Google Scholar

17. Saitoh, K, Fujisawa, T, Kirihara, T, Koshiba, M. Approximate empirical relations for nonlinear photonic crystal fibers. Opt Express 2006;14:6572–82. https://doi.org/10.1364/oe.14.006572.Search in Google Scholar PubMed

18. Hayata, K, Koshiba, M, Suzuki, M. Finite-element solution of arbitrarily nonlinear, graded-index slab waveguides. Electron Lett 1987;23:429–31. https://doi.org/10.1049/el:19870311.10.1049/el:19870311Search in Google Scholar

19. 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:G156–62. https://doi.org/10.1364/ao.48.00g156.Search in Google Scholar PubMed

20. 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. https://doi.org/10.1016/0030-4018(95)00706-7.Search in Google Scholar

21. 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;11:285–9.Search in Google Scholar

22. Patra, P, Gangopadhyay, S, Sarkar, SN. Confinement and excitation of the fundamental mode in single-mode graded index fibers of low V number: estimation by a simple technique. J Opt Commun 2001;22:166–70. https://doi.org/10.1515/joc.2001.22.5.166.Search in Google Scholar

23. Gangopadhyay, S, Sengupta, M, Mondal, SK, Das, G, Sarkar, SN. Novel method for studying single-mode fibers involving Chebyshev technique. J Opt Commun 1997;18:75–8. https://doi.org/10.1515/joc.1997.18.2.75.Search in Google Scholar

24. 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;21:225–8. https://doi.org/10.1515/joc.2000.21.6.225.Search in Google Scholar

25. 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. https://doi.org/10.1002/mop.28227.Search in Google Scholar

26. Roy, K, Majumdar, A, Gangopadhyay, S. Simple but accurate method for estimation of the effect of Kerr nonlinearity on confinement and excitation of the fundamental mode in single mode graded index fiber. Optik 2020;216:164939. https://doi.org/10.1016/j.ijleo.2020.164939.Search in Google Scholar

27. Mukherjee, T, Majumdar, A, Gangopadhyay, S. Influence of Kerr nonlinearity on group delay and modal dispersion parameters of single-mode graded index fibers: evaluation by a simple but accurate method. J Opt Commun 2020. https://doi.org/10.1515/joc-2020-0192.Search in Google Scholar

28. Rakshit, R, Majumdar, A, Maiti, S, Gangopadhyay, S. Influence of Kerr nonlinearity on single-mode dispersion-shifted and dispersion-flattened directional couplers: analysis by a simple but accurate method. Opt Quant Electron 2022;54:118. https://doi.org/10.1007/s11082-021-03492-9.Search in Google Scholar

29. Majumdar, A, Mukherjee, T, Gangopadhyay, S. Estimation of Petermann I, Petermann II spot sizes for Kerr type nonlinear dispersion-shifted along with dispersion-flattened optical fibers in fundamental mode guidance applying a simple but accurate formalism. J Nonlinear Opt Phys Mater 2023:2350070. https://doi.org/10.1142/s0218863523500704.Search in Google Scholar

30. Maiti, S, Majumdar, A, Biswas, SK, Gangopadhyay, S. Evaluation of splice loss of single-mode graded index fiber in presence of kerr nonlinearity. Optik 2020;203:163962. https://doi.org/10.1016/j.ijleo.2019.163962.Search in Google Scholar

31. Rakshit, R, Majumdar, A, Gangopadhyay, S. A simple but accurate method for prediction of splice loss in mono-mode dispersion shifted and dispersion flattened fibers in presence of Kerr nonlinearity. J Opt Commun 2021. https://doi.org/10.1515/joc-2020-0259.Search in Google Scholar

32. Amin, AA, Ali, A, Chen, X, Shieh, W. LP01/LP11 dual-mode and dual polarization CO-OFDM transmission on two-mode fiber. Electron Lett 2011;47:606–8. https://doi.org/10.1049/el.2011.0638.Search in Google Scholar

33. Eguchi, M. Dispersion-compensating dual-mode optical fibers desirable for erbium-doped- fiber-amplified systems. J Opt Soc Am B 2001;18:737–42. https://doi.org/10.1364/josab.18.000737.Search in Google Scholar

34. Eguchi, M, Koshiba, M, Tsuji, Y. Dispersion compensation based on dual-mode optical fiber with inhomogeneous profile core. J Lightwave Technol 2002;14:2387–94. https://doi.org/10.1109/50.541234.Search in Google Scholar

35. Ray, BK, Majumdar, A, Gangopadhyay, S. Radial distribution of pump and signal intensities in step index EDFA for LP11 mode in Kerr nonlinear condition. J Opt Commun 2022. https://doi.org/10.1515/joc-2022-0109.Search in Google Scholar

36. Pedersen, B. Small-signal erbium-doped fiber amplifiers pumped at 980nm: a design study. Opt. Quantum Electron 1994;26:S237–84.10.1007/BF00384679Search in Google Scholar

37. Watson, GN. A treatise on the theory of Bessel functions. UK: Cambridge University Press; 1944.Search in Google Scholar

38. Abramowitz, M, Stegun, IA. Handbook of mathematical functions. New York: Dover Publications; 1981.Search in Google Scholar

Received: 2024-06-28

Accepted: 2024-07-30

Published Online: 2024-08-20

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https://doi.org/10.1515/joc-2024-0168

Keywords for this article

triangular index fiber; Kerr nonlinearity; LP11 mode; splice loss; transverse and angular offsets