Soliton propagation in lossy optical fibers
DOI:
https://doi.org/10.5433/1679-0375.2019v40n2p97Keywords:
Optical Communication, Soliton, Finite Differences, Dissipation, Nonlinear Amplification,Abstract
In this work we study the propagation of solitons in lossy optical fibers. The main objective of this work is to study the loss of energy of the soliton wave during propagation and then to evaluate the impact of this loss on the transmission of the soliton signal. In this context, a numerical scheme was developed to solve a system of complex partial differential equations (CPDE) that describes the propagation of solitons in optical fibers with loss and nonlinear amplification mechanisms. The numerical procedure is based on the mathematical theory of Taylor series of complex functions. We adapted the Finite Difference Method (FDM) to approximate derivatives of complex functions. Then, we solve the algebraic system resulting from the discretization, implicitly, through the relaxation Gauss-Seidel method (RGSM). The numerical study of CPDE system with linear and cubic attenuation showed that soliton waves undergo attenuation, dispersion, and oscillation effects. On the other hand, we find that by considering the nonlinear term (cubic term) as an optical amplification, it is possible to partially compensate the attenuation of the optical signal. Finally, we show that a gain of 9% triples the propagation distance of the fundamental soliton wave, when the dissipation rate is 1%Metrics
Metrics Loading ...
References
AGRAWAL, G. P. {\it Nonlinear Fiber Optics}. 6th ed., San Diego: Academic Press, 2019.
ALGETY SITE. In: https://www.crunchbase.com/organization/algety
ARTIGAS, D.; TORNER, L.; AKLMEDIEV, N. N. Dynamics of quadratic soliton excitation. {\it Optics Communications Journal}, v. 162, p. 347-356, 1999.
ASHRAF, R.; AHMAD, M. O.; YOUNIS, M.; ALI, K.; RIZVI, S. T. R. Dipole and Gausson soliton for ultrashort laser pulse with high order dispersion. {\it Superlattices and Microstructures}, v. 109, p.504-510, 2017.
CHEMNITZ, M.; GEGHARDT, M.; GAIDA, C.; STUTZKI, F.; KOBELKE, J.; LIMBERT, J.; TUNNERMANN, A.; SCHMIDT, M. A. Hybrid soliton dynamics in liquid-core fibers. {\it Nature Communications}, v. 8, p. 42-52, 2017.
CIRILO, E. R.; NATTI, P. L.; ROMEIRO, N. M. L.; NATTI, E. R. T. Determination of the optimal relaxation parameter in a numerical procedure of solitons propagation. {\it Revista Ciências Exatas e Naturais}, v. 10, p. 77-94, 2008.
CIRILO, E. R.; NATTI, P. L.; ROMEIRO, N. M. L.; NATTI, E. R. T.; OLIVEIRA, C. F. Soliton in ideal optical fibers – a numerical development. {\it Semina: Exact and Technological Sciences}, v. 31, p. 57-68, 2010.
EFTEKHAR, M. A.; EZNAVEH, Z. S.; AVILES, H. E. L.; BENIS, S.; LOPEZ, J. E. A.; KOLESIK, M.; WISE, F.; CORREA, R. A.; CHRISTODOULIDES, D. N. Accelerated nonlinear interactions in graded-index multimode fibers. {\it Nature Communications}, v.10, p. 1638-1647, 2019.
FUKUI, K.; KASAMATSU, T.; MORIE, M.; OHHIRA, R.; ITO, T.; SEKIYA, K.; OGASAHARA, D.; ONO, T. 10.92-Tb/s (273 x 40-Gb/s) triple-band ultra-dense WDM optical-repeatered transmission experiment," in {\it Optical Fiber Communication Conference and International Conference on Quantum Information}, OSA Technical Digest Series, paper PD24, 2001. In: https://www.osapublishing.org/abstract.cfm?uri=OFC-2001-PD24
GALLÉAS, W.; YMAI, L. H.; NATTI, P. L.; NATTI, E. R. T. Solitons wave in dieletric optical fibers (in Portuguese), {\it Revista Brasileira de Ensino de Física}, v. 25, p. 294-304, 2003.
KOHL R.; BISWAS, A.; MILOVIC, D.; ZERRAD, E. Optical soliton perturbation in a non-Kerr law media. {\it Optics \& Laser Technology}, v. 40, p. 647-662, 2008.
KUMAR, D. R.; RAO, B. P. Soliton interaction in birefringent optical fibers: Effects of nonlinear gain devices. {\it Optik}, v. 123, p. 117-124, 2012.
LATAS, S. C. V.; FERREIRA, M. F. S. Stable soliton propagation with self-frequency shift. {\it Mathematics and Computers in Simulation}, v. 74, p. 379-387, 2007.
LUO, J.; SUN, B.; JI, J.; TAN, E. L.; ZHANG, Y.; YU, X. High-efficiency femtosecond Raman soliton generation with a tunable wavelength beyond 2 $\mu$m. {\it Optics Letters}, v. 42, p. 1568-1571, 2017.
MENYUK, C. R.; SCHIEK, R.; TORNER L. Solitary waves due to $\chi^{(2)}$:$\chi^{(2)}$ cascading. {\it Journal of Optics of the Society American B – Optical Physics}, v. 11, p. 2434-2443, 1994.
OLIVEIRA, C. F.; NATTI, P. L.; CIRILO, E. R.; ROMEIRO, N. M. L.; NATTI, E. R. T. Numerical stability of solitons waves through splices in quadratic optical media. {\it Acta Scientiarum. Technology}, to appear in 2020.
PALMIERI, L.; SCHENATO, L. Distributed optical fiber sensing based on Rayleigh scattering. {\it The Open Optics Journal}, v. 7, p. 104-127, 2013.
QUEIROZ, D. A.; NATTI, P. L.; ROMEIRO, N. M. L.; NATTI, E. R. T. A numerical development of the dynamical equations of solitons in optical fibers (in Portuguese). {\it Semina: Exact and Technological Sciences}, v. 27, p. 121-128, 2006.
SMITH, N. J.; KNOX, F.M.; DORAN, N. J.; BLOW, K. J.; BENNION, I. Enhanced power solitons in optical fibres with periodic dispersion management. {\it Electronics Letters}, v. 32, p. 54-55, 1996.
TAYLOR, J. R. {\it Optical Solitons Theory and Experiment}. Cambridge: Cambridge University Press, 1992.
TRIKI, H.; BISWAS, A.; MILOVIC, D.; BELIC, M. Chirped femtosecond pulses in the higher-order nonlinear Schrodinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities. {\it Optics Communications}, v. 366, p. 362-369, 2016.
WANG, W. C.; ZHOU, B.; XU, S. H.; YANG, Z. M.; ZHANG, Q. Y. Recent advances in soft optical glass fiber lasers. {\it Progress in Material Sciences}, v. 101, p. 90-171, 2019.
WEN, B.; YANGBAO, D.; SHI, X.; FU, X. (2018). Evolution of finite-energy Airy pulse interaction with high-power soliton pulse in optical fiber with higher-order effects. {\it Optik}, v. 152, p. 61-68, 2018.
YAMAI, L. H.; GALLÉAS, W.; NATTI, P. L.; NATTI, E. R. T. Stability of solitons in $\chi^{2}$-type dielectric optical fibers (in Portuguese). {\it Revista Ciências Exatas e Naturais}, v. 6, p. 9-29, 2004.
YUSHKO, O. V.; REDYUK, A. A.; FEDORUK, M. P.; TURITSYN, S. K. Coherent soliton communication lines. {\it Journal of Experimental and Theoretical Physics}, v. 119, p. 787-794, 2014.
ZAJNULINA, M.; BOHN, M.; BODENMULLER, D.; BLOW, K.; BOGGIO, J. M. C.; RIEZNIK, A. A.; ROTH, M. M. Characteristics and stability of soliton crystals in optical fibres for the purpose of optical frequency comb generation. {\it Optics Communications}, v. 393, p. 95-102, 2017.
ALGETY SITE. In: https://www.crunchbase.com/organization/algety
ARTIGAS, D.; TORNER, L.; AKLMEDIEV, N. N. Dynamics of quadratic soliton excitation. {\it Optics Communications Journal}, v. 162, p. 347-356, 1999.
ASHRAF, R.; AHMAD, M. O.; YOUNIS, M.; ALI, K.; RIZVI, S. T. R. Dipole and Gausson soliton for ultrashort laser pulse with high order dispersion. {\it Superlattices and Microstructures}, v. 109, p.504-510, 2017.
CHEMNITZ, M.; GEGHARDT, M.; GAIDA, C.; STUTZKI, F.; KOBELKE, J.; LIMBERT, J.; TUNNERMANN, A.; SCHMIDT, M. A. Hybrid soliton dynamics in liquid-core fibers. {\it Nature Communications}, v. 8, p. 42-52, 2017.
CIRILO, E. R.; NATTI, P. L.; ROMEIRO, N. M. L.; NATTI, E. R. T. Determination of the optimal relaxation parameter in a numerical procedure of solitons propagation. {\it Revista Ciências Exatas e Naturais}, v. 10, p. 77-94, 2008.
CIRILO, E. R.; NATTI, P. L.; ROMEIRO, N. M. L.; NATTI, E. R. T.; OLIVEIRA, C. F. Soliton in ideal optical fibers – a numerical development. {\it Semina: Exact and Technological Sciences}, v. 31, p. 57-68, 2010.
EFTEKHAR, M. A.; EZNAVEH, Z. S.; AVILES, H. E. L.; BENIS, S.; LOPEZ, J. E. A.; KOLESIK, M.; WISE, F.; CORREA, R. A.; CHRISTODOULIDES, D. N. Accelerated nonlinear interactions in graded-index multimode fibers. {\it Nature Communications}, v.10, p. 1638-1647, 2019.
FUKUI, K.; KASAMATSU, T.; MORIE, M.; OHHIRA, R.; ITO, T.; SEKIYA, K.; OGASAHARA, D.; ONO, T. 10.92-Tb/s (273 x 40-Gb/s) triple-band ultra-dense WDM optical-repeatered transmission experiment," in {\it Optical Fiber Communication Conference and International Conference on Quantum Information}, OSA Technical Digest Series, paper PD24, 2001. In: https://www.osapublishing.org/abstract.cfm?uri=OFC-2001-PD24
GALLÉAS, W.; YMAI, L. H.; NATTI, P. L.; NATTI, E. R. T. Solitons wave in dieletric optical fibers (in Portuguese), {\it Revista Brasileira de Ensino de Física}, v. 25, p. 294-304, 2003.
KOHL R.; BISWAS, A.; MILOVIC, D.; ZERRAD, E. Optical soliton perturbation in a non-Kerr law media. {\it Optics \& Laser Technology}, v. 40, p. 647-662, 2008.
KUMAR, D. R.; RAO, B. P. Soliton interaction in birefringent optical fibers: Effects of nonlinear gain devices. {\it Optik}, v. 123, p. 117-124, 2012.
LATAS, S. C. V.; FERREIRA, M. F. S. Stable soliton propagation with self-frequency shift. {\it Mathematics and Computers in Simulation}, v. 74, p. 379-387, 2007.
LUO, J.; SUN, B.; JI, J.; TAN, E. L.; ZHANG, Y.; YU, X. High-efficiency femtosecond Raman soliton generation with a tunable wavelength beyond 2 $\mu$m. {\it Optics Letters}, v. 42, p. 1568-1571, 2017.
MENYUK, C. R.; SCHIEK, R.; TORNER L. Solitary waves due to $\chi^{(2)}$:$\chi^{(2)}$ cascading. {\it Journal of Optics of the Society American B – Optical Physics}, v. 11, p. 2434-2443, 1994.
OLIVEIRA, C. F.; NATTI, P. L.; CIRILO, E. R.; ROMEIRO, N. M. L.; NATTI, E. R. T. Numerical stability of solitons waves through splices in quadratic optical media. {\it Acta Scientiarum. Technology}, to appear in 2020.
PALMIERI, L.; SCHENATO, L. Distributed optical fiber sensing based on Rayleigh scattering. {\it The Open Optics Journal}, v. 7, p. 104-127, 2013.
QUEIROZ, D. A.; NATTI, P. L.; ROMEIRO, N. M. L.; NATTI, E. R. T. A numerical development of the dynamical equations of solitons in optical fibers (in Portuguese). {\it Semina: Exact and Technological Sciences}, v. 27, p. 121-128, 2006.
SMITH, N. J.; KNOX, F.M.; DORAN, N. J.; BLOW, K. J.; BENNION, I. Enhanced power solitons in optical fibres with periodic dispersion management. {\it Electronics Letters}, v. 32, p. 54-55, 1996.
TAYLOR, J. R. {\it Optical Solitons Theory and Experiment}. Cambridge: Cambridge University Press, 1992.
TRIKI, H.; BISWAS, A.; MILOVIC, D.; BELIC, M. Chirped femtosecond pulses in the higher-order nonlinear Schrodinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities. {\it Optics Communications}, v. 366, p. 362-369, 2016.
WANG, W. C.; ZHOU, B.; XU, S. H.; YANG, Z. M.; ZHANG, Q. Y. Recent advances in soft optical glass fiber lasers. {\it Progress in Material Sciences}, v. 101, p. 90-171, 2019.
WEN, B.; YANGBAO, D.; SHI, X.; FU, X. (2018). Evolution of finite-energy Airy pulse interaction with high-power soliton pulse in optical fiber with higher-order effects. {\it Optik}, v. 152, p. 61-68, 2018.
YAMAI, L. H.; GALLÉAS, W.; NATTI, P. L.; NATTI, E. R. T. Stability of solitons in $\chi^{2}$-type dielectric optical fibers (in Portuguese). {\it Revista Ciências Exatas e Naturais}, v. 6, p. 9-29, 2004.
YUSHKO, O. V.; REDYUK, A. A.; FEDORUK, M. P.; TURITSYN, S. K. Coherent soliton communication lines. {\it Journal of Experimental and Theoretical Physics}, v. 119, p. 787-794, 2014.
ZAJNULINA, M.; BOHN, M.; BODENMULLER, D.; BLOW, K.; BOGGIO, J. M. C.; RIEZNIK, A. A.; ROTH, M. M. Characteristics and stability of soliton crystals in optical fibres for the purpose of optical frequency comb generation. {\it Optics Communications}, v. 393, p. 95-102, 2017.
Downloads
Published
2019-12-18
How to Cite
Dall’Agnol, C., Natti, P. L., Cirilo, E. R., Romeiro, N. M. L., & TakanoNatti, Érica R. (2019). Soliton propagation in lossy optical fibers. Semina: Ciências Exatas E Tecnológicas, 40(2), 97–106. https://doi.org/10.5433/1679-0375.2019v40n2p97
Issue
Section
Original Article
License
The Copyright Declaration for articles published in this journal is the author’s right. Since manuscripts are published in an open access Journal, they are free to use, with their own attributions, in educational and non-commercial applications. The Journal has the right to make, in the original document, changes regarding linguistic norms, orthography, and grammar, with the purpose of ensuring the standard norms of the language and the credibility of the Journal. It will, however, respect the writing style of the authors. When necessary, conceptual changes, corrections, or suggestions will be forwarded to the authors. In such cases, the manuscript shall be subjected to a new evaluation after revision. Responsibility for the opinions expressed in the manuscripts lies entirely with the authors.
This journal is licensed with a license Creative Commons Attribution-NonCommercial 4.0 International.
