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Propagation properties of optical soliton in an erbium-doped tapered parabolic index nonlinear fiber: soliton control

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Abstract

In this paper, with the aid of symbolic computation, we investigate the generalized nonlinear Schrödinger Maxwell–Bloch equation, which describes the propagation of the optical soliton through an inhomogeneous two-level dielectric tapered fiber medium. By virtue of the Darboux transformation method, two-soliton solutions are generated based on the constructed Lax pair and figures are plotted to illustrate the properties of the obtained solutions. Moreover, through manipulating the dispersion and nonlinearity profiles, various soliton control systems are investigated which is promising for potential applications in the design of soliton compressor, soliton amplification and high-speed optical devices in ultralarge capacity transmission systems. This means that we are able to control the soliton types with suitably selected values of the parameters. Additionally more soliton control techniques are proposed and investigated. We expect that the above analysis could be observed in future experiments.

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References

  1. Serkin, V.N., Chapsla, V.M., Percino, J., Belyaeva, T.L.: Nonlinear tunneling of temporal and spatial optical solitons through organic thin films and polymeric waveguides. Opt. Commun. 192, 237 (2001)

    Article  Google Scholar 

  2. Lamb Jr., G.L.: Elements of Soliton Theory. Wiley, NewYork (1980)

    MATH  Google Scholar 

  3. Agrawal, G.P.: Nonlinear Fiber Optics, 3rd edn. Academic Press, California (2002)

    MATH  Google Scholar 

  4. Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fiber. I. Anomalous dispersion. Appl. Phys. Lett. 23, 142–144 (1973)

    Article  Google Scholar 

  5. Mollenauer, L.F., Stolen, R.H., Gordon, J.P.: Experimental observation of pico second pulse narrowing and solitons in optical fibers. Phys. Rev. Lett. 45, 1095–1098 (1980)

    Article  Google Scholar 

  6. Luo, H.G., Zhao, D., He, X.G.: Exactly controllable transmission of non-autonomous optical solitons. Phys. Rev. A. 79, 063802 (2009)

    Article  Google Scholar 

  7. Maimistov, A.I., Basharov, A.M.: Nonlinear Optical Waves. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  8. Desurvire, E.: Erbium-Doped Fiber Amplifiers: Principles and Applications. Wiley, New York (1994)

    Google Scholar 

  9. McCall, S.L., Hahn, E.L.: Self-induced transparency by pulsed coherent light. Phys. Rev. Lett. 18, 908 (1967)

    Article  Google Scholar 

  10. Nakazawa, M., Yamada, E., Kubota, H.: Coexistence of self-induced transparency soliton and nonlinear Schrödinger soliton. Phys. Rev. Lett. 66, 2625–2628 (1991)

    Article  Google Scholar 

  11. Mani Rajan, M.S., Mahalingam, A., Uthayakumar, A.: Non-Linear tunneling of nonautonomous optical solitons in combined nonlinear Schrödinger and Maxwell–Bloch systems. J. Opt. 14, 105204 (2012)

    Article  Google Scholar 

  12. Uthayakumar, A., Mahalingam, A., Han, Y.G., Lee, S.B.: Optical soliton propagation in erbium-doped fibre with variable dispersion and nonlinear effects. J. Mod. Opt. 53, 1619–1626 (2006)

    Article  MATH  Google Scholar 

  13. Mani Rajan, M.S., Mahalingam, A., Uthayakumar, A.: Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation. Ann. Phys. 346, 1–13 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu, W.J., Tian, B.: Symbolic computation on soliton solutions for variable-coefficient nonlinear Schrödinger equation in nonlinear optics. Opt. Quantum Electron. 43, 147–162 (2012)

    Article  Google Scholar 

  15. Rajan, Mani: Multi-soliton propagation in a generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch system with loss/gain driven by an external potential. J. Math. Phys. 54, 043514 (2013)

    Article  MATH  Google Scholar 

  16. Mahalingam, A., Porsezian, K., Mani Rajan, M.S., Uthayakumar, A.: Propagation of dispersion nonlinearity managed solitons in an inhomogeneous erbium doped fiber system. J. Phys. A: Math. Theor. 42, 165101 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Cordeiro, C.M.B., Wadsworth, W.J., Birks, T.A., Russell, P.S.J.: Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser. Opt. Lett. 30, 1980–1982 (2005)

    Article  Google Scholar 

  18. Krause, M., Renner, H., Brinkmeyer, E.: Efficient Raman lasing in tapered silicon waveguides. Spectroscopy 21, 26 (2006)

    Google Scholar 

  19. Goyal, A., Gupta, R., Kumar, C.N., Raju, T.S., Panigrahi, P.K.: Controlling optical similaritons in a graded-index nonlinear waveguide by tailoring of the tapering profile. Opt. Commun. 300, 236–243 (2013)

    Article  Google Scholar 

  20. Gupta, R., Kumar, C.N., Vivek, M.Vyas, Panigrahi, P.K.: Manipulating rogue wave triplet in optical waveguides through tapering. Phys. Lett. A 379, 314–318 (2015)

    Article  MathSciNet  Google Scholar 

  21. Arun Prakash, S., Malathi, V., Mani Rajan, M.S.: Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber. J. Mod. Opt. 63, 468–476 (2016)

    Article  Google Scholar 

  22. Levy, D.S., Scarmozzino, R., Osgood, R.M.: Length reduction of tapered N \(\times \) N MMI devices. J. IEEE Photonics Technol. Lett. 10, 830–832 (1998)

    Article  Google Scholar 

  23. Verma, R.K., Sharma, A.K., Gupta, B.D.: Surface plasmon resonance based tapered fiber optic sensor with different taper profiles. Opt. Commun. 281, 1486–1491 (2008)

    Article  Google Scholar 

  24. Burns, W.K., Abebe, M., Villarruel, C.A.: Parabolic model for shape of fiber taper. Appl. Opt. 24, 2753 (1985)

    Article  Google Scholar 

  25. Ikeda, H., Matsumoto, M., Hasegawa, A.: Transmission control of dark solitons by means of nonlinear gain. Opt. Lett. 20, 1113–1115 (1995)

    Article  Google Scholar 

  26. Sukhorukov, A.A., Kivshar, Y.S.: Soliton control and Bloch-wave filtering in periodic photonic lattices. Opt. Lett. 30, 1849–1851 (2005)

    Article  Google Scholar 

  27. Luo, H.G., Zhao, D., He, X.G.: Exactly controllable transmission of nonautonomous optical solitons. Phys. Rev. A 79, 063802 (2009)

    Article  Google Scholar 

  28. Dai, C.Q., Wang, Y.Y.: Spatiotemporal localizations in (3 + 1)-dimensional PT-symmetric and strongly nonlocal nonlinear media. Nonlinear Dyn. 83, 2453–2459 (2016)

    Article  MathSciNet  Google Scholar 

  29. Dai, C.Q., Wang, Y.Y., Liu, J.: Spatiotemporal Hermite–Gaussian solitons of a (3 + 1)-dimensional partially nonlocal nonlinear Schrodinger equation. Nonlinear Dyn. 84, 1157–1161 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. Serkin, V.N., Hasegawa, A.: Novel soliton solutions of the nonlinear Schrödinger equation model. Phys. Rev. Lett. 85, 4502–4505 (2000)

    Article  Google Scholar 

  31. Serkin, V.N., Hasegawa, A.: Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain. JETP Lett. 72, 89–92 (2000)

    Article  Google Scholar 

  32. Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons. J. Mod. Opt. 57, 1456 (2010)

    Article  MATH  Google Scholar 

  33. Wang, L., Li, S., Qi, F.H.: Breather-to-soliton and rogue wave-to-soliton transitions in a resonant erbium-doped fiber system with higher-order effects. Nonlinear Dyn. 85, 389–398 (2016)

    Article  MathSciNet  Google Scholar 

  34. Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Geiger–Nuttall law for Schrödinger solitons. J. Mod. Opt. 60, 116–127 (2013)

    Article  Google Scholar 

  35. Belyaeva, T.L., Serkin, V.N.: Wave-particle duality of solitons and solitonic analog of the Ramsauer–Townsend effect. Eur. Phys. J. D 66, 153 (2012)

    Article  Google Scholar 

  36. Belyaeva, T.L., Serkin, V.N., Hernandez-Tenorio, C., Garcia-Santibañez, F.: Enigmas of optical and matter-wave soliton nonlinear tunneling. J. Mod. Opt. 57, 1087–1099 (2010)

    Article  MATH  Google Scholar 

  37. Yomba, E., Zakeri, G.A.: Rogue-pair and dark-bright-rogue waves of the coupled nonlinear Schrödinger equations from inhomogeneous femtosecond optical fibers. Chaos 26, 083115 (2016)

    Article  MathSciNet  Google Scholar 

  38. Belyaeva, T.L., Serkin, V.N., Agüero, M.A., Hernandez-Tenorio, C., Kovachev, L.M.: Hidden features of the soliton adaptation law to external potentials: optical and matter-wave 3D nonautonomous soliton bullets. Laser Phys. 21, 258–263 (2011)

    Article  Google Scholar 

  39. Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Nonautonomous solitons in external potentials. Phys. Rev. Lett. 98, 074102 (2007)

    Article  Google Scholar 

  40. Barak, A., Peleg, O., Stucchio, C., Soffer, A., Segev, M.: Observation of soliton tunneling phenomena and soliton ejection. Phys. Rev. Lett. 100, 153901 (2008)

    Article  Google Scholar 

  41. Ablowitz, M.J., Kaup, D.J., Newell, A.C., Segur, H.: Nonlinear-evolution equations of physical significance. Phys. Rev. Lett. 31, 125 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  42. Matveev, V.B., Salle, M.A.: Darboux Transformations and Solitons. Springer, Berlin (1991)

    Book  MATH  Google Scholar 

  43. Mani Rajan, M.S., Mahalingam, A.: Nonautonomous solitons in modified inhomogeneous Hirota equation: soliton control and soliton interaction. Nonlinear Dyn. 79, 2469–2484 (2015)

    Article  MathSciNet  Google Scholar 

  44. Rajan, Mani: Dynamics of optical soliton in a tapered erbium-doped fiber under periodic distributed amplification system. Nonlinear Dyn. 85, 599–606 (2016)

    Article  Google Scholar 

  45. Li, Biao, Chen, Yong: Symbolic computation and solitons of the nonlinear Schrödinger equation in inhomogeneous optical fiber media. Chaos Solitons Fractals 33, 532–539 (2007)

    Article  Google Scholar 

  46. Wang, Y.F., Tian, B., Li, M., Wang, P., Wang, M.: Integrability and soliton-like solutions for the coupled higher-order nonlinear Schrdinger equations with variable coefficients in inhomogeneous optical fibers. Commun. Nonlinear Sci. Numer. Simul. 19, 1783–1791 (2014)

    Article  MathSciNet  Google Scholar 

  47. Serkin, V.N., Belyaeva, T.L.: Optimal control of optical soliton parameters: Part 1. The Lax representation in the problem of soliton management. Quantum Electron. 31, 1007–1015 (2001)

    Article  Google Scholar 

  48. Wang, P., Feng, L., Shang, T., Guo, L., Cheng, G., Du, Y.: Analytical soliton solutions for the cubic–quintic nonlinear Schrödinger equation with Raman effect in the nonuniform management systems. Nonlinear Dyn. 79, 387–395 (2015)

    Article  MathSciNet  Google Scholar 

  49. Liu, W.J., Pang, L., Yan, H., Lei, M.: Optical soliton shaping in dispersion decreasing fibers. Nonlinear Dyn. 84, 2205–2209 (2016)

    Article  MathSciNet  Google Scholar 

  50. Serkin, V.N., Hasegawa, A.: Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion managements. IEEE J. Sel. Top. Quantum Electron. 8, 418 (2002)

    Article  Google Scholar 

  51. Dai, C.Q., Wang, Y.Y., Zhang, J.F.: Nonlinear similariton tunneling effect in the birefringent fiber. Opt. Express 18, 17548 (2010)

    Article  Google Scholar 

  52. Loomba, S.: Mani Rajan, M.S., Gupta, R., Kaur, H., Kumar, C.N.: Nonlinear tunneling of optical similaritons in a tapered graded index nonlinear waveguide. Opt. Commun. 324, 286–295 (2014)

    Article  Google Scholar 

  53. Mahalingam, A., Mani Rajan, M.S.: Influence of generalized external potentials on nonlinear tunneling of nonautonomous solitons: soliton management. Opt. Fiber Technol. 25, 44–50 (2015)

    Article  Google Scholar 

  54. Wang, J., Li, L., Li, Z., Zhou, G.S., Mihalache, D., Malomed, B.A.: Generation, compression and propagation of pulse trains under higher order effects. Opt. Commun. 263, 328–336 (2006)

  55. Wang, J., Li, L., Jia, S.: Exact chirped gray soliton solutions of the nonlinear Schrödinger equation with variable coefficients. Opt. Commun. 274, 223–230 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Jerusalem College of Engineering, Chennai, India

    K. Subramanian

  2. Department of Physics, Presidency College, Chennai, India

    T. Alagesan

  3. Department of Physics, Anna University, Chennai, India

    A. Mahalingam

  4. Department of Physics, University College of Engineering, Anna University, Ramanathapuram, India

    M. S. Mani Rajan

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  1. K. Subramanian
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  2. T. Alagesan
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  3. A. Mahalingam
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  4. M. S. Mani Rajan
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Correspondence to M. S. Mani Rajan.

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Subramanian, K., Alagesan, T., Mahalingam, A. et al. Propagation properties of optical soliton in an erbium-doped tapered parabolic index nonlinear fiber: soliton control. Nonlinear Dyn 87, 1575–1587 (2017). https://doi.org/10.1007/s11071-016-3134-1

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