Skip to main content
SpringerLink
Log in

Analytical and numerical demonstration of phase characteristics on two solitons under the influence of third-order dispersion

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

In the present work, influence of third-order dispersion (TOD) on phase change properties of two-soliton model is numerically and analytically investigated. Using perturbation theory approach and split-step Fourier transform, phase characteristics of two solitons pulse are evolved and solved by nonlinear Schrodinger’s equation. Each phase variation in the form of temporal shift under the base of third-order dispersion is also numerically devoted using the moments equation. As a result, it was found that the shift of soliton pulse mainly depends on third-order dispersion parameter β3. With the good agreement between analytical and numerical analysis, the impact of TOD has realized in a single channel telecommunication system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Agrawal, G.P.: Nonlinear Fiber Optics. Academic, San Diego (2001)

    MATH  Google Scholar 

  • Aitchison, J.S., Weiner, A.M., Silberberg, Y., Leaird, D.E., Oliver, M.K., Jackel, J.L., Smith, P.W.E.: Experimental observation of spatial soliton interactions. Opt. Lett. 16, 5–17 (1991)

    Article  ADS  Google Scholar 

  • Al-Samman, A.M., Rahman, T.A., Azmi, M.H., Hindia, M.N.: Large-scale path loss models and time dispersion in an outdoor line-of-sight environment for 5G wireless communications. AEU Int. J. Electron. Commun. 70, 1515–1521 (2018)

    Article  Google Scholar 

  • Baleanu, D., Inc, M., Aliyu, A.I., Yusuf, A.: Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger’s equation with repulsive delta potential. Superlattices Microstruct. 111, 546–555 (2017)

    Article  ADS  Google Scholar 

  • Biswas, A., Mirzazadeh, M., Eslami, M., Milovic, D., Belic, M.: Solitons in optical metamaterials by functional variable method and first integral approach. Frequenz 68, 525–530 (2014)

    Article  ADS  Google Scholar 

  • Dudley, J.M., Provino, L., Grossard, N., Maillotte, H., Windeler, R.S., Eggleton, B.J., Coen, S.: Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping. JOSA B 19, 765–771 (2002)

    Article  ADS  Google Scholar 

  • Elgin, J.N., Brabec, T., Kelly, S.M.J.: A perturbative theory of soliton propagation in the presence of third-order dispersion. Opt. Commun. 114, 321–328 (1995)

    Article  ADS  Google Scholar 

  • Eslami, M.: Trial solution technique to chiral nonlinear Schrödinger’s equation in (1 + 2) dimensions. Nonlinear Dyn. 79, 2469–2484 (2015)

    Article  Google Scholar 

  • Gordon, J.P.: Interaction forces among solitons in optical fibers. Opt. Lett. 8, 596–598 (1983)

    Article  ADS  Google Scholar 

  • Hause, A., Mitschke, F.: Reduced soliton interaction by Raman self-frequency-shift. Phys. Rev. A 800, 63824-1–63824-8 (2009)

    Google Scholar 

  • Hermansson, B., Yevick, D.: Numerical investigation of soliton interaction. Electron. Lett. 19, 570–571 (1983)

    Article  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A.: Solitons and conservation laws to the resonance nonlinear Shrödinger’s equation with both spatio-temporal and inter-modal dispersions. Optik 142, 509–522 (2017a)

    Article  ADS  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A.: Optical solitons to the nonlinear Shrödinger’s equation with spatio-temporal dispersion using complex amplitude ansatz. J. Mod. Opt. 64, 2273–2280 (2017b)

    Article  ADS  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A.: Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion. Mod. Phys. Lett. B 31, 1750163 (2017c)

  • Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Optical solitons, conservation laws and modulation instability analysis for the modified nonlinear Schrödinger’s equation for Davydov solitons. J. Electromagn. Waves Appl. 32, 858–873 (2017d)

    Article  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Optical solitons for Biswas–Milovic Model in nonlinear optics by Sine-Gordon equation method. Optik 157, 274–276 (2018a)

    ADS  Google Scholar 

  • Inc, M., Aliyua, A.I., Yusuf, A., Baleanu, D.: Combined optical solitary waves and conservation laws for nonlinear Chen–Lee–Liu equation in optical fibers. Optik 158, 297–304 (2018b)

    Article  ADS  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Optical solitons for complex Ginzburg-Landau model in nonlinear optics. Optik 158, 368–375 (2018c)

    Article  ADS  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A.: Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes. Mod. Phys. Lett. B 32, 1850014-1–185001418500141850014185001424 (2018d)

    ADS  MathSciNet  Google Scholar 

  • Inc, M., Yusuf, A., Aliyu, A.I., Baleanu, D.: Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics. Opt. Quantum Electron. 50, 1–14 (2018e)

    Article  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Novel optical solitary waves and modulation instability analysis for the coupled nonlinear Schrödinger equation in monomode step-index optical fibers. Superlattices Microstruct. 113, 745–753 (2018f)

    Article  ADS  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A., Baleanu, D.: Gray optical soliton, linear stability analysis and conservation laws via multipliers to the cubic nonlinear Schrödinger equation. Optik 164, 472–478 (2018g)

    Article  ADS  Google Scholar 

  • Inc, M., Aliyu, A.I., Yusuf, A.: On the classification of conservation laws and soliton solutions of the long short-wave interaction system. Mod. Phys. Lett. B 32, 1850202–1–1850202–15 (2018h)

    MathSciNet  Google Scholar 

  • Krolikowski, W., Luther-Davies, B., Denz, C., Tschudi, T.: Annihilation of photorefractive solitons. Opt. Lett. 23, 97–99 (1998)

    Article  ADS  Google Scholar 

  • Liu, W.J., Leia, M.: All-optical switches using solitons within nonlinear fibers. J. Electromagn. Waves Appl. 27, 2288–2297 (2013)

    Article  Google Scholar 

  • 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 

  • Liu, W.J., Tian, B., Xu, T., Jiang, Y.: Analytic study on bound solitons and soliton collisions for the coupled nonlinear Schrödinger equations. J. Mod. Opt. 59, 470–483 (2012)

    Article  ADS  Google Scholar 

  • Mani Naicker, B., Jawahar, A., Radha, S.: Study on soliton phase characteristics in 100 Gbps single-channel telecommunication system. Int. J. Commun Syst 30, 1–15 (2016)

    Google Scholar 

  • 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 

  • Mani Rajan, M.S., Mahalingam, A., Uthayakumar, A., Porsezian, K.: Observation of two soliton propagation in an erbium doped inhomogeneous lossy fiber with phase modulation. Commun. Nonlinear Sci. Numer. Simul. 18, 1410–1432 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  • Mani, B., Chitra, K., Sivasubramanian, A.: Study on fundamental and higher order soliton with and without third-order dispersion near zero dispersion point of single mode fiber. J. Nonlinear Opt. Phys. Mater. 23, 1–23 (2014)

    Article  Google Scholar 

  • Mani, B., Chitra, K., Sivasubramanian, A.: Realization of soliton interaction in 100 Gbps uncompensated single channel telecommunication system implemented with various telecom fibers. Opt. Quantum Electron. 47, 1637–1658 (2015a)

    Article  Google Scholar 

  • Mani, B., Jawahar, A., Sivasubramanian, A., Chitra, K.: Role of negative-third order dispersion, intrapulse Raman scattering and self-steepening effect on soliton intra-channel interaction. Int. Conf. Photon. Solut. 9659, 1–13 (2015b)

    Google Scholar 

  • Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M.F., Biswas, A., Belic, M.: Optical solitons in nonlinear directional couplers by sine–cosine function method and Bernoulli’s equation approach. Nonlinear Dyn. 81, 1933–1949 (2015)

    Article  MathSciNet  Google Scholar 

  • Mirzazadeh, M., Ekici, M., Sonmezoglu, A., Eslami, M., Zhou, Q., Kara, A.H., Milovic, D., Belic, M.: Optical solitons with complex Ginzburg–Landau equation. Nonlinear Dyn. 85, 1979–2016 (2016)

    Article  MathSciNet  Google Scholar 

  • Mollenauer, L.F., Smith, K.: Demonstration of soliton transmission over more than 4000 km in fiber with loss periodically compensated by Raman Gain. Opt. Lett. 13, 675–677 (1988)

    Article  ADS  Google Scholar 

  • Mollenauer, L.F., Holmdel, N.J., Evangelides, S.G.: Long distance soliton propagation using lumped amplifiers and dispersion shifted fiber. J. Lightwave Technol. 9, 194–197 (1991)

    Article  ADS  Google Scholar 

  • Nakazawa, M.: Soliton transmission in telecommunication networks. IEEE Commun. Mag. 32, 34–41 (1994)

    Article  Google Scholar 

  • Nakazawa, M., Kubota, H., Suzuki, K., Yamada, E., Sahara, A.: Recent progress in soliton transmission technology. Chaos 10, 486–514 (2000)

    Article  ADS  Google Scholar 

  • Rohrmann, P., Hause, A., Mitschke, F.: Solitons beyond binary: possibility of fiber-optic transmission of two bits per clock period. Sci. Rep. 2, 1–4 (2012)

    Article  Google Scholar 

  • Rotschild, C., Alfassi, B., Oren Cohen, O., Segev, M.: Long-range interactions between optical solitons. Nat. Phys. 2, 769–774 (2006)

    Article  Google Scholar 

  • Santhanam, J., Agrawal, G.P.: Raman-induced spectral shifts in optical fibers: general theory based on the moment method. Opt. Commun. 222, 413–420 (2003)

    Article  ADS  Google Scholar 

  • Segev, M., Stegeman, G.: Self trapping of optical beams, spatial solitons. Phys. Today 51, 42–48 (1998)

    Article  Google Scholar 

  • Shih, M., Segev, M.: Incoherent collisions between two-dimensional bright steady-state photorefractive spatial screening solitons. Opt. Lett. 21, 1538–1540 (1996)

    Article  ADS  Google Scholar 

  • Sonmezoglu, A., Yao, M., Ekici, M., Mirzazadeh, M., Zhou, Q.: Explicit solitons in the parabolic law nonlinear negative-index materials. Nonlinear Dyn. 88, 595–607 (2017)

    Article  Google Scholar 

  • Takia, H., Azou, S., Hamie, A., Morel, P., Housseini, A.A., Alaeddine, A., Sharaiha, A.: Chirping techniques for enhancing the performance of SOA-based UWB over fiber systems: an experimental demonstration. AEU Int. J. Electron. Commun. 94, 221–225 (2018)

    Article  Google Scholar 

  • Tikhonenko, V., Christou, J., Luther-Davies, B.: Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium. Phys. Rev. Lett. 76, 2698–2701 (1996)

    Article  ADS  Google Scholar 

  • Tsoy, E.N., De Sterke, C.M.: Dynamics of ultrashort pulses near zero dispersion wavelength. JOSA B 23, 2425–2433 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  • Udaiyakumar, R., Vijayakumari, P., Mani Rajan, M.S., Mani, B.: Combined influence of third order dispersion (TOD) and intra-pulse Raman scattering (IRS) on initially phase imparted solitons. Optik 164, 33–45 (2018)

    Article  Google Scholar 

  • Xu, Z., Li, L., Li, Z., Zhou, G.S.: Soliton interaction under the influence of higher-order effects. Opt. Commun. 210, 375–384 (2002)

    Article  ADS  Google Scholar 

  • Yu, W., Ekici, M., Mirzazadeh, M., Zhou, Q., Liu, W.J.: Periodic oscillations of dark solitons in nonlinear optics. Optik 165, 341–344 (2018)

    Article  ADS  Google Scholar 

  • Yushko, O.V., Redyuk, A.A.: Soliton communication lines based on spectrally efficient modulation formats. Quantum Electron. 44, 606–611 (2014)

    Article  ADS  Google Scholar 

  • Yushko, O.V., Redyuk, A., Fedoruk, M., Blow, K.J., Doran, N.J., Ellis, A.D., Turitsyn, S.: Timing and phase jitter suppression in coherent soliton transmission. Opt. Lett. 39, 6308–6311 (2014a)

    Article  ADS  Google Scholar 

  • Yushko, O.V., Redyuk, A.A., Fedoruk, M.P., Turitsyn, S.K.: Coherent soliton communication lines. JETP 119, 787–794 (2014b)

    Article  ADS  Google Scholar 

  • Zhou, Q., Mirzazadeh, M., Ekici, M., Sonmezoglu, A.: Analytical study of solitons in non-Kerr nonlinear negative index materials. Nonlinear Dyn. 86, 623–638 (2016a)

    Article  MathSciNet  Google Scholar 

  • Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas–Milovic equation by extended trial equation method. Nonlinear Dyn. 84, 1883–1900 (2016b)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Sri Krishna College of Technology, Coimbatore, India

    R. Udaiyakumar

  2. Industrial Engineering Department, College of Engineering, University of Haïl, Haïl City, 2440, Saudi Arabia

    Naim Ben Ali

  3. Photovoltaic and Semiconductor Materials Laboratory, El-Manar University, Le Belvedere, 1002, Tunis, Tunisia

    Naim Ben Ali

  4. Prorogue Research Consultancy, New Delhi, India

    Bhupeshwaran Mani Naicker

  5. Department of Physics, University College of Engineering, Anna University, Ramanathapuram, 623513, India

    M. S. Mani Rajan

  6. Computational Optics Research Group, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    P. Yupapin & I. S. Amiri

  7. Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    I. S. Amiri

Authors
  1. R. Udaiyakumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naim Ben Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bhupeshwaran Mani Naicker
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. S. Mani Rajan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. Yupapin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. I. S. Amiri
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The first and fourth authors as Udaiyakumar and Mani Rajan have given their valuable support to complete the analytical part. The second and third authors as Ben Ali and Bhupeshwaran have made their attempt successfully in the simulation part. The fifth and sixth authors as Amiri and Yupapin have written the paper and have organized the sections.

Corresponding author

Correspondence to I. S. Amiri.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Udaiyakumar, R., Ali, N.B., Naicker, B.M. et al. Analytical and numerical demonstration of phase characteristics on two solitons under the influence of third-order dispersion. Opt Quant Electron 51, 163 (2019). https://doi.org/10.1007/s11082-019-1879-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-019-1879-8

Keywords

Search

Navigation