Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

Weitian Yu; Qin Zhou; Mohammad Mirzazadeh; Wenjun Liu; Anjan Biswas

doi:10.1016/j.jare.2018.09.001

Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics

J Adv Res. 2018 Sep 7:15:69-76. doi: 10.1016/j.jare.2018.09.001. eCollection 2019 Jan.

Authors

Weitian Yu¹, Qin Zhou², Mohammad Mirzazadeh³, Wenjun Liu^{1

4}, Anjan Biswas^{5

6}

Affiliations

¹ State Key Laboratory of Information Photonics and Optical Communications, School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China.
² School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, China.
³ Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran.
⁴ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
⁵ Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA.
⁶ Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa.

Abstract

In nonlinear optics, the soliton transmission in different forms can be described with the use of nonlinear Schrödinger (NLS) equations. Here, the soliton transmission is investigated by solving the NLS equation with the reciprocal of the group velocity $β_{1} (z)$ , the group velocity dispersion coefficient $β_{2} (z)$ and nonlinear coefficient $γ (z)$ . Two-soliton solutions for the NLS equation are obtained through the Hirota method. According to the solutions obtained, $β_{1} (z)$ and $γ (z)$ with different function forms are taken to study the characteristics of solitons. The effect of the phase shift on the soliton interaction is discussed, and the non-oscillating soliton amplification, which is transmitted in a bound state, is explored. Parabolic solitons with oscillations are analysed. Moreover, parabolic solitons can be reduced to dromion-like structures. Results indicate that the transmission of solitons can be adjusted with the group velocity dispersion and Kerr nonlinearity coefficients. The phase shift, amplification, oscillation and attenuation of solitons can also be controlled by other related parameters. This work accomplishes the theoretical study of transmission characteristics of optical solitons in spatially dependent inhomogeneous optical fibres. The conclusions of this research have theoretical guidance for the research of optical amplifier, all-optical switches and mode-locked lasers.

Keywords: Amplification; Attenuation; Oscillation; Solitons; vcNLS.