Propagation and interaction between special fractional soliton and soliton molecules in the inhomogeneous fiber.

INTRODUCTION: Fractional nonlinear models have been widely used in the research of nonlinear science. A fractional nonlinear Schrödinger equation with distributed coefficients is considered to describe the propagation of pi-second pulses in inhomogeneous fiber systems. However, soliton molecules based on the fractional nonlinear Schrödinger equation are hardly reported although many fractional soliton structures have been studied. OBJECTIVES: This paper discusses the propagation and interaction between special fractional soliton and soliton molecules based on analytical solutions of a fractional nonlinear Schrödinger equation. METHODS: Two analytical methods, including the variable-coefficient fractional mapping method and Hirota method with the modified Riemann-Liouville fractional derivative rule, are used to obtain analytical non-travelling wave solutions and multi-soliton approximate solutions. RESULTS: Analytical non-travelling wave solutions and multi-soliton approximate solutions are derived. The form conditions of soliton molecules are given, and the dynamical characteristics and interactions between special fractional solitons, multi-solitons and soliton molecules are discussed in the periodic inhomogeneous fiber and the exponential dispersion decreasing fiber. CONCLUSION: Analytical chirp-free and chirped non-traveling wave solutions and multi-soliton approximate solutions including soliton molecules are obtained. Based on these solutions, dynamical characteristics and interactions between special fractional solitons, multi-solitons and soliton molecules are discussed. These theoretical studies are of great help to understand the propagation of optical pulses in fibers.

Gold Nanorods as Saturable Absorber for Harmonic Soliton Molecules Generation.

Gold nanorods (GNRs) has been investigated in the field of chemistry, optoelectronics, and medicine for their tenability, compatibility, electromagnetics, and excellent photonics properties. Especially, GNRs, used to generate ultrashort pulse, have been studied recently. However, multiple pulses evolution based on GNRs needs to be further explored. In this article, GNRs are synthesized by seed-mediated growth method, characterized systematically and been chosen as saturable absorber (SA) to apply in ultrafast photonics. The GNRs SA presents a saturable intensity of 266 MW/cm2, modulation depth of 0.6%, and non-saturable loss of 51%. Furthermore, a passively mode-locked erbium-doped fiber laser based on GNRs SA with femtosecond pulse is demonstrated. Thanks to the excellent properties of GNRs, by adjusting the cavity polarization direction with the proposed GNRs SA, soliton molecules operation with spectrum modulation period of 3.3 nm and pulse modulation interval of 2.238 ps is directly obtained. For the most important, 9th-order harmonic soliton molecules have been generated in the laser cavity for the first time. It is demonstrated that GNRs can be a novel type of non-linear optical (NLO) device and have potential applications in the field of ultrafast photonics.