Optical Bullets and Their Modulational Instability Analysis

Abstract

The current work is devoted to investigating the multidimensional solitons known as optical bullets in optical fiber media. The governing model is a (3+1)-dimensional nonlinear Schrödinger system (3D-NLSS). The study is based on deriving the traveling wave reduction from the 3D-NLSS that constructs an elliptic-like equation. The exact solutions of the latter equation are extracted with the aid of two analytic approaches, the projective Riccati equations and the Bernoulli differential equation. Upon applying both methods, a plethora of assorted solutions for the 3D-NLSS are created, which describe mixed optical solitons having the profiles of bright, dark, and singular solitons. Additionally, the employed techniques provide several kinds of periodic wave solutions. The physical structures of some of the derived solutions are depicted to interpret the nature of the medium characterized by the 3D-NLSS. In addition, the modulation instability of the discussed model is examined by making use of the linear stability analysis.

Optical Bullets and Domain Walls with Cross Spatio-Dispersion and Having Kudryashov’s form of Self-Phase Modulation

“…The key principle of the sustainment of optical solitons, optical dromions, optical bullets and domain walls is the existence of a delicate balance between Chromatic Dispersion (CD) and Self-Phase Modulation (SPM). There has been a deluge of results that have been reported on such forms of pulses which were established based on this fundamental principle [1][2][3][4][5][6][7][8][9][10]. The current paper moves a couple of steps further.…”

“…Within the scope of this work, we explore the extended (3 + 1)-dimensional NLSE, which is structured based on Kudryashov's form of SPM, as described below [1,2,3,9] ( )…”

“…That being said, if b 1 = b 2 = 0, the dual-power law nonlinearity manifests itself in the extended (3 + 1)-dimensional NLSE. Both the field envelope, given as q = q(x, y, z, t), and the chromatic (1) dispersion, represented by a 1 , are included in this equation. This equation's linear temporal evolution of the field comes from the first term, with i = 1 − .…”

“…The technique [4] will be extensively explained in this section, showcasing its application in obtaining domain walls and singular soliton solutions for equation (1). Following the principles of the homogeneous balance method, equation ( 9) is found to have a solution represented by: ( ) ( )…”