Suppression of symmetry-breaking bifurcations of optical solitons in parity-time symmetric potentials

Abstract

Optical soliton refers to any optical field that maintains its special structure during propagation because of the balance between diffraction and self-phase modulation of the medium. The dynamics of optical solitons are investigated comprehensively due to their fundamental structures and potential applications. In particular, optical solitons play an important role in fiber optic communication system that uses pulses of infrared light to transmit information from one place to another over a long distance. The propagation of the electromagnetic wave in optical fibers is modeled by the cubic-quintic nonlinear Schrödinger (CQNLS) equation iΨ_z+Ψ_{xx}+α|Ψ|^2Ψ+β|Ψ|^4Ψ=0, where Ψ(x,z) is normalized complex-valued slowly varying pulse envelope of the electric field, z is the scaled propagation distance, x is the transverse coordinate, Ψ_{xx} corresponds to diffraction, α and β are the coefficients of cubic and quintic nonlinearities, respectively. A higher-order dispersion needs to be considered for performance enhancement along trans-oceanic and trans-continental distances. Fourth order dispersion needs to be taken into account for short pulse widths where the group velocity dispersion changes within the spectral bandwidth of the signal. In addition, it is known from many studies in the literature that an external potential added to the system can be also beneficial for performance improvement. In this thesis, we consider the nonlinear paraxial beam propagation in cubic-quintic nonlinearity with a complex parity-time (PT) symmetric potential and fourth order dispersion. This propagation is modeled by the following CQNLS equation iΨ_z+Ψ_{xx}−γΨ_{xxxx}+V(x)Ψ+α|Ψ|^2Ψ+β|Ψ|^4Ψ=0, where γ>0 is the coupling constant of the fourth order dispersion, V(x) represents a complex PT-symmetric potential. In this thesis, we consider PT-symmetric potentials that are of the form V(x)=g^2(x)+c0*g(x)+ig′(x) where g(x) is an arbitrary real and even function, c0 is an arbitrary real constant and PT-symmetric solitons undergo symmetry breaking. We take a localized double-hump function g(x) in the form of g(x)=A*[exp(−(x+x0)^2)+exp(−(x−x0)^2)] where A and x0 are related to the modulation strength and separation of PT-symmetric potential, respectively. The soliton solutions of CQNLS equation with fourth order dispersion and a complex PT-symmetric potential are numerically obtained by means of the squared-operator method since the equation is nonintegrable. The linear stability analysis of the numerically obtained solitons is examined by linear spectrum analysis and the nonlinear stability analysis is examined by nonlinear evolution with split-step Fourier method. The existence of symmetry breaking of solitons and suppression of symmetry-breaking bifurcations have been investigated. To examine the effect of fourth order dispersion on this symmetry breaking, the coefficient of fourth order dispersion γ is incremented gradually. Consequently, we have demonstrated that the symmetry-breaking bifurcation of the solitons in this problem is completely suppressed as the strength of the fourth order dispersion increases. Moreover, increasing the strength of fourth order dispersion positively influences the linear and nonlinear stability behaviors of solitons.