The existence and stability of fundamental, dipole, and tripole solitons in Kerr nonlinear media with parity-time symmetric Gaussian complex potentials are reported. Fundamental solitons are stable not only in deep potentials but also in shallow potentials. Dipole and tripole solitons are stable only in deep potentials, and tripole solitons are stable in deeper potentials than for dipole solitons. The stable regions of solitons increase with increasing potential depth. The power of solitons increases with increasing propagation constant or decreasing modulation depth of the potentials.
We investigate the nonlinear dynamics of (1+1)-dimensional optical beam in the system described by the space-fractional Schrödinger equation with the Kerr nonlinearity. Using the variational method, the analytical soliton solutions are obtained for different values of the fractional Lévy index α. All solitons are demonstrated to be stable for 1<α≤2. However, when α=1, the beam undergoes a catastrophic collapse (blow-up) like its counterpart in the (1+2)-dimensional system at α=2. The collapse distance is analytically obtained and a physical explanation for the collapse is given.
The fractional Fourier transform ͑FRFT͒ naturally exists in strongly nonlocal nonlinear ͑SNN͒ media and the propagation of optical beams in SNN media can be simply regarded as a self-induced FRFT. Through the FRFT technique the evolution of fields in SNN media can be conveniently dealt with, and an arbitrary square-integrable input field presents itself generally as a revivable higher-order spatial soliton which reconstructs its profile periodically after every four Fourier transforms. The self-induced FRFT illuminates the prospects for SNN media in new applications such as continuously tunable nonlinearity-induced FRFT devices.
Nonlocal spatial optical solitons 4.1 Introduction to optical soliton researchAs an introduction to the subject of nonlocal spatial optical solitons, in this section we briefly introduce the history of optical soliton research and the related basic concepts, which include the optical Kerr effect and its spatial and temporal nonlocality, the model of nonlinear slowly varying optical envelopes, the solution of the model, and its physical connotation, etc. This section is the basis to read and understand the following sections. Historical background of optical solitonsAlmost all of the literatures related to solitons mention the story that the famous British engineer Russell observed the soliton (water) wave for the first time in a canal in 1834 [1]. However, the history of optical soliton is not as long as that of the mechanical soliton. In fact, since the Japanese scholar Hasegawa theoretically predicted the possibility of the existence of optical solitons in 1973 [2,3], the research on optical solitons has just stepped into its forties.So what is "soliton" exactly? We usually call the local traveling-wave solutions¹ of the nonlinear wave equation as "solitary waves," and the stable solitary waves, which do not disappear after mutual collision and are without any change or with only slight change in the shape and propagation speed (like the case of the two-particle collisions), are called solitons. The so-called optical solitons are local optical waves (optical envelopes) that propagate in optical nonlinear media, and include temporal optical solitons, spatial optical solitons, and spatiotemporal optical solitons. On one hand, the optical pulse broadens when propagating in an optical waveguide due to dispersion effect; correspondingly, the optical beam diverges during its propagation because of the diffraction effect. On the other hand, due to the self-induced nonlinear refractive index, the optical pulse is compressed (or the optical beam is focused). The 1 Local solutions refer to the solutions of nonlinear differential equations in the confined space (or time) area, and such solutions tend to zero or constant at infinity. UnauthenticatedDownload Date | 6/26/16 1:39 AM temporal (or spatial) optical soliton is a stable propagation state for the optical pulse (or optical beam) when the linear dispersion (or diffraction) effect balances the nonlinear effects precisely and thus the pulse duration (or beam width) keeps invariant. As the name suggests, the spatiotemporal optical soliton is a stable propagation state of optical pulsed beam whose shape keeps invariant in three-dimensional spatiotemporal coordinates (three dimensions are left when one dimension of propagation-direction is removed from the four-dimensional space-time). A. Temporal optical solitonsThe optical solitons firstly predicted theoretically [2] and observed experimentally [4] are temporal optical solitons.² In 1973, Hasegawa and Tappert published their pioneering work on the optical soliton research. They studied the propagation of optical pulse i...
The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with nonlocal nonlinearity are reported. It is found that nonlocality can expand the stability region of defect solitons. For positive or zero defects, fundamental and dipole solitons can exist stably in the semi-infinite gap and the first gap, respectively. For negative defects, fundamental solitons can be stable in both the semi-infinite gap and the first gap, whereas dipole solitons are unstable in the first gap. There exist a maximum degree of nonlocal nonlinearity, above which the fundamental solitons in the semi-infinite gap and the dipole solitons in the first gap do not exist for negative defects. The influence of the imaginary part of the PT-symmetric potentials on soliton stability is given. When the modulation depth of the PT-symmetric lattices is small, defect solitons can be stable for positive and zero defects, even if the PT-symmetric potential is above the phase transition point.
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