Similaritons in nonlinear optical systems

Abstract

By using the lens-type transformation, exact soliton and quasi-soliton similaritons are found in (1+1), (2+1) and (3+1)-dimensional nonlinear Schrödinger equations in the context of nonlinear optical fiber amplifiers and graded-index waveguide amplifiers. The novel analytical and numerical results show that, in addition to the exact solitonic optical waves, quasi-solitonic optical waves with Gaussian, parabolic, vortex and ring soliton profiles can evolve exact self-similarly without any radiation.

Controllable optical rogue waves: Recurrence, annihilation and sustainment

“…To find this kind of analytic solution for Eq. (1), we employ the lens-type transformation [26][27][28][29][30][31],…”

Spatial solitons in a medium with lumped amplification and dissipation

“…The standard variational approach for the dissipative system is given by [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] ∂ ∂z…”

“…It is a powerful method for the amplification and focusing of spatial solitons to overcome inevitable energy losses. [24][25][26] It was shown that highly efficient and distortionless amplification can be realized through the similaritons. 27 This work analyzes the dynamics of (2+1)D spatial solitons in dissipative graded index Kerr media.…”

Self-similar propagation in a graded-index nonlinear-fiber amplifier with an external source

“…The first issue is the discovery of exact self-similar waves, which are mainly described by the exact solitary wave solutions, including bright and dark soliton solutions, quasisoliton solutions, solitary nonlinear Bloch waves, and solitons on the continuous-wave background [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The other is the asymptotic self-similar waves, which are mainly described by the compact parabolic, Hermite, Gaussian, and hybrid functions in which the parabolic self-similar solutions are more intriguing because they can be easily generated from arbitrary input optical waves and retain robustness for the higher initial power [18][19][20][21][22][23][24][25][26]. In particular, exact self-similar solitary waves have been found in optical fibers for variable dispersion, nonlinearity, and gain profile, but the functional forms of these parameters cannot be chosen independently [8,9].…”