STUDY OF THE EXISTENCE AND STABILITY OF SPATIAL SOLITON BEAMS IN HIGHER-ORDER NONLINEAR OPTICAL FIBERS WITH GAIN AND LOSS
DOI:
https://doi.org/10.18173/2354-1059.2026-0032Keywords:
Nonlinear optical fiber, higher-order nonlinear medium, dissipative solitons, nonlinear Schrödinger equation, numerical methodsAbstract
In this paper, we employ an integrated numerical procedure for computing spatial soliton beams, or stable nonlinear guided modes, in non-Hermitian photonic waveguides. The physical systems considered here are higher-order nonlinear optical fibers with step-index (SI) and graded-index (GRIN) profiles. The fiber material exhibits appreciable two-photon absorption, which acts as a nonlinear loss mechanism. To obtain stable guided modes in these fibers, external pumping is introduced to provide linear gain. Starting from prescribed input optical beams, we obtain stable fundamental and vortex beams after sufficiently long propagation in the nonlinear fibers. These nonlinear dissipative modes are formed through a balance among diffraction, nonlinear effects, gain, and loss. The numerical results show that fundamental beams can be stabilized in both SI and GRIN fibers, whereas stable vortex beams are supported only in the GRIN fiber. The numerical contribution is the coordinated three-stage continuation procedure rather than any of the individual algorithms: conservative stationary seeds are first generated, gain and nonlinear loss are then introduced adiabatically, and the resulting dissipative states are finally validated by long-distance propagation with fixed parameters, including perturbation tests. The different vortex behavior in the two profiles indicates that the smooth radial confinement of the GRIN potential is important for preserving the annular vortex structure, whereas the flat SI core does not provide the same distributed restoring confinement.
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