Numerical Modeling of Solitons in a Low Birefringent Optical Fiber (original) (raw)
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Optik - International Journal for Light and Electron Optics, 2009
In this paper, the results of numerical analysis are demonstrated for sech pulse (soliton) propagation in a birefringent optical fiber using computer modeling and simulation. Here, the initial pulse is polarized linearly and guided into the fiber at an angle of 451 to its polarization axes. The birefringence-induced time delay of 200 and 440 ps between X and Y polarization components has been reported at a fiber length of 631.72 km (10 soliton periods) by considering linear and nonlinear regimes, respectively. The Kerr nonlinearity, which stabilizes solitons against spreading due to GVD, also stabilizes them against splitting due to birefringence. A similar fact is true for the birefringent walk-off. Above a certain soliton order (N th), the evolution scenario is qualitatively different and two orthogonally polarized components of the soliton move with a common group velocity despite their different modal indices or polarization mode dispersion (PMD) at a fiber length of 631.72 km (10 soliton periods) and 1264.344 km (20 soliton periods) over a nonlinear regime at y6 ¼451. The physical effect responsible for this type of behavior is the cross-phase modulation (XPM) between the two polarization components.
Journal of The Optical Society of America B-optical Physics, 1999
In dual-core fibers the variation of the coupling coefficient with frequency leads to intermodal dispersion that perturbs the switching of ultrashort pulses. Using a new version of the split-step Fourier method based on a model that includes intermodal dispersion, we show that this effect cannot be neglected when the switching of picosecond solitons at different wavelengths in half-beat twin-core fiber couplers is analyzed, although picosecond solitons at the central wavelength are not significantly affected. We also show that to study the switching of wavelength-division-multiplexed solitons one should always take into account the effect of intermodal dispersion.
Polarization dynamics and interactions of solitons in a birefringent optical fiber
Physical Review A, 1991
Dynamics of vector solitons are studied within the framework of the general model of coupled nonlinear Schrodinger equations. The analysis is based upon the perturbation theory for the case when the system is close to the exactly integrable Manakov form. Evolution of the soliton's polarization, coupled by the linear-birefringence terms (which take account of the difference in the group velocity between two linearly polarized modes) to the positional degree of freedom of the soliton, is studied. A four-dimensional dynamical system for the two coupled degrees of freedom integrates to a two-dimensional conservative system. Depending on the value of an arbitrary integration constant, there are four different types of the phase portrait of the latter system. For each value of the polarization angle, there exist two stationary vector solitons, at least one of them being stable. Generic trajectories on the two-dimensional phase plane correspond to oscillations of the polarization coupled to oscillations of the position of the soliton. A generalized model including the polarization-rotating linear coupling is also analyzed. Next, interaction of two slightly overlapping vector solitons is considered, and it is demonstrated that a stable bound state is possible. A stable periodic chain of the slightly overlapping solitons is also found. Finally, radiative decay of a vector soliton is investigated for the case when it has a large component in one subsystem and a small component in another subsystem.
Soliton switching and propagation in nonlinear fiber couplers: analytical results
Journal of the Optical Society of America B, 1993
The propagation and the switching of solitons in nonlinear optical fiber couplers have been investigated with a variational method within the framework of the Lagrangian density formulation. Simple analytical solutions have been found to the coupled nonlinear Schrodinger equations that govern the soliton propagation in a nonlinear fiber coupler. It is shown that the soliton propagation and switching behavior predicted by the present analytical method agrees well with results from numerical analysis. In particular, we found that the present analysis is accurate in predicting soliton switching from one core to the other. In addition, our analysis leads us to the discovery of new soliton eigenstates and to the determination of the bifurcation behavior of solitons in nonlinear fiber couplers.
2021
In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show
Optical solitons in birefringent fibers with spatio-temporal dispersion
Optik, 2014
This paper studies the propagation of solitons through birefringent fibers in the presence of spatiotemporal dispersion. Both Kerr and parabolic laws of nonlinearity are addressed. The exact 1-soliton solutions are obtained. There are several constraint conditions that ensure soliton solutions are derived. Three types of solitons are obtained: bright, dark and singular solitons.
Optical solitons: Mathematical model and simulations
Optical solitons travel in nonlinear dispersive optical fiber that can mathematically modeled by forced nonlinear Schrödinger Equation (fNLS). A precise numerical simulation is employed to simulate optical solitons travel based on the mathematical model equation modeled in ideal lossless fiber and fiber loss. The outcomes from simulations further clarify the effects of fiber loss during transmission of signal which distorted the balanced effects between self-phase modulation (SPM) and group velocity dispersion (GVD) in nonlinear optical fiber with fiber. Furthermore, the outcomes have met the agreement with the simulation done by engineering software.
Resonant splitting of a vector soliton in a periodically inhomogeneous birefringent optical fiber
Physical review, 1994
We analyze the dynamics of a two-component (vector) soliton in a model of a birefringent nonlinear optical fiber with a periodic spatial modulation of the birefringence parameter (group velocity difference). Evolution equations for the parameters of the vector soliton are derived by means of a variational technique. Numerical simulations of these equations demonstrate that the critical modulation amplitude necessary for splitting, regarded as a function of the soliton s energy, has a deep minimum very close to the point at which direct resonance takes place between the periodic modulation and an internal eigenmode of the vector soliton in the form of small relative oscillations of the centers of the two components. A shallower minimum, which can be related to another internal eigenmode of the vector soliton, is also found. We further briefly consider the internal vibrations of the vector soliton driven by a constant force, which corresponds to the birefringence growing linearly with propagation distance. The effect predicted has practical relevance to ultrashort (femtosecond) optical solitons, and it can be employed in the design of fiber-optical logic elements.
Femtosecond soliton pulses in birefringent optical fibers
Journal of The Optical Society of America B-optical Physics, 1997
We consider femtosecond soliton-pulse propagation in a birefringent optical fiber where rapidly oscillating terms, the difference in polarization dispersions, and the difference in group velocities of the two polarization components have to be taken into account. We demonstrate the existence of a novel class of linearly polarized soliton states (with the linear polarization ranging from 0 to 2). We also find the elliptically polarized soliton states, which do not appear to be acceptable to the coupled nonlinear Schrödinger equations describing the pulse evolution in the birefringent fiber when the different dispersions between the two polarizations are ignored and the group-velocity difference is taken into account. More importantly, the corresponding stability analysis reveals that within certain operating regions the fast soliton can be stable and the slow soliton can be unstable, whereas in the others the fast soliton is unstable and the slow soliton is stable, in contrast to those reported earlier by neglecting different polarization dispersions. On the other hand, both the linearly polarized soliton states and the elliptically polarized soliton states are found to be unstable. This indicates that for high-capacity coherent soliton communication in the femtosecond regime, the pulse must be launched along either the slow or the fast axis of a practical polarization-maintaining fiber. Finally, the potential applications of weakly unstable linearly polarized soliton states for ultrafast soliton switching are discussed.
Optical and Quantum Electronics, 2021
In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations