Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber (original) (raw)
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The theory of the power dependence of the polarization of optical pulses in birefringent optical fibers with Kerr-like nonlinearity is presented in detail. Fundamental discussions are given of the nature of the polarization, and the coupled Schrodinger equations satisfied by the components of the polarization are derived in detail from first principles. It is shown how the Cartesian and circularly polarized field representations relate to each other and to the existing literature. Extensions that include self-steepening and applications to twisted fibers are also given. It is argued that, since high-order solitons evolve on a much shorter length scale, relative to the soliton length, than lower-order solitons, a more useful indication of the significance of dispersion is given by some pulse-compression distance based on the initial compression rate of the pulse, owing to self-phase modulation. This evidence is presented numerically for an initial condition using a 100-W pulse for a fiber having ap = 1.8 X 10-9 as its nonlinear coefficient and assuming an initial pulse width of 3.3 psec. The effect of dispersion and birefringence on a nonlinear pulse with the power equally distributed between the fast (y) and slow (x) axes of a birefringent optical fiber is given for a fiber with an intrinsic birefringence that gives a beat length of 20 m. In the evolution of the fields for zero group-velocity dispersion, it is shown that a portion of the power transfers from the fast axis the slow axis and back and continues to oscillate back and forth between the two. The evolution in the presence of dispersion ((d") = 5 X 10-26) without any intrinsic birefringence shows that this case is close to the standard N = 3 soliton case. In both of the above cases, the structure of the pulse evolves as it travels down the z axis, but there is no overall breakup of the pulse. If both dispersion and the assumed birefringence are present, splitting into two separate pulses is seen, with, in addition, some permanent transfer of energy from the fast to slow mode.
JURNAL ILMU FISIKA | UNIVERSITAS ANDALAS, 2020
Benchmarking of the numerical split-step Fourier method in solving a soliton propagation equation in a nonlinear optical medium is considered. This study is carried out by comparing the solutions calculated by numerics with those obtained by analytics. In particular, the soliton propagation equation used as the object of observation is the nonlinear Schrödinger (NLS) equation, which describes optical solitons in optical fiber. By using the split-step Fourier method, we show that the split-step Fourier method is accurate. We also confirm that the nonlinear and dispersion parameters of the optical fiber influence the soliton propagation.
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.
Wave Motion, 2013
In this paper, the vector-soliton bound states (VSBSs) are investigated for the coupled mixed derivative nonlinear Schrödinger equations, which can describe the pulse propagation in the femtosecond regime of birefringent optical fibers. Symmetric and asymmetric VSBSs with the periodic collisions are obtained and analyzed. The intensity profile and collision period of the bound state are related to the ratio of the real parts of two wavenumbers. The separation factors are introduced in the solutions to linearly adjust the soliton separations. Amplitude-changing collisions between the VSBS and vector bright solitons are also obtained. Via the split-step Fourier method, stability analysis shows that the VSBSs can resist the finite initial perturbations. In addition, the derivative cubic nonlinearity and cubic nonlinearity terms are found to both have no influence on the types of VSBSs, but leads to one-sided compression, center shifts and amplitude decrease of the VSBSs. Energy-exchanging phenomena during the amplitude-changing collisions are not affected, either.