Pulse propagation in optical fiber links with randomness in the dispersion is investigated theoretically and numerically for systems with and without dispersion management. The main effects of locally correlated noise are inevitable pulse destruction and statistical broadening. However, periodic/quasi-periodic management of fiber randomness, achieved by setting the accumulated dispersion to its nominal value (pinning), essentially decreases pulse broadening. If the pinning period is short enough, we observe a statistical state that is numerically indistinguishable from the steady state in the dispersion-managed case.
Solitons in discrete optical systems have been a topic of keen interest over the past decade. In a diffraction managed waveguide array, where the waveguide's diffraction profile is varied periodically in the direction of propagation, the slow evolution of the electric field envelope is modelled by a nonlocal discrete equation that exhibits soliton solutions numerically. In this paper, we verify the validity of the asymptotic approximation, demonstrating that solutions of the averaged equation are close in the l 2 sense to those of the original model for long time scales. Moreover, we prove that the averaged equation has stable ground state solutions, complementing previous experimental and numerical observations. Finally, we show that for a generalization of the averaged equation, ground states of an associated Hamiltonian exist if and only if their l 2 norm exceeds a certain excitation threshold, which depends on the system's dimension and degree of nonlinearity.
The evolution of optical pulses in fiber optic communication systems with strong, higher order dispersion management is modeled by a cubic nonlinear Schrödinger equation with periodically varying linear dispersion at second and third order. Through an averaging procedure, we derive an approximate model for the slow evolution of such pulses, and show that this system possesses a stable ground state solution. Furthermore, we characterize the ground state numerically. The results explain the experimental observation of higher order DM solitons, providing theoretical justification for modern communication systems design.
The problem of existence of ground states in higher-order dispersion managed NLS equation is considered. The ground states are stationary solutions to dispersive equations with nonlocal nonlinearity which arise as averaging approximations in the context of strong dispersion management in optical communications. The main result of this note states that the averaged equation possesses ground state solutions in the practically and conceptually important case of the vanishing residual dispersions.
We present a theoretical and experimental analysis of supercontinuum generation in very short lengths of high-nonlinearity photonic crystal fibers. The Raman response function for Schott SF6 glass is presented for what is believed to be the first time and used for numerical modeling of pulse propagation. Simulation and experiments are in excellent agreement and demonstrate the rapid transition to regimes of spectral complexity due to higher-order nonlinear effects.
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