By M. F. Mahmood, Computational Science and Engineering Research Center, Howard University, Washington, DC 20059

Abstract The trapping behavior of two chirped solitons forming a bound state in a single-mode birefringent fiber is investigat­ed on the basis of a model of coupled nonlinear Schroedinger equations. The positive initial chirp plays an important role in controlling the threshold amplitude for soliton trapping without causing excessive pulse broadening.

A significant amount of progress has been achieved in fast-acting soliton based telecommunication systems. In the anomalous dispersion regime of a fiber, group-velocity dis­persion and nonlinear self-phase modulation cooperate in such a way that the fiber can support solitons. Solitons pre­sent a unique opportunity for performing a range of all-optical processing functions in nonlinear optical fibers. This observation is based on the fact that, even in nonlin­ear fiber systems that have no exact solitons, an injected soliton like pulse displays a remarkable degree of phase coherence over the whole pulse making it possible to iden­tify each soliton bit as an information carrier for high data rate transmission (5 Gbits/sec or more) over long dis­tances. The door for long distance optically amplified com­munications will soon be opened with the installation of the transoceanic systems TAT 12/13 and TPC.1

Optical fibers commonly exhibit an anisotropic effect known as birefringence as a result of which the fundamen­tal mode of a single-mode fiber splits up into two orthogo­nal polarization modes through the Kerr effect. The bire­fringence in fibers leads to walk-off between the pulses in orthogonal polarizations. The effect is observable when two optical modes are propagating in a birefringent optical fiber, so most of the theoretical models have been in the form of coupled nonlinear Schroedinger (CNLS) equations.2-9 The localized solitary pulse evolution in a highly birefringent fiber has been studied theoretically6 and experimentally7 on the basis of a model of CNLS equations without the oscillating terms arising from nonlinear polar­ization, under the assumption that the two polarizations exhibit different group-velocities. It is found that above a certain threshold amplitude, the two partial pulses of equal amplitudes trap one another through cross-phase modula­tion and propagate as a single two-component pulse in a highly birefringent fiber. In this situation, the two polariza­tions shift their central frequencies to make their group-velocities equal.

Optical pulses generated from semiconductor lasers are, often accompanied by an initial frequency chirp. It is expected that initial frequency chirp can affect the soliton-trapping propagation behavior making it possible to realize soliton-trapping gates using a simple combination of semi­conductor lasers and optical amplifiers. Earlier theoretical studies of soliton interactions in highly birefringent fibers considered the case of chirp free solitons and no account was taken of the effects of initial frequency chirp.

This note presents an essence of nonlinear propaga-

tion of frequency chirped optical solitons in a highly bire-fringent fiber in terms of a model of CNLS equations.2,6,8

An adiabatic approach using a time-averaged variational principle8-10 is followed to analyze the nonlinear coupling of chirped soliton pulses in the two polarizations. Starting with the CNLS equations 2

in conjunction with the following initial conditions

on the pulses in each polarization having the same ampli­tude A and chirp parameter C; and using NLS solitons as trial functions in an averaged Lagrangian formulation, a set of coupled ordinary differential equations (ODEs) is derived to obtain a threshold amplitude

for soliton trapping to form a bound state in a highly bire-fringent singlemode fiber.

The chirp could be positive or negative with respect to pulse broadening. For the transmission of a 5 psec pulse, typical values for δ, the relative group velocity of the two modes determined by the birefringence lie in the range 0.3-3.0. For birefringent fibers ε = ⅔ example if one chooses δ = 0.5 and sets C = 0.07, soliton trapping can be facilitated at a threshold amplitude as low as A = 0.83 given by (3) as compared to A = 0.93 in the absence of initial frequency chirp.6 Also, too much initial chirp can be detrimental to a soliton transmission system. In other words, threshold amplitude for soliton trapping can be controlled by varying the chirp parameter without causing excessive pulse broad­ening and to enable soliton trapping even at low optical power threshold. This study should be of considerable interest to the experimental effort on soliton ring networks.

Acknowledgments This work was partially sponsored by the Army High Performance Computing Research Center under the aus-

Engineering & Laboratory Notes

Chirped Optical Solitons in Single-mode Birefringent Fibers

Engineering & Laboratory Notes

pices of the Department of Army, Army Research Laboratory cooperative agreement number DAAH 04-95-2-0003/con-tract number DAAH 04-95-C-0008.

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