Nonlinear Dynamics of Mode-locking Optical Fiber Ring Lasers

We consider a model of a mode-locked fiber ring laser for which the evolution of a propagating pulse in a birefringent optical fiber is periodically perturbed by rotation of the polarization state owing to the presence of a passive polarizer. The stable modes of operation of this laser that correspond to pulse trains with uniform amplitudes are fully classified. Four parameters, i.e., polarization, phase, amplitude, and chirp, are essential for an understanding of the resultant pulse-train uniformity. A reduced set of four coupled nonlinear differential equations that describe the leading-order pulse dynamics is found by use of the variational nature of the governing equations. Pulse-train uniformity is achieved in three parameter regimes in which the amplitude and the chirp decouple from the polarization and the phase. Alignment of the polarizer either near the slow or the fast axis of the fiber is sufficient to establish this stable mode locking.

[1]  William L. Kath,et al.  Hamiltonian dynamics of solutions in optical fibers , 1991 .

[2]  W. Kath,et al.  Pulse propagation in nonlinear optical fiber lines that employ phase-sensitive parametric amplifiers , 1994 .

[3]  M. Fermann,et al.  Passive mode locking by using nonlinear polarization evolution in a polarization-maintaining erbium-doped fiber. , 1993, Optics letters.

[4]  J. Nathan Kutz,et al.  Stability of Pulses in Nonlinear Optical Fibers Using Phase-Sensitive Amplifiers , 1996, SIAM J. Appl. Math..

[5]  Hermann A. Haus,et al.  Additive-pulse modelocking in fiber lasers , 1994 .

[6]  M. H. Ober,et al.  Mode locking with cross-phase and self-phase modulation. , 1991, Optics letters.

[7]  S. R. Bolton,et al.  Period doubling and quasi-periodicity in additive-pulse mode-locked lasers. , 1995, Optics letters.

[8]  G. Stegeman,et al.  Polarized soliton instability and branching in birefringent fibers , 1989 .

[9]  W. Kath,et al.  Stabilizing dark solitons by periodic phase-sensitive amplification. , 1996, Optics letters.

[10]  Keren Bergman,et al.  Polarization-locked temporal vector solitons in a fiber laser: experiment , 2000 .

[11]  Akira Hasegawa,et al.  Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion , 1973 .

[12]  Philip Holmes,et al.  Dynamics and Bifurcations of a Planar Map Modeling Dispersion Managed Breathers , 1999, SIAM J. Appl. Math..

[13]  L Grüner-Nielsen,et al.  Demonstration of massive wavelength-division multiplexing over transoceanic distances by use of dispersion-managed solitons. , 2000, Optics letters.

[14]  J. N. Kutz,et al.  Hamiltonian dynamics of dispersion-managed breathers , 1998 .

[15]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[16]  J. Kutz,et al.  Pulse-train uniformity in optical fiber lasers passively mode-locked by nonlinear polarization rotation , 2000, IEEE Journal of Quantum Electronics.

[17]  H. Haus,et al.  Self-starting additive pulse mode-locked erbium fibre ring laser , 1992 .

[18]  S. V. Manakov.  On the theory of two-dimensional stationary self-focusing of electromagnetic waves , 1973 .