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Asymptotic Analysis of Pulse Dynamics in Mode‐Locked Lasers
Author(s) -
Ablowitz Mark J.,
Horikis Theodoros P.,
Nixon Sean D.,
Zhu Yi
Publication year - 2009
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2009.00441.x
Subject(s) - amplitude , adiabatic process , physics , soliton , nonlinear schrödinger equation , nonlinear system , perturbation theory (quantum mechanics) , perturbation (astronomy) , pulse (music) , schrödinger equation , classical mechanics , quantum electrodynamics , quantum mechanics , voltage
Solitons of the power‐energy saturation (PES) equation are studied using adiabatic perturbation theory. In the anomalous regime individual soliton pulses are found to be well approximated by solutions of the classical nonlinear Schrödinger (NLS) equation with the key parameters of the soliton changing slowly as they evolve. Evolution equations are found for the pulse amplitude(s), velocity(ies), position(s), and phase(s) using integral relations derived from the PES equation. The results from the integral relations are shown to agree with multi‐scale perturbation theory. It is shown that the single soliton case exhibits mode‐locking behavior for a wide range of parameters, while the higher states form effective bound states. Using the fact that there is weak overlap between tails of interacting solitons, evolution equations are derived for the relative amplitudes, velocities, positions, and phase differences. Comparisons of interacting soliton behavior between the PES equation and the classical NLS equation are also exhibited.