Erbium Laser Model for Two-Wavelength Operation

(Received 25 April 1994, revised 25 October 1994, accepted 9 December 1994)

Abstract
A theoretical modeling of dual wavelength operation of erbium-doped fibre lasers is presented. The model is a generalization of the one used in the single mode theory, based on the existence of isolated ions and ion pairs coupled via the laser field. Analytical results are obtained in the steady state. The linear stability analysis of the coupled equations shows the existence of two pairs of complex conjugate eigenvalues and two real negative eigenvalues. These results imply that the system is driving by two frequencies : one associated with the classical relaxation oscillation and a low frequency characteristic of a bimodal system. When the ion pair concentration is increased, the real part of one pair of conjugate eigenvalues becomes positive. In such a situation, self-pulsing and chaotic dynamics occur together with antiphase effects between two mode intensities. Locking of the low frequency on a subharmonic of the high frequency is also obtained leading to nT-periodic orbits.