We present an analytical model of the self- and cross-phase-modulation-induced modulation instabilities in nonlinear, dispersive, homogeneously broadened, unsaturable fiber amplifiers. The rigorous treatment of the gain dispersion and of the gain-induced, near-resonance refractive-index dispersion permits description of the general case of arbitrary detuning between the laser frequency and the resonance and arbitrary bandwidth of the amplifying transition. Simple closed-form expressions are obtained for the combined gain coefficients and, in the self-phase-modulation-induced case only, for the integrated gain. A qualitatively new modulation-instability regime of an isolated wave in the normal group-velocity-dispersion region is described.
© 1998 Optical Society of America
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.4080) Fiber optics and optical communications : Modulation
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.5060) Fiber optics and optical communications : Phase modulation
Todor Mirtchev, "Off-resonant self- and cross-phase-modulation-induced modulation instabilities in single-mode rare-earth-doped fiber amplifiers," J. Opt. Soc. Am. B 15, 171-180 (1998)