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Journal of the Optical Society of America B

Off-resonant self- and cross-phase-modulation-induced modulation instabilities in single-mode rare-earth-doped fiber amplifiers

T. Mirtchev

Published Jan 1, 1998• 8 citations
Publisher

Abstract

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.

DOI
10.1364/josab.15.000171

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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.
Presents an analytical model which describes the dynamics of the modulation instability in a nonlinear, dispersive, homogeneously broadened and nonsaturable fiber amplifiers. The general case of arbitrary detuning between the laser frequency and the resonance frequency and arbitrary bandwidth of the amplifying transition is treated. The model accounts both for the gain dispersion and for the gain-induced, near resonant refractive index dispersion, Simple closed form expressions for the combined gain coefficients of the Stokes and anti-Stokes frequencies are obtained.
We investigate analytically the occurrence of modulation instability in doped fiber lasers and amplifiers using a Maxwell–Bloch description for the dopants and without making the usual parabolic-gain approximation. We find a new modulation instability occurring near the Rabi frequency, which is not predicted by the conventional complex Ginzburg–Landau model. We discuss the implications of this new instability for fiber amplifiers and lasers and analyze the effects of the saturable host absorption on the laser instabilities. Atomic detuning is shown to significantly enhance the new modulation instability, in both the normal- and the anomalous-dispersion regimes.
The temporal envelope profile and the phase of a steady-state pulse propagating through a resonant medium in the presence of nonresonant nonlinearity are derived. The formation of solitonlike pulses takes place as a result of the balance of the self-phase modulation generated by nonresonant nonlinearity and the nonlinear resonant group-velocity dispersion induced by the self-induced-transparency effect in a resonant medium. Self-phase-modulation action leads to distortion of the pulse when its power and inverse duration exceed the critical values Pcr and τcr-1. We show the destructive role of self-phase modulation in the case of self-induced-transparency pulse generation in a laser with erbium-doped fiber as an intracavity coherent absorber.
This paper reports the measurement and analysis of signal power-induced changes in the refractive index spectrum of an aluminosilicate erbium-doped fiber amplifier (EDFA). For a constant 980 nm pump power of 11 mW, a 1553 nm signal power of 4.6 mW caused a peak-to-trough change in refractive index of (3.8/spl plusmn/0.4)/spl times/10/sup -8/ across the EDFA gain spectrum. A Kramers-Kronig transform of the signal-induced change in absorption coefficient agreed well with the measured change in refractive index. This result conflicts with the behavior of the system predicted by a homogeneously broadened two-level model and suggests limitations in the representation of the Er/sup 3+/:glass system by a discrete set of homogeneously broadened transitions.
Gain dynamics and refractive index changes in fiber amplifiers are important in many areas. For example, the knowledge of the frequency responses for seed and pump power modulation are required to actively stabilize low noise fiber amplifiers. Slow and fast light via coherent population oscillations rely on the change of group index to delay or advance pulses, and refractive index changes in fiber amplifiers are a possible explanation for mode fluctuations in high power fiber amplifiers. Here, we analyze the frequency dependent influence of seed and pump power modulation on the fiber amplifier output power and the refractive index. We explain the observed power and refractive index modulation with an analytic model originally developed for telecom amplifiers and discuss a further simplification of the model.
A novel measurement system provides determination of pump induced phase shifts in erbium doped fibers with an accuracy of /spl sim//spl pi//20. Using this system, a systematical analysis of the pump induced modulation of the refractive index and dispersions for a signal at 1550 nm and a pump at 980 nm is reported. The analysis contains measurements of pump induced refractive index changes as function of wavelength, pump power, and doping concentration. A model taking account of the contribution to the refractive index changes from optical transitions between /sup 4/I/sub 15/2/ states and /sup 4/I/sub 13/2/ states in Er/sup 3+/ yields good agreement to experimental results apart from a wavelength independent offset. The offset is interpreted to originate from high energetic optical transitions. The results show that for a large refractive index modulation, a short and highly doped fiber should be used with limited amplified spontaneous emission effect. In optical communication systems comprising erbium doped fiber amplifiers, a tradeoff between dispersion and amplification must be made.