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IEEE Journal of Quantum Electronics

Output Phase Characteristics of a Nonlinear Regenerative Fiber Amplifier

Christopher J. Corcoran, Kenneth A. Pasch

Published May 24, 2007• 15 citations
Publisher

Abstract

A simple regenerative fiber amplifier with a nonlinear refractive index is described and analyzed. Using standard equations of operation, we model the circulating intensity within the resonant cavity and determine the nonlinear phase response to changes in this intensity over the entire range of initial cavity detuning. Simple stability criteria are established and described. It is shown that the presence of sufficient nonlinearity leads to stable regions of operation with consistent phase-intensity relationships. Based on these results, the phase of the amplifier output is predicted relative to the injected field for the entire range of initial detuning

DOI
10.1109/jqe.2007.893899

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A simple regenerative fiber amplifier with a nonlinear refractive index is described and analyzed. Using standard equations of operation, we model the circulating intensity within the resonant cavity and determine the nonlinear phase response to changes in this intensity over the entire range of initial cavity detuning. Simple stability criteria are established and described. It is shown that the presence of sufficient nonlinearity leads to stable regions of operation with consistent phase-intensity relationships. Based on these results, the phase of the amplifier output is predicted relative to the injected field for the entire range of initial detuning
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.
We present an analytic and numerical analysis of regenerative oscillation in the lossless nonlinear Fabry-Perot based on a semiclassical model. We show that unstable positive slope regions may exist along all branches of the steady-state transfer curve which lead to regenerative oscillation or to precipitation to lower branches. The stability of these oscillations is analyzed in terms of the dynamic behavior of the nonlinear index. Our analytic expressions for the period, amplitude, waveform, and phase relation of the output intensity and index oscillations are shown to agree with numerical results to better than 10 percent. We investigate the possibility of experimental observation of regenerative oscillation, and show that it may be present under reasonable experimental conditions.
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.
In optical fibers, nonlinear dispersion due to the same third-order susceptibility as that responsible for parametric mixing significantly alters the squeezing behavior in a traveling wave geometry, giving the squeezed quadrature an intensity dependent phase and reducing the overall squeezing. Phase noise is not squeezed at all. In the case of a fiber ring resonator, the nonlinear susceptibility will also lead to dispersive optical bistability and the squeezing will be strongly dependent on pump and sideband detuning. Yurke1 has analyzed squeezing due to backward four-wave mixing in a cavity, but the pump wave did not circulate in the cavity, and bistability was not dealt with. We have developed a theory of the resonant fiber ring interferometer, where the pump wave is near resonance with an interferometer mode and the circulating power is thereby enhanced. For perfect pump resonance and for frequencies corresponding to sideband resonance, the overall enhancement of the squeezing in the output mode compared to the traveling wave case is proportional to the square of the resonator finesse. The best squeezing in the output mode is always found for this condition of sideband resonance. The phase of the minimum noise quadrature is quite sensitive to both pump and sideband detuning. This feature may provide a means for avoiding excess thermal phase noise due to guided acoustic wave Brillouin scattering in the fiber itself. At the critical points for dispersive optical bistability in such a resonator and for sideband resonance (i.e., noise frequencies which are multiples of the resonator free spectral range), perfect squeezing of the output light is predicted. This result was also obtained previously for the case of degenerate mixing in a resonant cavity by Collett and Walls.2 Our current theory does not account for the reduction in squeezing due to the loss present in such a resonator.2 Since the loss is also enhanced by a factor of the resonator finesse, this is of some concern and will limit the maximum useful finesse for quantum noise squeezing. The major source of loss is the single-mode directional coupler, which for currently available technology is of the order of a few percent.