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Optics Express

Brillouin-like amplification in rare-earth-doped optical fibers

Andrei A. Fotiadi, Dmitry A. Korobko, И. О. Золотовский, James Roy Taylor

Published Oct 25, 2021• 11 citations
Publisher

Abstract

We present a theoretical formalism to describe the amplification of two monochromatic waves counter-propagating in a rare-earth-doped optical fiber amplifier. Interaction of the waves through a dynamical population inversion grating inscribed in the active fiber by the waves during their amplification results in a strong power transfer from one wave to another providing a preferable amplification of one wave at the expense of another. In this sense, the effect is similar to stimulated Brillouin scattering and is expected to be observed with both pumped and unpumped rare-earth-doped fibers possessing a finite polarizability difference between the excited and ground states.

DOI
10.1364/oe.437424

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We present a theoretical formalism to describe the amplification of two monochromatic waves counter-propagating in a rare-earth-doped optical fiber amplifier. Interaction of the waves through a dynamical population inversion grating inscribed in the active fiber by the waves during their amplification results in a strong power transfer from one wave to another providing a preferable amplification of one wave at the expense of another. In this sense, the effect is similar to stimulated Brillouin scattering and is expected to be observed with both pumped and unpumped rare-earth-doped fibers possessing a finite polarizability difference between the excited and ground states.
We present a theoretical formalism to describe the amplification of two monochromatic waves counter-propagating in a rare-earth-doped optical fiber amplifier. Interaction of the waves through a dynamical population inversion grating inscribed in the active fiber by the waves during their amplification results in a strong power transfer from one wave to another providing a preferable amplification of one wave at the expense of another. In this sense, the effect is similar to stimulated Brillouin scattering and is expected to be observed with both pumped and unpumped rare-earth-doped fibers possessing a finite polarizability difference between the excited and ground states.
We develop a theoretical model describing the mutual amplification of two counter-propagating monochromatic waves in a rare-earth-doped fiber amplifier. It is shown that the interference between the waves forms a dynamic population inversion grating within the active fiber core, which, in turn, mediates a nonlinear coupling between the waves. This coupling enables energy transfer from one optical wave to the other, leading to preferential amplification of one of them at the expense of the opposite-propagating field. The phenomenon occurs in both pumped and unpumped active fibers provided there exists a nonzero difference in the polarizabilities of the dopant ions in their ground and excited states. Such dynamical interactions can substantially modify the local gain profile and open a pathway to novel optical amplification regimes.
Brillouin amplification, the most prominent effect implemented with Brillouin dynamical gratings (BDG), enables exponential narrowband gain that is Stokes-shifted by some value in the GHz range. In this process, the interaction of the counterpropagating pump and Stokes waves through a BDG they produce causes an increase of the Stokes-shifted wave amplitude and decrease of the pump wave amplitude during their propagation through the fiber. Here, we report on a similar effect that could be implemented in rare-earth-doped fibers with the population inversion dynamical gratings. The effect is the most pronounced in a bidirectional rare-earth-doped optical fiber amplifier. Two monochromatic optical signal waves are introduced into the fiber from opposite ends and experience amplification (if the fiber is pumped) or attenuation (if the fiber is unpumped) as they propagate through the fiber. The signal waves are coherent on a sub-kHz level and slightly detuned. In terms commonly accepted in stimulated Brillouin scattering these counterpropagating signal waves correspond to what is referred to as "pump" and "Stokes" waves. However, in contrast to the Brillouin process, their interference inside the rare-earth-doped fiber creates not acoustic, but the population inversion dynamical gain grating. Then interaction between the signal waves and created population inversion dynamical gratings cause a strong power transfer from one signal wave to another.
The polarization-related properties of stimulated Brillouin scattering (SBS) processes in long, randomly birefringent, standard optical fibers are examined. Evolution equations for the pump and signal waves, in the presence of both birefringence and SBS, are provided in Jones and Stokes spaces. It is shown that in the undepleted pump regime, the amplification of the SBS signal wave is equivalent to that of a linear medium with polarization-dependent gain. The process is associated with a pair of orthogonal states of polarizations (SOPs) of the signal wave, which undergo maximum and minimum amplification. In long, standard fibers, the Jones vector of the probe SOP which corresponds to maximum amplification is aligned with the complex conjugate of the pump wave Jones vector. The maximum and minimum SBS gain coefficients in such fibers equal two-thirds and one-third of the gain coefficient that is predicted by scalar theory, respectively. The large differential gain of the SBS process gives rise to an effective pulling of the amplified Stokes probe wave SOP, towards that of maximum amplification. Lastly, Stokes wave pulses that are aligned for maximum and minimum amplification experience different group delays, which manifest as polarization-related distortions in SBS slow light setups.
Optical solitons are expected to play a key role in single-mode optical-fiber communication systems. However, they are still degraded by the linear fiber loss. Therefore, in order to be realistically feasible, soliton-based systems will need repeaters to enhance the signal, and, from a practical point of view, optical amplifiers are preferable to electro-optical ones. The use of Raman nonlinearity,1 and, more recently, the use of rare-earth-doped fibers,2 have been proposed for such optical amplification. We have numerically simulated pulse propagation through singlemode silica fibers doped with passive two-level atoms in an attempt to cancel the linear fiber loss by the well known doping resonant nonlinearities. Our first results, from experiments carried out in a variety of circum-stances, indicate that the linear rate of loss may be diminished with a proper choice of parameters but that the doped fiber by itself is unable to support steady propagation.
Signal amplification is analyzed in strongly pumped fiber amplifiers both for three-level and four-level transitions, including scattering loss and excited state absorption. Simple analytic expressions are derived for the signal amplification and pump attenuation, along the fiber length, when either the signal and the pump are injected at the same fiber end (forward pumping) or when they are injected at the two opposite ends (backward pumping). Numerical examples for rare-earth doped fibers show excellent agreement between the analytical solution and the exact numerical solutions of the rate-equations for practical operating conditions.