We present a detailed overview of stimulated Brillouin scattering (SBS) in
 single-mode optical fibers. The review is divided into two parts. In the first part,
 we discuss the fundamentals of SBS. A particular emphasis is given to analytical
 calculation of the backreflected power and SBS threshold (SBST) in optical fibers
 with various index profiles. For this, we consider acousto-optic interaction in the
 guiding geometry and derive the modal overlap integral, which describes the
 dependence of the Brillouin gain on the refractive index profile of the optical
 fiber. We analyze Stokes backreflected power initiated by thermal phonons, compare
 values of the SBST calculated from different approximations, and discuss the SBST
 dependence on the fiber length. We also review an analytical approach to calculate
 the gain of Brillouin fiber amplifiers (BFAs) in the regime of pump depletion. In the
 high-gain regime, fiber loss is a nonnegligible effect and needs to be accounted for
 along with the pump depletion. We provide an accurate analytic expression for the BFA
 gain and show results of experimental validation. Finally, we review methods to
 suppress SBS including index-controlled acoustic guiding or segmented fiber links.
 The second part of the review deals with recent advances in fiber-optic applications
 where SBS is a relevant effect. In particular, we discuss the impact of SBS on the
 radio-over-fiber technology, enhancement of the SBS efficiency in Raman-pumped
 fibers, slow light due to SBS and SBS-based optical delay lines, Brillouin
 fiber-optic sensors, and SBS mitigation in high-power fiber lasers, as well as SBS in
 multimode and microstructured fibers. A detailed derivation of evolutional equations
 in the guided wave geometry as well as key physical relations are given in
 appendices.

Stimulated Brillouin scattering in optical fibers

A recent renaissance in Brillouin scattering research has been driven by the increasing maturity of photonic integration platforms and nanophotonics. The result is a new breed of chip-based devices that exploit acousto-optic interactions to create lasers, amplifiers, filters, delay lines and isolators. Here, we provide a detailed overview of Brillouin scattering in integrated waveguides and resonators, covering key concepts such as the stimulation of the Brillouin process, in which the optical field itself induces acoustic vibrations, the importance of acoustic confinement, methods for calculating and measuring Brillouin gain, and the diversity of materials platforms and geometries. Our Review emphasizes emerging applications in microwave photonics, signal processing and sensing, and concludes with a perspective for future directions. Acousto-optical interactions within integrated optics platforms are reviewed with a discussion of the useful chip-based devices such as lasers, amplifiers, filters, isolators and more besides that can result.

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Brillouin integrated photonics

In this letter, we demonstrate very high-resolution optical spectrometry based on stimulated Brillouin scattering between a swept-tuned laser and a test optical signal. Measurement principles are presented along with spectral measurements of unmodulated and modulated optical sources showing 0.08-pm resolution and 80-dB dynamic range.

Very high resolution optical spectrometry by stimulated Brillouin scattering

A general analytic solution for Brillouin distributed sensing in optical fibers with sub-meter spatial resolution is obtained by solving the acoustical-optical coupled wave equations by a perturbation method. The Brillouin interaction of a triad of square pump pulses with a continuous signal is described, covering a wide range of pumping schemes. The model predicts how the acoustic wave, the signal amplitude and the optical gain spectral profile depend upon the pumping scheme. Sub-meter spatial resolution is demonstrated for bright-, dark- and π-shifted interrogating pump pulses, together with disturbing echo effects, and the results compare favorably with experimental data. This analytic solution is an excellent tool not only for optimizing the pumping scheme but also for post-processing the measured data to remove resolution degrading features.

Distributed Brillouin sensing with sub-meter spatial resolution: modeling and processing

Forward stimulated Brillouin scattering (FSBS) is observed in a standard 2-km-long highly nonlinear fiber. The frequency of FSBS arising from multiple radially guided acoustic resonances is observed up to gigahertz frequencies. The tight confinement of the light and acoustic field enhances the interaction and results in a large gain coefficient of 34.7 W−1 at a frequency of 933.8 MHz. We also find that the profile on the anti-Stokes side of the pump beam have lineshapes that are asymmetric, which we show is due to the interference between FSBS and the optical Kerr effect. The measured FSBS resonance linewidths are found to increase linearly with the acoustic frequency. Based on this scaling, we conclude that dominant contribution to the linewidth is from surface damping due to the fiber jacket and structural nonuniformities along the fiber.

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FSBS resonances observed in a standard highly nonlinear fiber

We first use the nonlocalized, fluctuating source model for the stimulated Brillouin scattering to get the exact spectrum of the Stokes wave in optical fibers with attenuation loss. A new relation for the evaluation of the critical pump power (or Brillouin threshold) depending on the fiber length is then introduced, which should be more precise than the well-known Smith formula. Furthermore, we give for the first time, to the best of our knowledge, an approximate solution for standard steady-state Brillouin equations, which consists of two simple relations.

Pierre Cambon

Papers

Theoretical evaluation of the Brillouin threshold and the steady-state Brillouin equations in standard single-mode optical fibers