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

The SBS threshold of a fiber with Brillouin frequency shift distribution along its length is investigated theoretically and experimentally. We obtain a simple equation for estimating the SBS threshold from the effective gain coefficient, which is calculated by using the Brillouin frequency distribution along its length. The dopant concentration dependence of the Brillouin frequency shift are measured for fibers with an F and GeO/sub 2/ codoped silica core. The evaluated frequency shift per unit of dopant concentration is 277 MHz/wt% and 45 MHz/wt% for F and GeO/sub 2/, respectively, at 1.55 /spl mu/m. The SBS threshold of a fiber with a nonuniform Brillouin frequency shift distribution prepared by the VAD method is investigated experimentally. The fiber exhibits 7 dB improvement in its SBS threshold. This value is in good agreement with one estimated by calculating the effective gain coefficient. This simple equation will be useful for estimating the SBS threshold of various fibers.

SBS threshold of a fiber with a Brillouin frequency shift distribution

Chapter 8 – Fiber Nonlinearities and Their Impact on Transmission Systems

Crosstalk in a two-wavelength 1550-nm standard fiber system at subcarrier frequencies 50-800 MHz is investigated. The dependence of the crosstalk on subcarrier frequency, wavelength spacing, and optical power is measured and analyzed. The observed crosstalk is attributed to three primary mechanisms: stimulated Raman scattering, cross-phase modulation, and the optical Kerr effect combined with polarization-dependent loss. At wavelength spacing greater than 9 nm, stimulated Raman scattering dominates. At wavelength spacing less than 5 nm, the primary contributor can be the optical Kerr effect with polarization dependent loss, except at higher modulation frequencies where cross-phase modulation also is significant. At even modest (by CATV standards) optical power, the crosstalk is as high as -40 to -45 dB.

Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems

The effect of temperature variation along a high-power fiber amplifier on the stimulated Brillouin scattering (SBS) threshold is considered theoretically. We show that for an end-pumped rare-earth-doped double-clad fiber the inhomogeneous distribution of temperature, which is caused by the absorption of pump radiation, may result in total suppression of SBS even for output powers well above 200 W.

Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers.

The effects of fiber uniformity on stimulated Brillouin scattering thresholds have been measured, and the theory for stimulated Brillouin scattering in uniform fibers has been extended to the case of nonuniform fibers. This theory enables the, design of long fiber spans with ten times higher stimulated Brillouin scattering thresholds. >

Stimulated Brillouin threshold dependence on fiber type and uniformity

The authors measure the stimulated Brillouin scattering threshold for a CW (continuous wave) laser externally modulated with an AM-VSB (amplitude modulation vestigial sideband) CATV (cable television) signal. The threshold is essentially unchanged from the unmodulated case. For injected powers above the threshold power, substantial degradation of the carrier to noise ratio is seen. >

Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems

Stimulated Brillouin scattering sets a limit on the injected power in light-wave systems.1 For single-channel systems of moderate length this effect is the dominant nonlinearity, with a threshold on the order of a few milliwatts.2 As transmitter powers increase, this effect will become an important factor in system design. It is known that the Brillouin gain spectra of fibers are affected by fiber uniformity and type.3,4 Thus, the threshold for stimulated Brillouin scattering should also depend on these parameters.

X. P. Mao

Papers

Stimulated Brillouin threshold dependence on fiber type and uniformity

Brillouin scattering in externally modulated lightwave AM-VSB CATV transmission systems

Stimulated Brillouin threshold dependence on fiber type and uniformity

Suppression of Brillouin scattering in lightwave AM-VSB CATV transmission systems

Brillouin scattering in lightwave AM-VSB CATV transmission systems