Optical nonlinearities give rise to many ubiquitous effects in optical fibers. These effects are interesting in themselves and can be detrimental in optical communications, but they also have many useful applications, especially for the implementation of all-optical functionalities in optical networks. In the present paper, we briefly review the different kinds of optical nonlinearities encountered in fibers, pointing out the essential material and fiber parameters that determine them. We describe the effects produced by each kind of nonlinearity, emphasizing their variations for different values of essential parameters. Throughout the paper, we refer to recent systems applications in which these effects have been dealt with or exploited.

Optical nonlinearities in fibers: review, recent examples, and systems applications

In Brillouin fiber lasers, the phase fluctuations of the pump laser are transferred to the emitted Stokes field after being strongly reduced. The result is a linewidth narrowing that we study both experimentally and theoretically. We derive simple expressions to connect the linewidths of the waves interacting in the fiber, and we show that the magnitude of the narrowing effect depends only on the acoustic damping rate and the cavity loss rate. We successfully compare these theoretical predictions with experimental results obtained by recording the response of a Brillouin fiber ring laser to frequency modulation of the pump field.

Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers

Actively Q-switched fiber lasers: Switching dynamics and nonlinear processes

Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we show that cascaded intra-mode FBS results in a pure phase modulation and discuss how this necessitates specific experimental methods for the observation of fiber-based and integrated FBS. Further, we discuss how the descriptions that have been established in these two classes of waveguides connect to each other and to the broader context of cavity opto-mechanics and Raman scattering. Finally, we draw an unexpected striking similarity between FBS and discrete diffraction phenomena in waveguide arrays, which makes FBS an interesting candidate for future research in quantum-optics.

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Cascaded forward Brillouin scattering to all Stokes orders

A stable optical comb with double-Brillouin-frequency spacing assisted by multiple four-wave mixing processes

The nonlinear dynamics of cw-pumped Brillouin long-fiber ring lasers that contain a large number of longitudinal modes N beneath the Brillouin gain curve is controlled by a single parameter, namely, the Stokes feedback R. Below Rcrit, a stable train of dissipative solitonic pulses is spontaneously structured at the round-trip frequency fr without any additional intracavity mode locking. Experimental observations in cw-pumped fiber ring cavities, supported by numerical simulation in a coherent space–time three-wave model that includes the optical Kerr effect, prove the universality of the self-pulsing mechanism. Stability analysis shows that below Rcrit the steady Brillouin mirror regime is destabilized through a Hopf bifurcation. For R<Rcrit<R0 the bifurcation is supercritical and exhibits an asymptotically monostable oscillatory regime at twice fr for high enough N or at fr for lower N, in a finite transition region. For R0<R<Rcrit, the bifurcation is subcritical and exhibits dynamic bistability between the steady and the pulsed regimes in a finite hysteresis region whose width is proportional to the Kerr parameter. For R small enough, the cavity longitudinal modes merge into a dissipative solitonic Brillouin pulse: the dynamic three-wave model yields self-structured asymptotically stable trains of pulses for any initial conditions, in fair quantitative agreement (for pulse width, intensity, shape, and period) with the experiments in the entire self-pulsing domain. Amplification of spontaneous emission breaks down the stable-pulse regime in long devices (i.e., high N), so the fiber noise amplitude is higher than the coherent amplitude that separates two consecutive pulses.

Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers

Pulse propagation in optical fibers may electrostrictively excite acoustic waves as a result of cladding Brillouin scattering, transversally propagating with respect to the fiber axis in the fiber’s cladding, and mechanical coating. We show, for the first time to our knowledge, experimentally and theoretically that these transverse resonances within finite frequency ranges may cooperatively couple with the acoustic longitudinal modes of a fiber resonator, giving rise to stable trains of either spread or compressed three-wave Brillouin solitons and propose a first stability map for the rich four-wave dissipative dynamics.

Soliton compression in Brillouin fiber lasers.

A coherent model of cladding Brillouin scattering (CBS) is proposed. This model describes both the so-called (spontaneous) guided acoustic wave Brillouin scattering (GAWBS) in the low field limit, and the 'long-range acoustic interaction' observed in solitonic fibre transmissions. The coupling of CBS with the optical Kerr effect is discussed.

Coherent model of cladding Brillouin scattering in singlemode fibres

Stimulated Brillouin scattering (SBS) in an optical fiber cavity resonantly couples an optical cw-pump and a backscattered Stokes wave with electrostrictively excited longitudinal GHz hypersound waves. Below a critical feedback the Stokes wave self-structurates into ns pulses, called Brillonin dissipative three-wave solitons; they are able in turn to electrostrictively excite lower frequency acoustic waves (fn = 5 MHz to 1 GHz), due to cladding Brillouin scattering (CBS), transversally propagating with respect to the fiber axis in the fiber's cladding. We derive a four-wave model which couples the transverse CBS dynamics to the nonlinear dissipative three-wave SBS dynamics. Above a critical coupling, the resonant CBS oscillations (f/FSR = integer) are strong enough to break the pulses, while stable compressed or decompressed pulses are still obtained in finite frequency ranges between resonant frequencies: the small damped low frequency CBS vibrations contribute to lock further longitudinal cavity modes which compose the compressed SBS soliton. A stability map is computed. Compression up to a factor 0.4 with respect to the bare Brillouin soliton is numerically obtained, yielding ns pulses of peak intensity up to 14 times the cw launched pump, in fair quantitative agreement with experiments done in long fiber ring cavities.

Soliton compression and locking in a Brillouin fiber ring laser

Summary from only given. Stimulated Brillouin scattering (SBS) of a cw pump E/sub p/ in an optical fiber is able to generate a counter propagating Stokes pulse E/sub B/ by resonant interaction with high frequency (GHz) axial acoustic waves E/sub a/. We have dynamically described and experimentally obtained the generation of stable trains of dissipative Brillouin solitons in fiber ring lasers below a critical feedback, when the cavities contain a large number of longitudinal modes N beneath the Brillouin gain curve. Stable self-pulsed regimes of nanosecond Brillouin solitons are obtained in a finite range of fiber length [namely 10<L(m)//spl lambda//sub p//sup 2/(/spl mu/m)<400], their Fourier transform spectra showing only a few number of cavity modes coupled together.

Isabelle Bongrand

Papers

Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers

Soliton compression in Brillouin fiber lasers.

Coherent model of cladding Brillouin scattering in singlemode fibres

Soliton compression and locking in a Brillouin fiber ring laser

Soliton squeezing through antiresonant electrostrictive mode coupling in a Brillouin fiber ring laser