Effective stimulated Brillouin gain in singlemode optical fibres

Botineau, J.; Picholle, Éric; Bahloul, Derradji

doi:10.1049/el:19951355

Cited by 20 publications

(6 citation statements)

References 3 publications

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“…II builds on an impressive body of theoretical and experimental work which demonstrates accurate prediction of SBS within microscale systems, including the work of 25,42,43,52,53], and many others. Our multiscale treatment fundamentally differs from previous work in that it (1) captures Brillouin nonlinearities associated with nonlinear polarization currents at boundaries, and (2) accounts for new contributions to Brillouin gain resulting from radiation pressures.…”

Section: Discussionmentioning

confidence: 99%

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Giant Enhancement of Stimulated Brillouin Scattering in The Sub-Wavelength Limit

Rakich

Reinke

Camacho

et al. 2012

Conference on Lasers and Electro-Optics 2012

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Stimulated Brillouin scattering (SBS) is traditionally viewed as a process whose strength is dictated by intrinsic material nonlinearities with little dependence on waveguide geometry. We show that this paradigm breaks down at the nanoscale, as tremendous radiation pressures produce new forms of SBS nonlinearities. A coherent combination of radiation pressure and electrostrictive forces is seen to enhance both forward and backward SBS processes by orders of magnitude, creating new geometric degrees of freedom through which photon-phonon coupling becomes highly tailorable. At nanoscales, the backward-SBS gain is seen to be 10 4 times greater than in conventional silica fibers with 100 times greater values than predicted by conventional SBS treatments. Furthermore, radically enhanced forward-SBS processes are 10 5 times larger than any known waveguide system. In addition, when nanoscale silicon waveguides are cooled to low temperatures, a further 10-100 times increase in SBS gain is seen as phonon losses are reduced. As a result, a 100-m segment of the waveguide has equivalent nonlinearity to a kilometer of fiber. Couplings of this magnitude would enable efficient chip-scale stimulated Brillouin scattering in silicon waveguides for the first time. More generally, we develop a new full-vectorial theoretical formulation of stimulated Brillouin scattering that accurately incorporates the effects of boundary-induced nonlinearities and radiation pressure, both of which are seen to have tremendous impact on photonphonon coupling at subwavelength scales. This formalism, which treats both intermode and intramode coupling within periodic and translationally invariant waveguide systems, reveals a rich landscape of new stimulated Brillouin processes when applied to nanoscale systems.

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Section: Discussionmentioning

confidence: 99%

“…(A1) is evaluated with the form of defined earlier, this formulation of SBS can be seen to be equivalent to that of Refs. [52,53], which is known to be remarkably accurate for the prediction of SBS gain within a wide range of microscale systems [2][3][4][5][6]11].…”

mentioning

confidence: 99%

Giant Enhancement of Stimulated Brillouin Scattering in The Sub-Wavelength Limit

Rakich

Reinke

Camacho

et al. 2012

Conference on Lasers and Electro-Optics 2012

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“…There have been many theoretical studies on calculating SBS gain through some forms of overlap integral between optical and elastic eigen-modes 1,2,6,24,[27][28][29][30][31] . These treatments, while accurate for microscale waveguides, suffer from two drawbacks for nanoscale waveguides.…”

Section: In Translationally Invariant Waveguides Sbs Can Be Categorimentioning

confidence: 99%

Slow light through tightly coupled light waves and acoustic waves in nanoscale waveguides

et al. 2013

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We develop a general framework of evaluating slow-light performance using Stimulated Brillouin Scattering (SBS) in optical waveguides via the overlap integral between optical and elastic eigen-modes. We show that spatial symmetry of the optical force dictates the selection rules of the excitable elastic modes. By applying this method to a rectangular silicon waveguide, we demonstrate the spatial distributions of optical force and elastic eigen-modes jointly determine the magnitude and scaling of SBS gain coefficient in both forward and backward SBS processes. We further apply this method to inter-modal SBS process, and demonstrate that the coupling between distinct optical modes is necessary to excite elastic modes with all possible symmetries. INTRODUCTIONStimulated Brillouin Scattering (SBS) is a third order nonlinear process in which two optical modes are coupled through an elastic mode 1,2 . In a waveguide system, the interference of pump and Stokes waves generates a time-varying optical force at the beat frequency. The optical force, while at resonance with an elastic mode at the phase-matching wavevector, excites the mechanical vibration of the waveguide, which can in turn scatter light between the pump and Stokes waves. Since its discovery, SBS has been extensively studied with a variety of applications in efficient phonon generation [3,4 , optical frequency conversion [5][6][7] , slow light [8][9][10][11] , and signal processing techniques 12,13 .The optical force that mediates SBS includes electrostriction force and radiation pressure 14,15 . Electrostriction is an intrinsic material nonlinearity, which arises from the tendency of materials to become compressed in the region of high optical intensity. In previous studies, electrostriction is treated as a bulk nonlinearity with only electrostriction body force taken into account 1,2 . We find that the discontinuities of optical intensities and photoelastic constants can generate electrostriction pressure on material boundaries. Radiation pressure is another boundary nonlinearity, which arises from the interaction of light with the material boundaries with discontinuous dielectric constant 16,17 . For nanoscale structures, radiation pressure is radically enhanced, enabling a variety of optomechanics applications [18][19][20][21][22][23] . Within nanoscale waveguides, the distributions of electrostriction force and radiation pressure are quite different. The interplay between these two effects creates new degree of freedoms of tailoring SBS process.In translationally invariant waveguides, SBS can be categorized into forward SBS (FSBS) and backward SBS (BSBS). In FSBS, the pump and Stokes waves propagate in the same direction, generating translationally invariant optical forces, which excite standing elastic modes 6 . In BSBS, the pump and Stokes waves propagate in the counter directions, generating translationally varying optical forces, which excite traveling elastic modes. SBS can also occur between distinct optical modes [24][25][26][27][28] . I...

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“…-La diffraction de l'onde acoustique dans la fibre est également responsable d'un élargisse-ment comme l'a prévu Zel'dovich en 1986 [Zel'dovich et Pilipetskii, 1986;Fotiadi, 2001]. -Enfin, il faut signaler l'article de Botineau [Botineau et al, 1995] qui pour sa part prend en compte les inhomogénéités de vitesse acoustique dans la fibre, qui seraient dues à la concentration en GeO 2 . Dans ce cas, le centre de la fibre et le bord n'ont pas la même fréquence de résonance (et c'est surtout vrai en FGI, car en FSI l'indice donc le dopant est à peu près constant) et le mode fondamental voit son spectre élargi.…”

Section: Causes D'élargissementunclassified

“…Sans être précis, ce calcul montre l'allure de l'effet d'une dispersion de la vitesse acoustique avec le dopage (donc l'indice). C'est un élargissement des calculs de Botineau [Botineau et al, 1995] au cas d'une fibre multimode. -L'élargissement dû à la somme des gains des différents modes décalés respectivement de Ω Bij .…”

Section: Causes D'élargissementunclassified

High power multimode fiber amplifier with wavefront reshaping for high beam quality recovery

Lombard

Brignon

Huignard

et al. 2006

Comptes Rendus. Physique

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Je remercie Jean-Paul Castéra de m'avoir accueilli à Thales Research and Technology où la majorité des travaux de thèse ont eu lieu en collaboration avec l'Institut d'Optique. Je remercie également Pierre Chavel pour avoir permis cette collaboration et pour m'avoir accueilli lors de la dernière année de thèse à l'Institut d'Optique.Je tiens aussi à remercier vivement François Sanchez et Alain Barthélémy, qui ont eu la lourde tâche de relire ce long document (et la longue tâche de relire ce lourd document). J'ai poussé le vice jusqu'à leur livrer le manuscrit au début des vacances d'été... encore désolé pour vos vacances.Mes remerciements vont aussi à Pierre Glorieux m'a fait l'honneur d'accepter la présidence de ce jury, de surcroît avec humour. Merci également à Bruno Desruelle et Jean-Louis Le Gouët qui ont eu la gentillesse de participer à ce jury. Enfin, un grand merci à Andrei Fotiadi, spécialiste de l'effet Brillouin, qui a accepté de faire le déplacement depuis la Belgique -et a supporté un manuscrit et une soutenance en français. Nous avons eu de nombreuses occasions de partager nos points de vue : merci aussi, Andrei, pour ces intéressants échanges.Je tiens à remercier chaleureusement les trois personnes qui m'ont directement encadré : Arnaud Brignon, Patrick Georges et Jean-Pierre Huignard. Arnaud, merci pour ton encadrement, ta disponibilité, tes conseils pragmatiques et efficaces et la confiance que tu as su m'accorder. Et pour ton humour, aussi ! Patrick, merci pour ton accompagnement tout au long de cette thèse. Bien que la partie expérimentale ne se soit pas déroulée dans ton laboratoire, tu as toujours su te tenir informé et être de bon conseil. Merci pour ton accueil lors de la dernière année et ton chaleureux soutien (qui rend cette période presque agréable !) pendant la rédaction de ce manuscrit, que tu as par ailleurs rigoureusement relu et corrigé. Jean-Pierre, merci pour vos visites régulières, pour votre enthousiasme communicatif pour votre imagination débordante. Nos échanges ont été extrêmement productifs et motivants.Je n'oublie pas Éric Lallier, Gilles Pauliat, Gaëlle Lucas-Leclin, Gérald Roosen, qui ont de près ou de loin participé à ces travaux. Éric, à qui la barbe sied, surtout celle de Père-Noël (qui en descendant du Ciel vers le 25 décembre 2002, m'a déposé une jolie diode de pompe de 300W dans mes petits souliers !), merci pour ta disponibilité et tes conseils utiles. Gilles, merci pour ta collaboration et ton aide précieuse sur le cristal photoréfractif.

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Effective stimulated Brillouin gain in singlemode optical fibres

Cited by 20 publications

References 3 publications

Giant Enhancement of Stimulated Brillouin Scattering in The Sub-Wavelength Limit

Giant Enhancement of Stimulated Brillouin Scattering in The Sub-Wavelength Limit

Slow light through tightly coupled light waves and acoustic waves in nanoscale waveguides

High power multimode fiber amplifier with wavefront reshaping for high beam quality recovery

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