Electrostrictive contribution to the intensity-dependent refractive index of optical fibers

Buckland, Eric L.; Boyd, Robert W.

doi:10.1364/ol.21.001117

Cited by 83 publications

(32 citation statements)

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“…With our parameters, we found f = 15.6 % in good agreement with experimental studies. 50 With these notations, it must be clear that the nonlinear coefficient γ that appears in the normalization of the field amplitude (see Ref. 28) must be understood as being the nonlinearity coefficient as seen by a c.w.…”

Section: Methodsmentioning

confidence: 99%

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Ultraweak long-range interactions of solitons observed over astronomical distances

et al. 2013

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We report what we believe is the weakest interaction between solitons ever observed. Our experiment involves temporal optical cavity solitons recirculating in a coherently-driven passive optical fibre ring resonator. We observe two solitons, separated by up to 8,000 times their width, changing their temporal separation by a fraction of an attosecond per round-trip of the 100 m-long resonator, or equivalently 1/10,000 of the wavelength of the soliton carrier wave per characteristic dispersive length. The interactions are so weak that, at the speed of light, they require an effective propagation distance of the order of an astronomical unit to fully develop, i.e. tens of millions of kilometres. The interaction is mediated by transverse acoustic waves generated in the optical fibre by the propagating solitons through electrostriction.Solitons are self-localized wave packets that do not spread, the dispersion of the supporting medium being cancelled by a nonlinear effect. 1-4 They are universal, and in many respects behave like particles. 2 They exert forces on each other and can interact in various ways, elastically or inelastically. 2,5,6 Here we report what we believe is by far the weakest form of soliton interaction ever observed. Using recirculating optical cavity solitons, we report interactions so weak that the solitons shift their positions by only about 10 −7 of their width -amounting to 1/10,000 of the wavelength of the soliton carrier wave -per characteristic dispersive length. At the speed of light, these interactions require effective propagation distances of the order of an astronomical unit (AU) to be revealed, i.e. tens of millions of kilometres. The sheer fact that we can actually observe such ultra-weak interactions in a noisy laboratory environment highlights the robustness and stability of solitons as never-before.Solitons occur in media as diverse as water, DNA, plasma, or ultra-cold gases, 1,7-12 but over the last 20 years optics has led the way in our understanding of soliton interactions because of the ease with which optical solitons can be studied experimentally. [13][14][15][16] Optical solitons have been shown to attract, repel, breakup, merge, orbit each-other or even annihilate. 5,17-21 As in various other media, soliton interactions can be either shortrange, occurring when the tails of neighbouring solitons overlap, 6,17,22,23 or long range, through a coupling with a non-local response, be it optical radiation, charge carriers, or thermal waves. 24-27 The weakest soliton interactions reported are long range, 24,25 but their observation is typically limited by the duration or propagation length over which the solitons can be maintained. In optics, this is often simply dictated by the size of a nonlinear crystal or the length of an optical fibre. To overcome this restriction, our experiment involves solitons recirculating in an optical fibre loop.More specifically, we consider temporal cavity solitons (CSs) propagating in a coherently-driven passive nonlinear fibre ring resonator. 28 Not...

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Section: Methodsmentioning

confidence: 99%

“…inclusive of the electrostriction contribution. 38,50 The impulse response of the actual refractive index perturbation δn that is plotted in Fig. 4a was obtained by considering that the intensity of the CS is a Dirac-δ function.…”

Section: Methodsmentioning

confidence: 99%

Ultraweak long-range interactions of solitons observed over astronomical distances

et al. 2013

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“…The interaction is important, e.g., for Brillouin scattering, diffraction of light by ultrasonic waves [1]. Brillouin scattering in optical fibers-coupling of longitudinal or transverse acoustic modes to optical waves through electrostriction-has been analyzed extensively, though generally not for solitons [2,3,4,5,6]. Sound waves acting on trains of optical solitons in fibers have been studied [7,8], but these interactions were essentially between acoustic continuous waves and their optical counterparts, subject to periodic modulation.…”

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confidence: 99%

“…We have derived effectively 1+1-dimensional coupled mode equations using standard methods [13,21] for light in a waveguide, adding a phonon field and acousto-optic coupling induced by electrostriction [1,2,3,4,5,7,8,9]:…”

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Optoacoustic Solitons in Bragg Gratings

2007

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Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.PACS numbers: 42.81. Dp, 42.70.Qs, 43.25.+y, 72.50.+b Introduction.-Light and sound tend to have widely disparate frequencies, wavelengths, and velocities. As a consequence, interaction between optical and acoustic signals is often weak. The interaction is important, e.g., for Brillouin scattering, diffraction of light by ultrasonic waves [1]. Brillouin scattering in optical fibers-coupling of longitudinal or transverse acoustic modes to optical waves through electrostriction-has been analyzed extensively, though generally not for solitons [2,3,4,5,6]. Sound waves acting on trains of optical solitons in fibers have been studied [7,8], but these interactions were essentially between acoustic continuous waves and their optical counterparts, subject to periodic modulation. Brillouin scattering has been employed in acousto-optic filters, in which light diffracts off an acoustic grating [6]. Brillouin scattering in fibers can lead to pulse compression [9] or formation of trains of very narrow optical solitons [10]. Interaction of phonons with optical nonlinear Schrödinger solitons, with nonlinearity due to electromagnetically-induced transparency, was analyzed in Ref. [11]. Reference [12] considered solitons in Bragg gratings, with electrostriction the only nonlinearity; the correct soliton solution is a limiting case of the results below.In this work, we consider light and acoustic waves in a cubic (χ (3) ) nonlinear medium with a Bragg grating, a fixed spatially periodic variation in the index of refraction [13]. Bragg gratings are typically written in the cladding of an optical fiber, though they have been induced by copropagating continuous waves [14]. Fiber Bragg gratings without electrostriction are known to support optical gap solitons, nonlinear solitary waves with frequencies in the band gap created by the Bragg grating [13,15,16]. Gap solitons can have arbitrarily small velocity, which has motivated great interest in them for stopping light, though creating very slow gap solitons experimentally has been difficult. Early experimental realizations of gap solitons had velocities approximately half the speed of light [16]. Various methods have been proposed for creating slow gap solitons: building up slow gap solitons directly by Raman amplif...

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Quantum Control of Molecular Processes

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Electrostrictive contribution to the intensity-dependent refractive index of optical fibers

Cited by 83 publications

References 8 publications

Ultraweak long-range interactions of solitons observed over astronomical distances

Ultraweak long-range interactions of solitons observed over astronomical distances

Optoacoustic Solitons in Bragg Gratings

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