Optoacoustic Solitons in Bragg Gratings

Abstract

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...

Sudden spontaneous acceleration and deceleration of gap-acoustic solitons

“…Electrostriction introduces a "supersonic" instability for GASs moving faster than the speed of sound [20]. In most cases, the result of the supersonic instability was the re-formation of a new GAS at a different velocity.…”

“…The momentum P GAS is especially critical. If a soliton experiences a supersonic instabilitythe instability of the GAS when the velocity is larger than the speed of sound (see [20])-the system following the instability cannot have more Hamiltonian, momentum, or photon energy than the original soliton. Because some of the faster-moving solitons have less momentum than the slower-moving solitons (and not significantly less Hamiltonian either), a slow-moving soliton may decay into a fast-moving soliton.…”

“…A subset of the GAS model, without self-phase modulation, was studied in [22]. Reference [23] found solitons in a system with two short-wavelength light fields interacting with a long-wavelength electromagnetic field; the interaction there is different from that in [20] or in this work, but there are family resemblances. Reference [24] looked at the interaction of light beams, i.e., propagation in space rather than in time, with sound waves via electrostriction.…”

“…We also generalize the model [20] to cover high wave number (Brillouin) acoustic wave interactions as well as low wave number (electrostrictive) acoustic waves, including the derivation of the governing equations for both acoustic waves in a unified manner.…”

“…References [17][18][19] rigorously showed that optical gap solitons are stable in the top half of the bandgap and unstable in most of the bottom half of the bandgap. Reference [20] generalized the optical gap soliton equations to a model that includes the dependence of the index of refraction on the density of the material and the phonon-photon interactions that result from it; that is, the effect of light on low wave number acoustic waves [21], and vice versa, was included in the model, and generalized "gap-acoustic soliton" solutions were found [20]. The GASs are similar to optical gap solitons, but they exhibit many intriguing novel dynamical properties, especially when the soliton velocities are small.…”