Gap-acoustic solitons (GASs) are stable pulses that exist in nonlinear Bragg waveguides. They are a mathematical generalization of gap solitons, in which the model includes the dependence of the refractive index on the material density. We derive unified dynamical equations for gap solitons along with Brillouin scattering, which also results from the dependence of the refractive index on the material density. We find accurate values of the coefficients for fused silica. The analysis of the GAS conserved quantities-Hamiltonian, momentum, photon energy (or number of photons), and material mass-shows dramatic differences compared to the model neglecting the dependence of the refractive index on the material density. In particular, subsonic GASs in fused silica have far more momentum at low velocities than at high velocities. The dependence of the GAS momentum on velocity due to acoustic effects is dramatic up to approximately 1% of the speed of light. These momentum-connected effects mean that instability of a slow GAS may make it suddenly accelerate to high speeds, and also that an unstable high-speed GAS can abruptly decelerate to close to zero velocity. The predictions are confirmed by a direct numerical simulation.

We show that gap-acoustic solitons, i.e., optical gap solitons with electrostrictive coupling to sound modes, can be produced with velocities down to less than 2.5% of the speed of light using a fiber Bragg grating that is linearly coupled to a non-Bragg fiber over a finite domain. Forward-and backward-moving light pulses in the non-Bragg fiber that reach the coupling region simultaneously couple into the Bragg fiber and form a moving soliton, which then propagates beyond the coupling region.There is great interest in slow light [1]. Spectacular slow light results have been achieved in Bose-Einstein condensates [2], but realizations in room temperature solid state materials are desirable for many applications. Optical fiber Bragg gratings (FBGs) can support one such slow light structure, the gap-acoustic soliton (GAS), i.e., an optical gap soliton with electrostrictive coupling to sound waves, which can have velocities from zero up to the group velocity in the medium [3][4][5][6][7]. Gap solitons have been produced in the lab with velocities as slow as 16% of the speed of light [6], but to date not slower. Suitable experimental media for GAS propagation are available, but it can be difficult to create the correct initial and/or boundary conditions to obtain a GAS in the first place. Methods proposed for producing slow GASs include: (1) fibers with gradually varying modulation depth (apodized) [8], as was employed in Ref.[6], (2) colliding faster moving gap solitons with each other [9] or with fiber defects [10,11], and (3) growing a soliton in-place with either distributed [12] or localized amplification [13]. We propose a method to produce GASs using a FBG and a non-Bragg fiber that are coupled over a finite distance, as illustrated in Fig. 1. We show that if light pulses, specially designed by reverse engineering, are sent into the non-Bragg fiber in the forward-and backward-moving directions such that they simultaneously reach the inter-fiber coupling region (see Fig. 2), a slow GAS can be created in the FBG. The parameters of the resulting soliton depend on the Bragg fiber parameters, the coupling to the non-Bragg fiber, and the widths, intensities, and phases of the input pulses. This inter-fiber coupling may be contrasted with soliton switching in uniformly coupled FBGs [14,15]. One of the essential differences in this work is that here the inter-fiber coupling region is finite, and the light switches exactly once, from the non-Bragg to the Bragg fiber and then remains in the FBG.A FBG may be coupled to the non-Bragg fiber by removing some of the cladding and bringing the fibers close together so that the evanescent waves of one fiber extend over the core of the other [16]. This results in linear coupling between the light in the two fibers, which is stronger when the fibers are closer [17,18]. The coupling region is finite, and varies smoothly from the uncoupled to the maximally coupled region.The dynamics of the system are described by the equationswhere z is the spatial coordinate, t is time, u 1 is the...

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