We present results of systematic investigations of gap solitons (GSs) in the generic model of periodically modulated Bragg gratings (BGs). The model includes periodic variation of the local reflectivity, and also a term representing the modulation of the local BG chirp and/or refractive index. The model may be realized, in addition to fiber BGs, in terms of spatial gratings, and also as a limit case of the Gross-Pitaevskii equation for Bose-Einstein condensates trapped in optical lattices. While the reflectivity modulation strongly destabilizes all solitons, the chirp modulation helps to stabilize a new family of BGs in a newly opened side bandgap at negative frequencies (gap No. -1). Completely stable solitons are found in this gap and in the central bandgap (No. 0). Long-lived but overall unstable solitons are found too in the side bandgap at positive frequencies. A distinctive feature of the fundamental solitons in gap No. -1 is their double-peak shape. Stable single- and double-peak solitons in bandgaps -1 and 0, respectively, demonstrate bistability, coexisting at equal values of the energy. Stable four- and three-peak bound states may be formed, in bandgap -1, by the double- and single-peak fundamental GSs. The quiescent single-peak GSs readily self-trap from input pulses coupled into the BG at a finite velocity. In the case of weak chirp modulation, stably moving solitons can be created in the central bandgap. The settings considered in this article may be used for the creation of solitons of standing light.
|Title of host publication||Handbook of Solitons|
|Subtitle of host publication||Research, Technology and Applications|
|Publisher||Nova Science Publishers, Inc.|
|Number of pages||21|
|State||Published - 1 Oct 2009|