Radiation from band-gap solitons

We investigate band-gap solitons, i.e. the solitons in Kerr-nonlinear media with periodic in space modulation of potential, and show that they are unstable for their eigenfrequencies around the middle of the band-gap, i.e. radiate into mode continua of the upper and lower bands. We identify the mechanism of four-wave mixing that causes the radiation of solitons. We also show that the gap solitons self-stabilize by losing their mass due to the radiation and thus recoil into the non-radiative area of the band-gap.