3-WAVE GAP SOLITONS IN WAVE-GUIDES WITH QUADRATIC NONLINEARITY

A model of the second-harmonic-generating (chi((2))) optical medium wi th a Bragg grating is considered. Two components of the fundamental ha rmonic (FH) are assumed to be resonantly coupled through the Bragg ref lection, while the second harmonic (SH) propagates pal allel to the gr ating, hence its dispersion (diffraction) must be explicitly taken int o consideration. It is demonstrated that the system can easily generat e stable three-wave gap solitons of two different types (free-tail and tail-locked ones) that are identified analytically according to the s tructure of their tails. The stationary fundamental solitons are sough t for analytically, by means of the variational approximation, and num erically. The results produced by the two approaches are in fairly rea sonable agreement. The existence boundaries of the soliton are found i n an exact form. The stability of the solitons is determined by direct partial differential equation simulations. A threshold value of an ef fective FH-SH mismatch parameter is found, the soliton being stable ab ove the threshold and unstable below it. The stability threshold stron gly depends on the soliton's wave-number shift k and very weakly on th e SH diffraction coefficient. Stationary two-soliton bound states are found, too, and it is demonstrated numerically that they are stable if the: mismatch exceeds another threshold, which is close to that for t he fundamental soliton. At k<0, the stability thresholds do not exist, as all the fundamental and two-solitons are stable. With the increase of the mismatch, the two-solitons disappear, developing a singularity at another, very high, threshold. The existence of the stable two-sol itons is a drastic difference of the present model from the earlier in vestigated chi((2)) systems. It is argued that both the fundamental so litons and two-solitons can be experimentally observed in currently av ailable optical materials with the quadratic nonlinearity. [S1063-651X (98)09811-0].