<title>Function of nonlinear susceptibility dispersion in modulational instability and soliton formation in quadratic-nonlinear medium</title>

Abstract

ABSTRACT Second harmonic generation was considered vith regard to dispersion of nonlinear susceptibility, and second- and third- order dispersion of the group-velocities. The case of a finite phase mismatch is analyzed analytically. The steady state pulses of the fundamental and second hannonic waves were found. Modulation instability of the continuous wave solutionis considered. The correction terms for MT thresholds, which are resulted from dispersion of non-linear susceptibility, werefound.Keywords: second harmonic, modulational instability 1. INTRODUCTION One of the effects that give rise to the development of nonlinear optics was the second harmonic generation. In the last yearsthis phenomenon newly attracts great attention1 . Quadratic nonlinearity does not give rise to the wave collapse and existenceof the three-dimensional stable 'light bullets' is not unlikely2. Possibility of existence of the mulfidimensional dark solitarywaves (optical vortices) in quadratic-nonlinear media from the viewpoint of modulational instability been considered3. if thewidth of an electromagnetic pulse is much larger than the period of the optical cycle, the pulse can be naturally described bymeans of its slowly varying envelope. This approximation is adequate for pulses of iO —