Complexes of in-phase two-dimensional laser solitons

The structure and motion of complexes of in-phase weakly coupled fundamental solitons in a wide-aperture class A laser with saturable absorption are analysed. The symmetry of the field distribution and its relation to the motion of the complex are studied. Due to the absence of wavefront dislocations in such complexes, the transverse radiation intensity and phase distributions are the symmetry objects, which simplifies analysis compared to the case when wavefront dislocations are present. Four types of the motion of soliton complexes are demonstrated: a motionless complex in the presence of two mirror symmetry axes; linear motion of the complex when only one mirror symmetry axis exists; rotation around a motionless centre of inertia in the absence of the mirror symmetry axis and in the presence of symmetry with respect to rotation through the angle 2π/M (M is an integer); and curvilinear (circular) motion of the centre of inertia and simultaneous rotation of the complex around the instantaneous position of the centre of inertia in the absence of symmetry elements.