Rotating patterns can be produced by two coaxial spiraling elliptic beams nonlocal
nonlinear media. The two constituent beams carry the orbital angular momentum (OAM),
which has the same or opposite signs. The resultant patterns exhibit revolving and
spinning rotations similar to the Sun-Earth system. The revolving-typed rotation comes
of the overall OAM, while the spinning-typed rotation results from the respective
OAM of the constituent beam. A kind of soliton patterns can stably exist, for which
a vortex is nested centrally in the rotating square-shaped optical envelope and four
peaks appear at four corners. The centrally nested vortex splits into two single vortex
for r not equal 1, with r being the power ratio between the two constituent beams.
The two single vortexes align vertically for r < 1 and horizontally for r > 1, and
their spacing increases with vertical bar r - 1 vertical bar. The theoretical results
give a possibility of the transforming from cross-phase-typed OAM into the helical-phase-typed
OAM, which may find potential applications in beam shaping and controlling. In addition,
the square optical envelope may exhibit advantages in the integration of optical components.
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