Structural stability of spiral beams and fine structure of an energy flow

The problem of structural stability wave systems with great numbers degrees freedom directly concerns the issue redistribution energy fluxes in structured vortex beams that ensure their under propagating and focusing. A special place this variety is occupied by spiral capable mapping complex figures, letters even words. Spiral contain an infinite set Laguerre-Gauss a strong sequence topological charges radial numbers, amplitudes phases are tightly matched. Therefore, plays role for applications. Using combination theory computer simulation, supported experiment, we ana-lyzed structure critical points flows two main types beams: triangular zero number framing faces both quantum numbers. Structural provided triads points, inside outside triangle, which direct light flux along generatrix hold when rotating beam. experiment showed simple beam turns out to be stable small alignment inaccuracies, whereas fram-ing requires careful