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

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

Zero Torque Compliant Mechanisms Employing Pre-buckled Beams

The concept of a statically balanced mechanism with a single rotational degree-of-freedom is presented. The proposed device achieves static balancing by combining positive stiffness elements and negative stiffness elements within an annular domain. Two designs are discussed. The first is composed of an Archimedean spiral and two pinned-pinned pre-buckled beams. The overall mechanism is modeled via an analytical approach and the element dimensions are optimized. The optimal configuration is then tested through finite element analysis (FEA). A second approach replaces the spiral beam with elastic custom-shaped spline beams. A FEA optimization is performed to determine the shape and size of such spline beams. The behavior of the negators is used as reference for the optimization so as to achieve a complete balancing. A physical prototype of each configuration is machined and tested. The comparison between predicted and acquired data confirmed the efficacy of the design methods.

Orbital angular momentum of the spiral beams

At first sight, any rotation generates some angular momentum (it is true for a solid body). But these characteristics (rotation and orbital angular momentum) are rather different for optics and mechanics. In optics there are the situation when the rotation is important. On the other hand, there are the cases where the nonzero orbital angular momentum is necessary. The main goal of this article is to investigate a relationship between a rotation under propagation of spiral beam and its angular momentum. It can be done the following conclusion: there is no any relation between rotation under propagation of spiral beam and its OAM.