We develop the effective experimental approach to generate multi-twisted beams (MTBs) with twisted intensity lobes by superimposing helical phases consisting of multiple independent sub-phases with different azimuthal shift factors. The MTBs' energy flows and propagation properties are also investigated, indicating that such beams exhibit twisted properties. The azimuthal shift factor determines the twisted intensity distributions, and the number of twisted lobes depends on the sub-phase number. The bright lobes of a MTB possess the shapes of thin spiral lines, and the intensity pattern depends on the topological charge. Diverse MTBs can be generated by flexibly manipulating the azimuthal shift factors and the sub-phase number. Also, various mirror-symmetrical twisted beams are constructed using the matrix flip scheme, further enriching the light structures of MTBs. Numerical simulation and experimental results are consistent. Furthermore, the capture and guide of microspheres via the MTBs are experimentally executed and demonstrate the feasibility and practicability of our generated MTBs. The various MTBs will likely give rise to potential applications in fabricating chiral nanostructures and manipulating microparticles.
Recently, optical vortices (OVs) have attracted substantial attention because they can provide an additional degree of freedom, i.e., orbital angular momentum (OAM). It is well known that the fractional OV (FOV) is interpreted as a weighted superposition of a series of integer OVs containing different OAM states. However, methods for controlling the sampling interval of the OAM state decomposition and determining the selected sampling OAM state are lacking. To address this issue, in this Letter, we propose a FOV by inserting multiple fractional phase jumps into whole phase jumps (2π), termed as a multi-fractional OV (MFOV). The MFOV is a generalized FOV possessing three adjustable parameters, including the number of azimuthal phase periods (APPs), N; the number of whole phase jumps in an APP, K; and the fractional phase jump, α. The results show that the intensity and OAM of the MFOV are shaped into different polygons based on the APP number. Through OAM state decomposition and OAM entropy techniques, we find that the MFOV is constructed by sparse sampling of the OAM states, with the sampling interval equal to N. Moreover, the probability of each sampling state is determined by the parameter α, and the state order of the maximal probability is controlled by the parameter K, as K * N. This work presents a clear physical interpretation of the FOV, which deepens our understanding of the FOV and facilitates potential applications, especially for multiplexing technology in optical communication based on OAM.
Using angular spectral representation, we demonstrate a generalized approach for generating high-dimensional elliptic umbilic and hyperbolic umbilic caustics by phase holograms. The wavefronts of such umbilic beams are investigated via the diffraction catastrophe theory determined by the potential function, which depends on the state and control parameters. We find that the hyperbolic umbilic beams degenerate into classical Airy beams when the two control parameters are simultaneously equal to zero, and elliptic umbilic beams possess an intriguing autofocusing property. Numerical results demonstrate that such beams exhibit clear umbilics in 3D caustic, which link the two separated parts. The dynamical evolutions verify that they both possess prominent self-healing properties. Moreover, we demonstrate that hyperbolic umbilic beams follow along a curve trajectory during propagation. As the numerical calculation of diffraction integral is relatively complex, we have developed an effective approach for successfully generating such beams by using phase hologram represented by angular spectrum. Our experimental results are in good agreement with the simulations. Such beams with intriguing properties are likely to be applied in emerging fields such as particle manipulation and optical micromachining.
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