Investigation on the Formation of Laser Transverse Pattern Possessing Optical Lattices

Optical lattices (OLs) with diverse transverse patterns and optical vortex lattices (OVLs) with special phase singularities have played important roles in the fields of atomic cooling, particle manipulation, quantum entanglement, and optical communication. As a matter of consensus until now, the OL patterns are generated by coherently superimposing multiple transverse modes with a fixed phase difference through the transverse mode locking (TML) effect. There are phase singularities in the dark area of this kind of OL pattern, so it is also called OVL pattern. However, in our research, it is found that some high-order complex symmetric OL patterns can hardly be analyzed by TML model. Instead, the analysis method of incoherent superposition of mode intensity could be applied. The OL pattern obtained by this method can be regarded as in non-TML state. Therefore, in this article, we mainly study the distinct characteristics and properties of OL patterns in TML and non-TML states. Through intensity comparison, interferometry, and beat frequency spectrum, we can effectively distinguish OL pattern in TML and non-TML states, which is of significance to explore the formation of laser transverse pattern possessing OL.

Focal beam structuring by triple mixing of optical vortex lattices

On-demand generation and reshaping of arrays of focused laser beams is highly desired in many areas of science and technology. In this work, we present a versatile approach for laser beam structuring in the focal plane of a lens by triple mixing of square and/or hexagonal optical vortex lattices (OVLs). In the artificial far field the input Gaussian beam is reshaped into ordered arrays of bright beams with flat phase profiles. This is remarkable, since the bright focal peaks are surrounded by hundreds of OVs with their dark cores and two-dimensional phase dislocations. Numerical simulations and experimental evidences for this are shown, including a broad discussion of some of the possible scenarios for such mixing: triple mixing of square-shaped OVLs, triple mixing of hexagonal OVLs, as well as the two combined cases of mixing square-hexagonal-hexagonal and square-square-hexagonal OVLs. The particular ordering of the input phase distributions of the OV lattices on the used spatial light modulators is found to affect the orientation of the structures ruled by the hexagonal OVL. Reliable control parameters for the creation of the desired focal beam structures are the respective lattice node spacings. The presented approach is flexible, easily realizable by using a single spatial light modulator, and thus accessible in many laboratories.

Emergence and melting of active vortex crystals

Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

Systematically Investigating the Structural Variety of Crystalline and Kaleidoscopic Vortex Lattices by Using Laser Beam Arrays

We theoretically demonstrate that a family of vortex-lattice structures can be flexibly generated using a multi-beam interference approach. Numerical calculation presents a variety of crystalline and kaleidoscopic patterns. Based on the numerical analysis, we experimentally realized these structure beams by combining an amplitude mask with multiple apertures and a spiral phase plate. The excellent agreement between the experimental and theoretical results not only validates the presented method, but also manifests the structure of vortex lattices.