Generation and Properties of Anomalous Optical Vortex Lattice
Objective Optical vortex beams have a high degree of flexibility in light field modulation due to their unique orbital angular momentum properties,which make them show high application prospect in a variety of fields. However,due to the single mode distribution of a single vortex,people have begun to study the optical vortex lattice (OVL) with a more flexible light field structure. OVL is a mode-rich structured light field with a higher degree of flexibility of modulation,which has a broad application prospect in multi-particle optical micro-manipulation and other fields. From the initial OVL with Ferris structures to the OVL under arbitrary curve arrangement and the OVL with switchable mixed-order topological charge,most of the current studies only focus on spatial mode distribution,dark core distribution,and topological charge size of the light field generated by the superposition of two beams. However,from the perspective of superimposed beams,there is still insufficient knowledge about how to achieve perfect OVL manipulation and explore the property of dark cores and topological charges under multiple parameters. Therefore,it is necessary to study a kind of OVL that can be locally modulated to further enrich its spatial mode distribution. This is of great significance for expanding the depth and breadth of lattice applications.Methods We propose a kind of flexibly modulated anomalous OVL (AOVL) by adopting computational holography combined with spatial light modulators (Fig. 2). The experiment employs Nd:YAG lasers as the light source. The 532 nm laser beam undergoes expansion and collimation via the pinhole filter PF and lens L1 ( f1=200 mm),thus generating parallel light. Then,the beam is further refined by the aperture A and the polarizer P1,ultimately generating a linearly polarized beam of the desired size. After passing through the beam-splitting BS1,the beams are divided into the reflected beam and transmitted beam. The reflected beam is illuminated on the spatial light modulator (SLM,HOLOEYE,PLUTO-VIS-016,pixel size of 8 μm×8 μm,resolution of 1920 pixel×1080 pixel) loaded with a phase mask plate. Then,it passes through the lens L2 ( f2=150 mm) for the Fourier transform,and the resulting beam is photographed and recorded by the complementary metal-oxide-semiconductor (CMOS,Basler acA1600-60gc,pixel size of 4.5 μm× 4.5 μm,resolution of 1600 pixel×1200 pixel). The transmitted beam passes through the mirrors M1 and M2,and then combined with the AOVL by the beam splitting BS2. The coaxial interference pattern is also recorded by the camera placed behind the polarizer P2.Results and Discussions The obtained AOVL can be employed to manipulate the number of dark cores,vortex signs,and spatial pattern distribution perfectly by controlling the topological charge values of the partition and the proportion of the superposed area. In the case of equal area superposition between the two beams,the positive and negative vortices in different partitions of the lattice can be controlled by changing the topological charge values of different partitions (Fig. 3). Additionally,in the case of non-equal area superposition between each partition of the superimposed beam,and changed superposition ratio of the partition,the experimental results show that under non-equal area superposition of a single beam,the "dark-core fusion" phenomenon will occur at the partition boundary of the AOVL,which means the half-integer dark core in Q1 and Q2 will fuse into a complete dark core,forming a single vortex (Fig. 4). In the case of superposition of two beams in a single partition and unequal area,the "topological charge fusion" phenomenon will occur at the partition boundary of the AOVL,which reveals positive and negative vortices will cancel out in the dark core,forming a long and narrow dark core without vortices (Fig. 5). Meanwhile,to verify the existence of vortex phases in the generated AOVL,we interfere the generated lattice with the plane wave,and obtain the interference patterns of "dark-core fusion" and "topological charge fusion" phenomena (Fig. 6).Conclusions Based on the arbitrary splicing technique,we realize a single optical vortex with continuous,smooth phase,and uniform light intensity distribution. Then,an AOVL with perfect manipulation can be generated in the experiment. The results show that the number of dark cores and the sign of vortices in different partitions of the lattice can be achieved by changing the size and sign of the topological charge in the corresponding partition of the superimposed beam under equal area superposition between the two beams. Additionally,in the case of non-equal area superposition between specific partitions of a single beam,the "dark-core fusion" phenomenon between non-integer dark cores will appear at the boundary. In the case of non-equal area superposition between specific partitions of two beams,the "topological charge fusion" phenomenon between non-integer opposite topological charges will appear in the overlap partition of two beams. This kind of light field has more abundant regulatory dimensions and provides a new idea for perfect OVL manipulation,with potential applications found in smart micro-manipulation,optical tweezers,and high-capacity optical communication.
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