利用周期型正交二元相位板产生正方阵列涡旋和螺旋光场

Generation of Square Optical Vortex Array and Optical Helix Array by Periodic Orthogonal Binary Phase Plate

设计了一种周期型正交二元相位板,其具有周期型矩形调制单元,各单元的相位调制量为0或π。该相位板的空间频谱具有中心直流分量为0的特点,分别对该频谱中心区域的4个一级频谱点和8个二级频谱点进行相位调制,可得到正方阵列光斑和正方阵列涡旋。阵列涡旋中各涡旋光束的拓扑荷数l=±1,在空间交错分布。由于两个正方阵列光场在垂直传播方向的横向周期恰好重合,且两个光场沿光轴方向的波数不同,因此叠加之后可以形成强度分布随传输距离旋转的正方阵列螺旋,阵列中存在两种具有相反螺旋方向的螺旋光束,同样在空间呈交错分布。此外,讨论了产生最佳螺旋光束的相位板设计条件,并给出理想情况下系统的能量利用率,所得实验结果验证了该方法的可行性。

Objective Due to its peculiar phase and intensity distribution,the vortex beam has attracted extensive attention in particle manipulation and communication.Interference of a vortex beam with a plane wave can generate a helix beam with peculiar helical intensity distribution,providing a potential research platform for studying nonlinear topological edge solitons and anomalous topological phases.Multiple vortex and helix beams arrange in a specific distribution to form the field of the optical vortex array(OVA)and optical helix array(OHA).The array has multiple phase singularities compared to a single beam,which has essential applications in multiparticle manipulation and multichannel communication.The wideranging applications of array fields rely on generating highquality optical fields.Currently,various methods have been proposed to generate OVA and OHA,such as using fractional Tabor effect,grating diffraction,or direct adoption of vortex lasers.In these methods,by employing the fractional Talbot effect,the field with the best contrast can only be obtained at a specific distance.The intensity distribution of the OVA generated by grating diffraction is not uniform,and the vortex laser suffers from low energy efficiency.Compared to the abovementioned methods,the field generated by the multibeam interference features propagation invariance and high efficiency and becomes one way to generate the OVA and OHA.Therefore,the adoption of multibeam interference to generate OVA and OHA is of potential research significance.Methods Based on the principle of multibeam interference,a periodic orthogonal binary phase plate is designed for generating square optical vortex array(SOVA)and square optical helix array(SOHA)fields.After filtering the spectrum of the phase plate,four symmetric spots in the central region of the spectrum and eight symmetric spots in the subcentral region of the spectrum are modulated separately.Then,the corresponding beams of these spots are obtained by the Fourier transform,and they interfere with each other to generate a square beam array(SBA)and a SOVA.The interference superposition of SBA and SOVA results in SOHA.Results and Discussions The designed binary phase plate has the same period and structure in two orthogonal directions.The difference in the phase modulation quantities of adjacent rectangular phase modulation units isπ(Fig.1).The central direct component of its spatial spectrum is 0.After filtering the spectrum,four spots of the central region and eight spots of the subcentral region are preserved(Fig.2).First,phase modulation is performed on the fourpoint sources located in the central region(Fig.3).After phase modulation,the SBA can be generated by fourpoint sources(Fig.4).In the SBA,the beam is distributed in a checkerboard shape,and the phase difference between adjacent beams isπ.Then,phase modulation is performed on eight points located in the subcentral region(Fig.5).The SOVA can be generated by the phasemodulated eight points(Fig.6).There are two kinds of staggered vortex beams with topological charge l=±1 in the array.The SOHA can be obtained by interfering with the SOVA and SBA,and the design parameters of the binary phase plate should meet b/a=1/6(Fig.7)to obtain SOHA with the best interference effect.Under such conditions,the SOVA and SBA have the same transverse distribution period.At the maximum amplitude of the vortex beam,the beams in SBA have the same amplitude value(Fig.8).In this case,the phase change direction of adjacent helix beams in the SOHA obtained is opposite(Fig.9).With the SOHA propagation,the intensity of helix beams presents a spiral distribution along the optical axis.The rotation directions of adjacent helix beams are opposite(Fig.10).Finally,we build a 4f optical path for experimental verification(Fig.11)and obtain experimental results consistent with the theoretical results(Fig.12).Conclusions In conclusion,we propose a method of generating SOVA and SOHA fields by utilizing a periodic orthogonal binary phase plate.The phase modulation of each unit of the phase plate is 0 orπ,and the central direct component of the spectrum of the phase plate is 0.By filtering and phase modulation of the phase plate spectrum,the SBA and the SOVA fields with propagation invariant characteristics can be generated by four spots in the central region and eight spots in the subcentral region respectively.There are two kinds of vortex beams with topological charge l=±1 in the array.The two square array fields have the same transverse spatial period,and the wave vectors of the two square array fields in the optical axis direction are different.Therefore,the SOHA in which intensity distribution rotates with the changing transmission distance can be obtained by the interference superposition of the SBA and the SOVA.The SOHA has two kinds of helix beams with opposite rotation directions.When the parameter of the phase plate is b/a=1/6,the SOHA with the best contrast can be generated.Simulation and experimental results demonstrate the feasibility of the proposed method.