用于VCSEL阵列光分布调控的自由曲面透镜阵列设计

Freeform Lens Array Design for Precise Control of Irradiance Distribution in VCSEL Array

针对垂直腔面发射激光器(VCSEL)设计了自由曲面整形透镜,使VCSEL输出光束在目标面呈均匀的辐照度分布。自由曲面透镜前表面为非球面,后表面为自由曲面。在设计自由曲面的设计过程中,在自由曲面透镜中间区域设置虚拟平面,根据虚拟平面和目标面能量之间的关系,确定自由曲面入射光束和出射光束的方向矢量,获得自由曲面采样点上各点的法向矢量。自由曲面的矢高和法向矢量之间构成了一个泊松方程。引进离散余弦变换的方法求解泊松方程,获得了自由曲面的矢高。模拟结果表明使用自由曲面整形透镜可将目标面辐照度均匀度提升到93.9%。为了适应在高功率场景中的应用,基于单个VCSEL模组的辐照度分布,应用蚁狮算法优化VCSEL模组之间的距离,对VCSEL模组阵列进行了二次光分布调控,使得阵列在目标面上的辐照度均匀度可以达到85.2%,光效率达到91.8%。

Objective The vertical-cavity surface-emitting laser(VCSEL)is a typical semiconductor laser widely employed in highspeed optical communication,optical sensors,pumped solid-state lasers or fiber lasers,LiDAR,and structured light applications.The irradiance distributions of the VCSELs typically conform to a Gaussian distribution.In various application scenarios such as laser processing and laser illumination,it is necessary to achieve a uniform irradiance distribution on the target plane.Among various methods for laser shaping,freeform optical components have gained increasing popularity due to their high optical efficiency and flexibility in controlling light distribution.However,there is a paucity of literature regarding the utilization of freeform optical elements for shaping VCSEL lasers,particularly in terms of designing freeform surfaces to manipulate irradiance distribution for VCSEL array modules.In this paper,we present the design of both a freeform lens and a freeform lens array specifically and tailor the light distributions for single VCSEL sources and VCSEL arrays respectively to achieve a uniform irradiance distribution on the target plane.Methods The design of a freeform shaping lens for VCSELs aims to achieve a uniform irradiance distribution on the target surface for the output beam.The front surface of the lens is aspherical,while the back surface is freeform.The rays emitted by the VCSEL are collimated through the aspherical surface,and the collimated beam is then incident on the freeform surface,through which the irradiance distribution is regulated to produce a uniform irradiance distribution on the target plane.During the design process,a virtual surface is incorporated within the middle region of the freeform lens to establish a relationship between its energy distribution and that of the target plane.This enables the determination of direction vectors of incident and outgoing rays,as well as obtaining normal vectors for each point on the sample points of the free-form surface.By formulating a Poisson equation relating sag of freeform surface and normal vector,we employ the discrete cosine transform method to solve it and obtain vector heights for achieving the desired performance.Due to the size of the VCSEL source,the rays emitted by the VCSEL still have a small divergence angle after passing through the aspherical collimation.The effect of the divergence angle on the uniformity of the irradiation distribution on the target surface is investigated.It is shown that the uniformity is reduced to 85%when the residual divergence angle reaches 3°.A VCSEL array consists of several individual VCSEL modules equipped with a freeform lens.An evaluation function is constructed that guarantees simultaneous control of the uniformity and efficiency of the irradiance distribution of the VCSEL module array.The optimal spacing between these modules is obtained using the evaluation function by employing the Antlion optimization algorithm.The optimal VCSEL array enables the generation of a uniform irradiance distribution on the target plane with high optical efficiency.Results and Discussions A freeform lens is specifically designed for a single VCSEL light source,featuring an aspherical front surface and a freeform back surface.The emitted beam from the VCSEL light source,with a waist of 0.1 mm and a divergence angle of 8°,is efficiently transformed into a square uniform spot of 10 mm×10 mm on the target plane,achieving an impressive irradiation uniformity of 93.9%.The second freeform lens is specifically designed for a VCSEL source with an emitting area of 1 mm×1 mm;however,it only achieves an irradiation uniformity of 53.5%on the target plane.Each VCSEL combined with the second freeform lens forms what we refer to as a VCSEL module.The optimal 3×3 array of modules is generated by employing the antlion optimization algorithm to determine the optimal spacing between VCSEL modules.With the implementation of an optimized VCSEL module array,we have successfully achieved a remarkable enhancement in irradiation uniformity,reaching up to 85.2%on the larger target plane of 30 mm×30 mm.Moreover,our study has demonstrated an impressive overall light efficiency level of 91.8%for the VCSEL array.Conclusions The relationship between the sags of the freeform surface and the normal vector of each sampling point is transformed into a Poisson equation in this paper,and the sags of the freeform surface are obtained using the discrete cosine transform(DCT)method.By employing this approach,a freeform lens can be designed to achieve uniform irradiance distribution on the target plane with a high level of uniformity reaching 93.9%.Furthermore,we address an optimization problem for VCSEL arrays by transforming it into an intensity homogenization problem through multiple image superposition.The analysis reveals that to achieve uniform irradiation distribution from VCSEL arrays,it is necessary to generate non-uniform irradiance distribution on edge regions by individual VCSEL modules.Based on nine VCSEL modules with the optimal spacing,we can achieve uniform irradiance distribution on the target plane with a uniformity of 85.2%and an optical efficiency of 91.8%.The forthcoming research will explore the impact of fabrication and assembly tolerances of the freeform lenses on irradiation uniformity.