物理学报2017，Vol.66Issue(4)：324-331,8.DOI:10.7498/aps.66.048701
运用四元数分析椭球微粒所受的光阱力
Using quaternions to analyze the trapping force of an ellipsoidal bead
摘要
Abstract
In the ray-optics (RO) model of optical tweezers, tracing refractive and reflected rays with vectors play impor-tant roles in calculating the trapping forces. Traditional ray-tracing method with solid geometry, to some extent, is complicated in determining the orientations of those refractive and reflected rays according to spatial incident rays. It is difficult to calculate the trapping forces for irregular particles. In this paper, quaternion is proposed to rotate ray vectors for simplifying the traces of all kinds of spatial rays. Then, it is appropriate to calculate the trapping force of an ellipsoid bead. Based on the algorithm of quaternion and the convention between the interface normal and angular directions, the direction of normal always points from optically denser medium to thinner medium. The rotation axis is the cross product of the incident ray and the interface normal. And the positive angular direction can be determined by right-hand rulebasedontheorientationoftherotationaxis.AccordingtoSnell'law,therotationanglebetweenthe incident ray and refractive/reflected ray can be determined. The quaternion for rotation consists of rotation axis and angle. So the refractive and reflected rays are both determined by quaternions of incident ray and rotation based on rotation rules. Furthermore, the force on interface can also be calculated according to momentum changes of the photon before and after the interface refraction and reflection. The quaternion method is used to analyze the effects of coverslip position and deformation ratio on the trapping efficiency of ellipsoid particles. Our simulative results show that the lateral and axial trapping efficiencies are obviously affected by the deformation of the ellipsoid itself. No matter whether the bead deforms transversely or axially, the transverse and axial trapping efficiencies both become larger at a specific deformation. Meantime, the increase of the spherical aberration reduces the maximum axial trapping efficiency, and the equilibrium position of the bead becomes farther away from the center. Using quaternion method, the calculation of refractive lightvector can be simplified in comparison with by using the method of Euclidean geometry or transformation matrix.Theoretically,this quaternion can be used to trace rays on any irregular geometric surfaces.Inconclusion,the method of quaternion can make ray tracing easier and extend the applications of RO model.关键词
四元数/光线追迹/椭球微粒/光阱力Key words
quaternion/ray tracing/ellipsoidal bead/trapping force引用本文复制引用
张书赫,梁振,周金华..运用四元数分析椭球微粒所受的光阱力[J].物理学报,2017,66(4):324-331,8.基金项目
Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 31400943), the Key Project of Natural Science Foundation of the Anhui Higher Education Institutions, China (Grant No. KJ2016A361), and the Grants for Scientific Research of BSKY from Anhui Medical University, China (Grant No. XJ201518). 国家自然科学基金青年基金项目(批准号: 31400943)、安徽高校自然科学研究重点项目(批准号: KJ2016A361)和安徽医科大学博士科研资助基金(批准号: XJ201518)资助的课题. （Grant No. 31400943）
