Calculation of optical forces on an ellipsoid using vectorial ray tracing method

Min-Cheng Zhong,Yin-Mei Li,Jin-Hua Zhou,Zi-Qiang Wang

doi:10.1364/oe.20.014928

Abstract

For a triaxial ellipsoid in an optical trap with spherical aberration, the optical forces, torque and stress are analyzed using vectorial ray tracing. The torque will automatically regulate ellipsoid's long axis parallel to optic axis. For a trapped ellipsoid with principal axes in the ratio 1:2:3, the high stress distribution appears in x-z plane. And the optical force at x-axis is weaker than at y-axis due to the shape size. While the ellipsoid departs laterally from trap center, the measurable maximum transverse forces will be weakened due to axial equilibrium and affected by inclined orientation. For an appropriate ring beam, the maximum optical forces are strong in three dimensions, thus, this optical trap is appropriate to trap cells for avoiding damage from laser.

Highlights

In many applications of optical tweezers, there were some irregular trapped particles, such as red blood cells (RBCs) [1], chloroplasts [2], growing yeast cells [3] and phospholipid vesicles [4].Those nonspherical particles can be regarded as spheroids or triaxial ellipsoids
The torque will automatically regulate its orientation and high stress appears on the surface of small fractional radius
Due to the effect of shape size, Q y max is much larger than Qx max in theoretical calculations for both a Gaussian and ring beams. while an ellipsoid departs laterally from trap center, Qx max will be enhanced and Q y max will be weakened by inclined pose

Summary

Introduction

In many applications of optical tweezers, there were some irregular trapped particles, such as red blood cells (RBCs) [1], chloroplasts [2], growing yeast cells [3] and phospholipid vesicles [4].Those nonspherical particles can be regarded as spheroids or triaxial ellipsoids. [20] calculated the radiation forces on a dielectric plate by a Gaussian beam Those results indicated the optical forces were related with particle shape and orientation. A discrete dipole approximation (DDA) method is used to calculate the stiffness of ellipsoidal particles with different size or shape [13]. It is unclear for characteristics of a triaxial ellipsoid in different optical traps. For tracing a single ray striking a triaxial ellipsoid, the incident angles of reflection and refraction will vary with striking location. The force needs to be calculated in every incident plane

Force on an interface

Beam profile

Senkrecht and parallel components of a single ray

Stress and torque

Results

Torque of an Ellipsoid

Stress of an ellipsoid

Optical Forces on an Ellipsoid

Summary