# Analysis of Confinement in Dual Spherical-Tapered Ended Fiber Optical Trap
## 4 Conclusions  
In this paper, we demonstrated highly efficient optical trapping in a counter-propagating fiber arrangement by using a dual spherical-tapered ended fiber optical trap instead of a dual flat ended fiber optical trap. A design of a low-cost, robust chip of a dual-fiber optical trap, using spherical-tapered ended fiber for optical trapping of particles, was presented and produced.  
The output light field when using spherical-tapered ended fiber and flat ended fibers was calculated. Compared with flat ended fiber, the light intensity distribution of spherical-tapered ended fiber could form a more focused spot. A polystyrene microsphere with a radius 3 \(\upmu\)m was captured in water in the dual-fiber optical trap. In this scenario, the force acting on the particle and the stiffness of the optical trap were simulated and the results were checked in an experiment. In the simulation, compared with flat ended fiber optical trap, the dual spherical-tapered ended fiber optical trap increased the axial stiffness from 0.15 \(\mathrm{pN/\upmu m}\) to 0.43 \(\mathrm{pN/\upmu m}\), and increased the lateral stiffness from 3.61 \(\mathrm{pN/\upmu m}\) to 11.46 \(\mathrm{pN/\upmu m}\). This meant particles could be captured more stably in the dual spherical-tapered ended fiber optical trap. We were able to gain the lateral and axial displacements change with time by a particle tracking algorithm in the experiment. Compared with the flat ended fiber optical trap, the dual spherical-tapered ended fiber optical trap increased the axial stiffness from 1.68 \(\mathrm{pN/\upmu m}\) to 1.76 \(\mathrm{pN/\upmu m}\), and increased the lateral stiffness from 0.44 \(\mathrm{pN/\upmu m}\) to 0.99 \(\mathrm{pN/\upmu m}\) in the experiment. It was proved by simulation and experiment that spherical-tapered ended fiber can obviously increase the stiffness in lateral and axial axis of the dual-fiber optical trap.  
In this work, we demonstrated the possibility of using the dual spherical-tapered ended fiber optical trap chip to realize stable particle capturing. It shows the great potential of micro-structured optical fibers for use in optical trapping and micro-manipulation. Both the cone angle and the radius of the top affect the stiffness of the lateral and axial optical trap, and investigation into this is to be carried out in the follow-up study. Furthermore, other optical fiber end structures can also change the optical trap stiffness, which is also the focus of follow-up research. By changing the micro-structure of the fiber, different optical traps can be customized according to requirements. This paves the way toward high stiffness optical trap chips for fiber optical trapping.  
Conceptualization, H.F., X.C. and G.X.; data curation, H.F.; formal analysis, H.F.; funding acquisition, Z.T. and H.L.; investigation, H.F. and H.A.; methodology, H.F., S.J. and X.C.; project administration, H.F., X.C. and G.X.; resources, H.F.; software, H.F.; supervision, S.J., Z.T., H.L. and G.X.; validation, H.F., H.A. and X.C.; visualization, H.F.; writing--original draft, H.F.; writing--review & editing, H.F. and X.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (Nos. 11904405 and 61975237).  
Not applicable.  
The authors declare no conflict of interest.