Abstract

In this paper we calculate the time-dependent forces between a swift electron traveling at constant velocity and a metallic nanoparticle made of either aluminum or gold. We consider that the nanoparticle responds as an electric point dipole and we use classical electrodynamics to calculate the force on both the nanoparticle and the electron. The values for the velocity of the electron and the radius of the nanoparticle were chosen in accordance with electron microscopy observations, and the impact parameter was selected to fulfill the constraints imposed by the dipole approximation. We found that there are times when the force on the nanoparticle is attractive and others when it is repulsive, and show that this is due to the delayed electromagnetic response of the nanoparticle. To establish the limits of validity of our approach, we calculate the total linear momentum transfer to the nanoparticle, and compare it with results obtained, in frequency space, using the full multipole expansion of the fields induced on the nanoparticle, considering the effects of electromagnetic radiation.

Highlights

  • The ability to manipulate objects at deep subwavelength dimensions is an interesting research area that aims to control and engineer structures at the nano- and micrometer scales [1,2,3,4,5]

  • We studied the interaction in time between a swift electron and a small metallic nanoparticle by assuming the latter as an electric point dipole

  • We calculated the forces between the swift electron and the nanoparticle as a function of time and we identified two different timescales: an attosecond timescale with forces on the order of piconewtons, and a femtosecond timescale with forces on the order of attonewtons

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Summary

INTRODUCTION

The ability to manipulate objects at deep subwavelength dimensions is an interesting research area that aims to control and engineer structures at the nano- and micrometer scales [1,2,3,4,5]. Optical tweezers are one example useful for the latter purpose In this technique, the electromagnetic forces produced by tightly focused laser beams allow to move and hold micro objects [4,5,6] and even plasmonic nanoparticles [3,7,8]. The recent ability to achieve subangstrom resolution in aberration-corrected scanning transmission electron microscopes (STEMs) [17,18,19,20,21] and parallel efforts to push the spectral resolution into the range of milli–electron volts [22,23,24] make STEM an attractive alternative tool for nanomanipulation with high spatial and spectral resolutions Further developments of these techniques require a full understanding of the interaction between NPs and electron beams.

THEORETICAL MODEL
Force on the nanoparticle
Force on the swift electron
Radiation emitted by the nanoparticle and conservation of linear momentum
COMPARISON OF THE DIPOLE APPROXIMATION WITH THE FULLY RETARDED WAVE SOLUTION
CONCLUSIONS

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