Electromagnetic forces on plasmonic nanoparticles induced by fast electron beams

Abstract

The total momentum transfer from fast electron beams, like those employed in scanning transmission electron microscopy ͑STEM͒, to plasmonic nanoparticles is calculated. The momentum transfer is obtained by integrating the electromagnetic forces acting on the particles over time. Numerical results for single and dimer metallic nanoparticles are presented, for sizes ranging between 2 and 80 nm. We analyze the momentum transfer in the case of metallic dimers where the different relevant parameters such as particle size, interparticle distance, and electron beam impact parameter are modified. It is shown that depending on the specific values of the parameters, the total momentum transfer yields a force that can be either attractive or repulsive. The time-average forces calculated for electron beams commonly employed in STEM are on the order of piconewtons, comparable in magnitude to optical forces and are thus capable of producing movement in the nanoparticles. This effect can be exploited in mechanical control of nanoparticle induced motion.

Attosecond and femtosecond forces exerted on gold nanoparticles induced by swift electrons

“…Integrating the forces over time, we find that total time-average attractive forces are larger than repulsive forces at large impact parameter (b > 5Å), but become comparable at small impact parameter (b < 5Å), leading to a cross-over from attractive to repulsive behavior, in agreement with frequency domain calculations 9,18 . Fig.…”

“…In this spherical geometry, the frequencydependent response fields in the sphere can be calculated using a multipolar expansion, satisfying boundary conditions on the surface of the spherical NP, and they are presented as follows (where CGS-atomic units are used). A detailed description of the derivation of expressions associated with the frequency-dependent electromagnetic fields is found in references 9,18 . Those expressions include retardation and relativistic effects which allow us to capture the physics of the high-speed events:…”

“…We report numerical results for the spatial and temporal behavior of lateral electromagnetic forces within a gold nanoparticle, to identify physical mechanisms for both attractive and repulsive manipulation of nanoparticles, recently observed usingÅngstrom-sized electron beams 8,9 .…”

“…While these techniques offer a wide range of capabilities in different size ranges, it is still difficult to deliberately manipulate objects at the atomic and nanoscale levels 12 . Recently, it has been found that an electron beam can be used to deliberately manipulate metal nanoparticles, even producing both attractive and repulsive forces 8,9,[13][14][15][16] .…”

Reconfigurable nanoantennas using electron-beam manipulation

“…Figure 3a,b show theoretically calculated modes excited by a beam positioned at (x 0 , y 0 ) ¼ (0, 5) and (0, 0) nm, respectively, about the gap centre. Whereas symmetric passage of the beam through the gap enhances electric-field intensity on the outside edges of the structure and tends to pull the p-BNAs apart 24,26 , the large in-gap intensities produced in the asymmetric cases induce significant gradient forces on the Au particles towards the gap centre 17 . By virtue of the fact that there exist many more in-gap modes, the resultant gradient force is attractive.…”