Toward Lossless Infrared Optical Trapping of Small Nanoparticles Using Nonradiative Anapole Modes

A challenge in plasmonic trapping of small nanoparticles is the heating due to the Joule effect of metallic components. This heating can be avoided with electromagnetic field confinement in high-refractive-index materials, but nanoparticle trapping is difficult because the electromagnetic fields are mostly confined inside the dielectric nanostructures. Herein, we present the design of an all-dielectric platform to capture small dielectric nanoparticles without heating the nanostructure. It consists of a Si nanodisk engineered to exhibit the second-order anapole mode at the infrared regime ($\lambda =980\mathrm{nm}$), where Si has negligible losses, with a slot at the center. A strong electromagnetic hot spot is created, thus allowing us to capture nanoparticles as small as 20 nm. The numerical calculations indicate that optical trapping in these all-dielectric nanostructures occurs without heating only in the infrared, since for visible wavelengths the heating levels are similar to those in plasmonic nanostructures.

Figure 1

Optical effective transverse potential and schematic representation of the high-refractive-index resonant nanostructure. The nanodisk is illuminated with a linearly polarized Gaussian laser beam from the bottom. The nanoparticle with $r=15\mathrm{nm}$ and $n_{\mathrm{np}}=2.0$ is placed 20 nm above the nanodisk, which is trapped by the near-field transmitted through the structure. The substrate is considered semi-infinite.

Figure 2

(a) Scattering cross section and normalized electromagnetic energy as functions of incident wavelength. The vertical dashed line indicates the second-order anapole resonance, featuring maximum electric and magnetic energies inside the nanodisk with minimum scattering values. (b) Normalized electric field profile associated with the second-order anapole mode in (a). The insets in (b) are used to illustrate the direction of oscillation of the electric field component of light.

Figure 3

Transverse optical forces (a) $F_x$ and (b) $F_y$ experienced by a dielectric nanoparticle, with $r=15\mathrm{nm}$ and $n_{\mathrm{np}}=2.0$, placed 20 nm above the nanodisk. (c) and (d) are the traces of the effective potential along the planes (a) $x=0$ and (b) $y=0$ for the nanoparticle, respectively.

Figure 4

Longitudinal optical force ($F_z$) field map generated on a nanoparticle with $r=15\mathrm{nm}$ with the center at $z=120\mathrm{nm}$. Comparative calculations of (b) longitudinal optical force and (b) the transverse effective potential for nanoparticles with radius $r=12\mathrm{nm}$, $r=15\mathrm{nm}$, and $r=18\mathrm{nm}$, as a function of their center position along the $z$ axis. The results in (a)–(c) were obtained for $n_{\mathrm{np}}=2.0$. (d) Minimum of the effective potential as a function of the nanoparticle refractive index. Calculations for a nanoparticle 20 nm ($z=120\mathrm{nm}$) away from the top of the nanodisk.

Figure 5

(a) Transverse total optical force $F_{xy}$ calculated for a nanoparticle with $r=10\mathrm{nm}$ and $n_{\mathrm{np}}=2.0$ with its center at 10 nm away from the nanodisk. (b) Normal optical force ($F_z$) on the nanoparticle inside the slot region. Numerical results in (b) were obtained within the dipolar approximation.

Figure 6

(a) Numerical results for the electromagnetic heat power density at $\lambda =924\mathrm{nm}$, at half the height of the nanodisk. (b) Steady-state spatial temperature distribution profile for the system in (a). (c) The maximum temperature increase (due to the excitation of the second-order anapole mode) as function of the nanodisk radius. The regions with and without electromagnetic losses, labeled as heating and no heating, are indicated. The circle within the heating region indicates the radius used for the thermal calculations in (a) and (b), whereas the radius pointed out in the no heating-region corresponds to the radius used for the nanoparticle trapping calculations.