Geometric tailoring of plasmonic nanotips for atom traps

We theoretically analyzed a scheme for optical trapping of neutral atoms by plasmonic nanotips. An analytic quasistatic model was developed for studying the requirements on geometry and material parameters needed for a successful trap generation. We then used the numerical solution of Maxwell's equations to study different types of tips and realized optical trapping potentials at distances of up to 90 nm away from the tip apex. A dipole approximation of numerical results is presented, allowing for capturing essential trap characteristics in a simple form. Finally, we analyze scattering rates, trap characteristics, and heating of an exemplary nanotip, revealing the importance of heat dissipation for the considered structures.

Figure 1

Modulus and phase (dashed line) of the polarizability $\alpha =\left|\alpha \right|e^{i\Phi }$ of a prolate spheroidal particle (major axis $A=10$ nm).

Figure 2

Prolate spheroidal silver particle in the quasistatic limit with a major axis of 10 nm at $\lambda =589$ nm with aspect ratio of (a) $0.38$ and (b) 0.18. Both images show the field intensity as a contour plot (factor of 2 between adjacent color steps) overlaid by the electric-field lines and the corresponding dipole orientation (blue arrow) for a certain instance of time.

Figure 3

Field intensity (factor of 2 between adjacent contour lines) of a prolate ellipsoid with major axis of 100 nm and aspect ratio of $0.23$ illuminated by (a) a plane wave incident from left and (b) a needle beam at $\lambda =589$ nm.

Figure 4

Contour plot of the time-averaged electric-field components $E_z$ and $E_{\rho }$ of the “needle beam” used for the excitation (factor of 1.2 between the color steps). The field is transverse magnetic and, consequently, $E_{\varphi }=0$. The beam incidence is sketched in Fig. 3.

Figure 5

(a) Dipole and (b) octupole moment of silver prolate spheroids with different major axis illuminated by a needle beam at $\lambda =589$ nm. The values are normalized by the particle's volume and the maximum value of the dipole moment for the spheroid with a major axis of $A=50$ nm. Note that the quasistatic solution is proportional to the particle volume and so the normalized dipole moment is independent of the particle size.

Figure 6

Normalized field intensity along the central axis of dipole fields with the same dipole moment but different phase mismatch $\Delta \Phi$ superposed with the exciting field. The blue horizontal line is the field intensity of the exciting field, i.e., $|E_0{|}^2$. For a better comparability, the curves were shifted in (b), so that the minimum position is at the same location. The degradation of the trap characteristics, such as confinement and trap deepness, for a increasing phase mismatch are visible.

Figure 7

Geometric model of (a) a metallic nanocone and (b) a SNOM tip used for generating a near-field trap. The structures are rotationally symmetric to the central axis.

Figure 8

Trap distance (apex to minimum) and corresponding phase mismatch vs cone angle ${\theta }_c$ for silver and gold nanocones of different height $(h=[80,150,200]$ nm) and wavelengths.

Figure 9

Field intensity of different $({\theta }_c=\left[{10}^{\circ },{15}^{\circ },{20}^{\circ }\right])$ Ag cones at $\lambda =420$ nm (factor of $\sqrt{2}$ between adjacent contour lines). When the trap minimum moves away, the trap volume increases. For better visibility of this effect, a single contour line of the same level was added.

Figure 10

(a),(b) Field intensity of a gold tip with ${\theta }_c=19.5^{\circ }$ at $\lambda =589$ nm excited by a needle beam (factor of 2 between adjacent contour lines). (c) Field intensity of the exciting field and the corresponding dipole field obtained by expanding the scattered field in the trap region.

Figure 11

Trap distance (apex to minimum) and corresponding phase mismatch vs cone angle ${\theta }_c$ for silver and gold SNOM tips at different wavelengths.

Figure 12

Simulation results for a silver tip with an apex angle of ${37}^{\circ }$ excited at $\lambda =405$ nm with an illuminating intensity of $500\mathrm{mW}/{\mu \mathrm{m}}^2$. (a) Optical potential calculated according to Eq. (11). (b) Scattering rate according to Eq. (13). (c) Optical potential, approximated CP potential, and resulting total potential along the axial direction below the tip apex. (d) Distribution of the temperature increase $\Delta T$.

Figure 13

Prolate spheroidal coordinates for a constant value of $\varphi$. The lines of equal values of $\tau$ and $\sigma$ are shown on a plane containing the z axis.