Spatiotemporal properties of nanoshell plasmonic response for strong-field experiments

Field enhancement behavior of a ${\mathrm{SiO}}_2$/Au nanoshell is studied in the framework of strong-field physics. Localized plasmonic fields induce local electric field enhancement with the potential to lead to the strong-field regime without the use of costly amplified lasers. In this framework, electrons are tunnel ionized from the nanoshell and accelerated by the local field being spatially inhomogeneous in terms of spectral and polarization properties. These processes are happening within a single laser shot, and thermal effects are therefore neglected. We show that the localized response to ultrashort femtosecond pulses can be investigated by extending Mie theory to multilayer spherical particles. Nanoshell plasmonic resonances can be easily tuned depending on the volume ratio between core and whole particle. Optimum geometric parameters of the nanoshell are selected for use with ultrashort pulses centered at 800 nm where most femtosecond oscillators operate. It is shown that phase and amplitude reshaping of the incident pulse by the plasmonic resonance can be partially corrected using active shaping leading to ultrashort response of the medium. Finally, free electron classical trajectories are calculated to highlight the inhomogeneous nature of the local enhancement in a strong-field picture.

Figure 1

Layout of a nanoshell excited by a incident electric field polarized along ${\mathbf{u}}_{\mathbf{x}}$ and propagating along ${\mathbf{u}}_{\mathbf{z}}$. Shell and core radii are respectively $a_1$ and $a_2$ while their permittivities are ${\varepsilon }_{\mathrm{shell}}$ and ${\varepsilon }_{\mathrm{core}}$. A medium of permittivity ${\varepsilon }_{\mathrm{env}}$ is surrounding the nanoshell.

Figure 2

${\mathrm{SiO}}_2$ core, gold shell intensity enhancement of the $x$ component (main contribution) as a function of wavelength and $\beta$ for (a) $R_{\mathrm{shell}}=a_1=20$ nm, (b) $R_{\mathrm{shell}}=60$ nm, and (c) $R_{\mathrm{shell}}=100$ nm. The dashed white lines are highlighting the 800 nm wavelength behavior from which the optimal $\beta$ has been chosen. White lines are line-outs along those dashed lines. (d) Spectral intensity enhancement and phase in units of $\pi$ for the optimum $\beta$ of each nanoshell size.

Figure 3

Total and partial local field enhancement on the nanoshell surface as a function of $\theta$ and $\varphi$ for $\lambda =800\mathrm{nm}$ and $\beta =0.74$.

Figure 4

(a) Local intensity enhancement ${\left|L\left(\mathbf{r}\right)\right|}^2$ in the $(Oxz)$ plane. (b) Line-out of ${\left|L\left(\mathbf{r}\right)\right|}^2$ for $\theta =81.5^{\circ }$. (c) Line-out of ${\left|L\left(\mathbf{r}\right)\right|}^2$ for $r=60$ nm.

Figure 5

Local field enhancement spatial phase variation in units of $\pi$. Left column: distribution for $r=a_1$. Right column: spatial cut in the $\left(Oxz\right)$ plane.

Figure 6

(a) Cut in the (Oxz) plane showing the direction and magnitude of the local electric field. (b) cut for $x=R_{\mathrm{shell}}$.

Figure 7

Spectrotemporal properties of the local field enhancement $L_x$. (a) Spectral amplitude (thick lines) and phase (dashed lines) of incident field (black) and spectral response of the nanoshell (purple). Their product gives the local field spectral amplitude (blue). The incident field phase is equal to zero. (b) Temporal profile of the local field corresponding to the spectra in panel (a). (c) Wigner representation of the local field (corresponding to blue curves in panels (a) and (b). (d) As in panel (c) but for an incident field spectral phase correcting for the nanoshell spectral phase (see text for details).

Figure 8

Set of electronic trajectories around a nanoshell excited with $I_{\max }^{\mathrm{loc}}=1\times {10}^{14}$ ${\mathrm{Wcm}}^{-2}$ at 800 nm in (a) and 1300 nm in (b). Rectangles are zooms of selected trajectories. The color scale represents the field intensity spatial evolution in units of $I_{\max }^{\mathrm{loc}}$. Blue and orange areas are, respectively, core and shell.

Figure 9

Electron excursion as a function of time of birth within the local field (in units of field period) for (a) ${\lambda }_0=800$ nm and (b) ${\lambda }_0=1300$ nm. Electrons are born at $r=60.1$ nm and $\theta ={74}^{\circ }$ for 800 nm and $\theta ={82}^{\circ }$ for 1300 nm. The color scale highlights the driving electric field in units of maximum intensity $I_{\max }^{\mathrm{loc}}=1\times {10}^{14}$ ${\mathrm{Wcm}}^{-2}$.