Controlling electron localization in ${{\text{H}}_2}^{+}$ by intense plasmon-enhanced laser fields

We present a theoretical study of the ${{\text{H}}_2}^{+}$ molecular ion wave-packet dynamics in plasmon-enhanced laser fields. These fields may be produced, for instance, when metallic nanostructures are illuminated by a laser pulse of moderated intensity. Their main property is that they vary in space on a nanometric scale. We demonstrate that the spatial inhomogeneous character of the plasmonic fields leads to an enhancement of electron localization (EL), an instrumental phenomenon to control molecular fragmentation. We suggest that the charge imbalance induced by the surface-plasmon resonance near the metallic nanostructure is the origin of the increase in the EL.

Figure 1

Top: Typical geometry parameters of the bow-tie shaped gold nanoantennas considered in our study. Here, we take $h=100$ nm, $t=40$ nm, and $g=20$ nm. The curvature radii of the tips are taken as 4 nm. The bond distance $R$ of the ${{\text{H}}_2}^{+}$ molecule is visually exaggerated for clarity. Bottom: The spatial profile of the field enhancement in the gap, along the $z$ axis, obtained from FDTD simulations. Circles are the actual enhancement determined by the meep code and the red (dashed) line is a polynomial fitting, as described in the text. Note that the laser electric-field peak amplitude is enhanced roughly by a factor of 2.5 near the metals compared with the center value, corresponding to 4 dB of increase in the laser intensity.

Figure 2

Top: (a) Temporal variation of $R$, i.e., $\langle R\left(t\right)\rangle$, (b) ionization probability $P_{\text{ion}}$, and (c) dissociation probability $P_{\text{dissoc}}$ of the ${{\text{H}}_2}^{+}$ molecule for $s=0$ (blue dashed lines) and $s=1$ (green solid lines) [see Eq. (4) for more details]. Center: Time dependence of the $R$-resolved probability distribution ${\left|\mathrm{\Psi }(R,t)\right|}^2$ of ${{\text{H}}_2}^{+}$ for $s=0$ (left) and $s=1$ (right). Bottom: (f) and (g) show the snapshots of the wave-packet distributions of $s=0$ and 1, when the wave packet is relaxed for a sufficient amount of time after the pulse ends. The laser intensity is $I=300$ $\mathrm{TW}/{\mathrm{cm}}^2$ and $\lambda =800$ nm. The pulse comprises ten total cycles (27 fs) and we use a flat-top pulse envelope with half-cycle ramp up or down. In panels (d)–(g) the color scale is logarithmic.

Figure 3

Variation of the asymmetry parameter ($A=P_{+}-P_{-}$) of ${{\text{H}}_2}^{+}$ as a function of plasmonic field intensity for $s=0$ (black dashed lines) and $s=1$ (red solid lines) [see Eq. (4) for details]. $A$ values are calculated after pulse is turned off and then the system is left to relax for a sufficient amount of time. We have performed calculations for two different wavelengths: (a) $\lambda =800$ nm and (b) $\lambda =1600$ nm. Insets show the absolute asymmetry parameter enhancement, i.e., the absolute ratio between $A$ of $s=1$ and 0 (in blue dotted lines), in the region $I=100\text{–}300$ $\mathrm{TW}/{\mathrm{cm}}^2$. The pulse comprises ten total cycles (27 fs for $\lambda =800$ nm and 54 fs for $\lambda =1600$ nm, respectively) and we use a flat-top pulse envelope with half-cycle ramp up or down. The spatial profile in both cases is the same as in Fig. 1 (bottom panel).

Figure 4

Top: An illustration showing the gap center of the nanostructure element, molecular center (centroid) of ${{\text{H}}_2}^{+}$, and offset with respect to the gap center. Full circles illustrates the positions of the nuclei. (a) Ionization probability $P_{\text{ion}}$, (b) dissociation probability $P_{\text{dissoc}}$, and (c) asymmetry parameter, $A=P_{+}-P_{-}$, as a function of the centroid offset. $P_{\text{ion}}$, $P_{\text{dissoc}}$, and $A$ are calculated after pulse is turned off and then the system is left to relax for a sufficient amount of time. The laser field parameters are the same as in Fig. 2.