High-order-harmonic generation driven by metal nanotip photoemission: Theory and simulations

We present theoretical predictions of high-order-harmonic generation resulting from the interaction of short femtosecond laser pulses with metal nanotips. It is demonstrated that high-energy electrons can be generated using nanotips as sources; furthermore, the recollision mechanism is proven to be intrinsically linked to this high-energy tail. If recollision exists, it should be possible to convert the energy gained by the electron in the continuum in a high-energy photon. Consequently, the emission of harmonic radiation appears to be viable. We employ a quantum mechanical time-dependent approach to model the electron dipole moment including both the laser experimental conditions and the bulk matter properties. The use of metal tips should provide an alternative way of generating coherent XUV light with a femtosecond laser field.

Figure 1

Plots of the high-order-harmonic spectra as a function of the harmonic order and CEP for a metal (Au) nanotip using a 2-fs FWHM laser pulse with $\lambda =800$ nm and (a) $E_0=10$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=-0.4$ GV m${}^{-1}$, (b) $E_0=10$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=2$ GV m${}^{-1}$, (c) $E_0=20$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=-0.4$ GV m${}^{-1}$, and (d) $E_0=20$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=2$ GV m${}^{-1}$.

Figure 2

Plots of the high-order-harmonic spectra as a function of the harmonic order and CEP for a metal (Au) nanotip using a 4-fs FWHM laser pulse with $\lambda =800$ nm and (a) $E_0=10$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=-0.4$ GV m${}^{-1}$, (b) $E_0=10$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=2$ GV m${}^{-1}$, (c) $E_0=20$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=-0.4$ GV m${}^{-1}$, and (d) $E_0=20$ GV m${}^{-1}$ and $E_{\mathrm{dc}}=2$ GV m${}^{-1}$.

Figure 3

Plots of the HHG spectra as a function of harmonic order for a metal (Au) nanotip using a trapezoidal shaped laser pulse with ten cycles of total time, $\lambda =685$ nm, and (a) $E_0=10$ GV m${}^{-1}$, (b) $E_0=15$ GV m${}^{-1}$, and (c) $E_0=20$ GV m${}^{-1}$. In all panels magenta denotes $E_{\mathrm{dc}}=-0.4$ GV m${}^{-1}$ and green $E_{\mathrm{dc}}=2$ GV m${}^{-1}$. Note that the harmonic yield scale ($y$ axis) is different in each panel.

Figure 4

Plots of the HHG spectra as a function of harmonic order for a metal (Au) nanotip using a trapezoidal laser pulse with ten cycles of total time, $\lambda =1800$ nm, and a peak laser electric field $E_0=10$ GV m${}^{-1}$. (a) Magenta denotes $E_{\mathrm{dc}}=-0.4$ GV m${}^{-1}$ and (b) green denotes $E_{\mathrm{dc}}=2$ GV m${}^{-1}$. Note that the harmonic yield scale ($y$ axis) is different in each panel.

Figure 5

Total energy of the electron (in terms of the harmonic order $n$) obtained from Newton's second law and plotted as a function of the ionization time $t_i$ [green (light gray) circles] or the recollision time $t_r$ [red (dark gray) circles]. The solid line parallel to the $x$ axis at around $n_c\approx 27$ shows the harmonic cutoff predicted by the conventional simple man's model (see the text).