First-principles study of ultrafast and nonlinear optical properties of graphite thin films

We theoretically investigate ultrafast and nonlinear optical properties of graphite thin films based on first-principles time-dependent density functional theory. We first calculate electron dynamics in a unit cell of graphite under a strong pulsed electric field and explore the transient optical properties of graphite. The optical response of graphite shows a sudden change from the conducting to the insulating phase at a certain intensity range of the applied electric field. It also appears to be a saturable absorption (SA) in the energy transfer from the electric field to electrons. We next investigate a light propagation in graphite thin films by solving the coupled dynamics of the electrons and the electromagnetic fields simultaneously. It is observed that the SA manifests in the propagation with small attenuation in the spatial region where the electric field amplitude is about $4\times {10}^{-2}\text{to}7\times {10}^{-2}\mathrm{V}/\AA$.

Figure 1

Schematic illustration of a calculated system: (a) Linearly polarized electric field irradiates an ABA-stacked graphite crystal normally, for which we use a rectangular unit cell with eight carbon atoms. (b) Nonuniform k-point distribution to sample the entire Brillouin zone (BZ) that contains 1656 coarse points and 6272 dense points. (c) Band structure and electron occupation in the weak (left) and strong (right) field cases.

Figure 2

Dielectric function of a crystalline graphite in the direction parallel to the layer: (a) the real part $\mathrm{Re}{\varepsilon }_{zz}$ and (b) the imaginary part $\mathrm{Im}{\varepsilon }_{zz}$. The experimental spectra are also plotted as black [56] and gray [57] broken curves.

Figure 3

(a) Applied electric field and (b)–(e) induced current density for four different maximal field amplitudes $E_{\max }$. The central frequency and the pulse duration are set to ${\omega }_1=1.55\mathrm{eV}$ and $T_P=80\mathrm{fs}$, respectively. In (b)–(e), purple lines show calculated current density using Eq. (5). Black broken line shows the linear results with $\sigma =0.047-0.018i\mathrm{au}$.

Figure 4

Temporal evolution of the complex conductivity calculated from the short-time Fourier transform in Eq. (13). (a) The real part, (b) the imaginary part, and (c) the phase angle of the conductivity are plotted for three cases of maximum electric field amplitude.

Figure 5

Excitation energy as a function of time $E_{\mathrm{ex}}\left(t\right)$ for four cases of different field amplitudes. The broken curve is calculated assuming the linear response $E_{\mathrm{ex}}^{\left(\mathrm{LR}\right)}\left(t\right)$.

Figure 6

Energy transfer from the pulse to the medium as a function of the maximum amplitude of the electric field $E_{\max }$ for four different pulse durations: $T_P=10,20,40$, and $80\mathrm{fs}$.

Figure 7

Temporal evolution of the projected density of states (pDoS) at the vicinity of the Fermi level. (a)–(c) The applied pulse duration and maximal field amplitudes are set as $T_P=40\mathrm{fs}$ and $E_{\max }=2.7\times {10}^{-2}\mathrm{V}/\AA$ and (d) $2.7\times {10}^{-1}\mathrm{V}/\AA$, which correspond to Figs. 3 and 3, respectively. The total density of states (tDoS) is plotted as a broken line.

Figure 8

Time evolution of the electric field of a laser pulse irradiating a graphite thin film of $50\mathrm{nm}$ thickness normally (gray region). Two different intensity cases are compared, the maximum intensity in the vacuum of $I={10}^{12}\mathrm{W}/{\mathrm{cm}}^2$ (red) and $I={10}^{10}\mathrm{W}/{\mathrm{cm}}^2$ (black). The pulse duration is set as $T_P=20\mathrm{fs}$.

Figure 9

Intensity dependence of reflection $R\left(I\right)$ and transmittion coefficients $T\left(I\right)$ for the thin film graphite of $50\mathrm{nm}$ thickness. The pulse duration is set to $T_P=20\mathrm{fs}$.

Figure 10

Time evolution of a pulsed light irradiating a graphite thin film of $250\mathrm{nm}$ thickness (gray region). A red line shows the electric field of a strong pulse with maximum intensity of $I={10}^{12}\mathrm{W}/{\mathrm{cm}}^2$. A dashed black line shows the electric field of a weak pulse magnified so that the incident pulses look the same.

Figure 11

Energy deposition as a function of distance from the surface (a) for a weak pulse and (b) for strong pulse cases.

Figure 12

(a) Deposited energy $E_{\mathrm{ex}}\left(x\right)$ in the thin-film graphite of 250 nm thickness as a function of the distance from the surface $x$, (b) maximum electric field amplitude at the depth $x$, and (c) deposited energy plotted against the maximum electric field amplitude. The curves shown are for pulses of intensities $I={10}^9\sim {10}^{13}\mathrm{W}/\mathrm{cm}2$. The pulse duration is set to $T_P=20\mathrm{fs}$ for all intensities.