First-principles simulation of intense single-cycle ultrashort light pulses interacting with diamond: Comparison study in attosecond and femtosecond regimes

The interaction of intense single-cycle ultrashort (0.1 to 9 fs) light pulses with diamond crystal and thin film is simulated, combining the dependent Kohn-Sham equation with the Maxwell equations. Distinct features are observed depending on the duration of the pulse. In the diamond crystal, maximum energy transfer from light pulse is observed with a pulse duration 0.3 fs. In this case, the phase of current density $J\left(t\right)$ coincides with that of the electric field $E\left(t\right)$. For the incident pulse of duration 0.1 fs, most of the light will transmit on passing the thin film. But for the pulse of duration 0.5 fs, there is more reflection than transmission. For light pulses of durations 7 and 9 fs in diamond crystal, traditional nonlinear behavior of energy transfer are observed. Interestingly, for the attosecond pulse, there is a linear scaling behavior with the pulse intensity below ${10}^{16}\mathrm{W}/{\mathrm{cm}}^2$ on the one hand and an unusual linear dynamic interference response behavior with the pulse width, determined by the interference of the different quantum pathways, on the other hand.

Figure 1

The calculated real (a) and imaginary parts (b) of dielectric function $\varepsilon \left(\omega \right)$ of diamond as a function of frequency in the ground state. The illustration of the bottom panel is the logarithmic function diagram of the imaginary part of $\varepsilon \left(\omega \right)$. The dark gray circle denotes the corresponding experimental data [55, 56].

Figure 2

The photon number density distribution with the single-cycle pulse intensity of $I_{\text{as}}={10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The panel corresponds to attosecond pulses with durations $T_{\text{as}}=0.1\mathrm{fs}, T_{\text{as}}=0.3\mathrm{fs}$, and $T_{\text{as}}=0.5\mathrm{fs}$. The illustration corresponds to femtosecond pulses with $T_{\mathrm{fs}}=7\mathrm{fs}$ and $T_{\mathrm{fs}}=9\mathrm{fs}$.

Figure 3

After the end of the pulse, the energy transfer of each atom from single-cycle pulse to the diamond crystal represented by Eq. (6), under different pulse durations and peak intensities.

Figure 4

After the end of the pulse, (a) the energy transfer of each atom from single-cycle pulse to the diamond crystal under different pulse durations. The red line represents the result of our simulation calculation. The violet line is the result of linear absorption calculated by Eq. (7). (b) The energy transfer rate of each atom in diamond crystal with various pulse durations. The upper axis is the average frequency $\omega$ corresponding to each pulse duration.

Figure 5

The upper panels corresponds to the time-dependent energy transfer $W\left(t\right)$ induced by the single-cycle intense light pulses $E\left(t\right)$ in diamond crystal with intensity of $I_{\text{as}}={10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and durations of $T\left(t\right)=0.1$–9 fs, respectively. The gray solid lines show the scaled pulse $E\left(t\right)$. The middle and lower panels show the time-dependent electric current density $J\left(t\right)$ pumped by $E_{\mathrm{as}-\mathrm{fs}}\left(t\right)$ with intensity of $I_{\text{as}}={10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and $I_{\text{as}}={10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, respectively.

Figure 6

(a) The schematic diagram of the calculated diamond crystal structure. The colored surface is the section $[1,-1,0]$ selected later. (b)–(f) The electron density difference distribution in diamond crystal pumped by the single-cycle intense light pulses with $I_{\text{as}}={10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ and $T=0.1$–9 fs, respectively. (g) The ground state electron density. Red area indicates increasing of electron density, while blue indicates decreasing.

Figure 7

The electronic density of states (DOS), occupation number (OCC) in an unit cell of diamond crystal at ground state, and after the laser pulse ends, the difference of occupation number (DOO) between ground state and excited state under varying pulse duration and peak intensity. The vertical solid line in the panel indicates the Fermi level $E_{\text{F}}$ and the gray dashed line represents the zero line. The DOOs under lower intensity pulse are rescaled.

Figure 8

(${\mathrm{a}}_1$) At the initial moment ($t=0$), the distribution of electric field ($E_{\text{Z,}\text{as}}$) in space. (${\mathrm{a}}_2)–({\mathrm{a}}_4$) At $t=6$ T, the distribution of electric field ($E_{\text{Z,}\text{as}}$) in space with three different types of attosecond single-cycle laser pulses ($T_{\text{W}}=0.1\mathrm{fs}, T_{\text{WZ}}=0.3\mathrm{fs}$, and $T_{\text{Z}}=0.5\mathrm{fs}$, respectively). (${\mathrm{a}}_5$) and (${\text{a}}_6$) The distribution of electric field ($E_{\text{Z},\mathrm{fs}}$) at $t=2$ T in space with femtosecond pulse of $T_{\mathrm{fs}}=7\mathrm{fs}$ and $T_{\mathrm{fs}}=9\mathrm{fs}$, respectively. The laser pulse with a peak intensity of $I_{\text{as}}={10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ transmits perpendicular to the diamond film with thickness of $d=29.988\mathrm{nm}$. The gray area ($0<X<29.988\mathrm{nm}$) represents the diamond film, and the area where $X<0$ and $X>29.988\mathrm{nm}$ represents the vacuum.

Figure 9

Corresponding to the laser parameters in Fig. 8, the distribution of absorption energy ($W_{\text{abs}}$) in the diamond film.

Figure 10

(a) Time-frequency representation obtained by using a Morlet transform, (b) frequency distribution spectrum, (c) space-wave-vector representation obtained by using a Morlet transform, and (d) wave-vector distribution spectrum, of the incident electric field with the peak intensity of ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ and $T_{\text{WZ}}=0.3\mathrm{fs}$.

Figure 11

Morlet transformations of the spatial distribution of the incident fields with the peak intensity of ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ and three different types of attosecond laser pulses ($T_{\text{W}}=0.1\mathrm{fs}, T_{\text{WZ}}=0.3\mathrm{fs}$, and $T_{\text{Z}}=0.5\mathrm{fs}$) correspond to the upper panels (${\mathrm{a}}_1$)–(${\mathrm{c}}_1$), respectively. Morlet transformations of the reflected fields and the transmitted fields correspond to the middle panels (${\mathrm{a}}_2$)–(${\mathrm{c}}_2$) and the lower panels (${\mathrm{a}}_3$)–(${\mathrm{c}}_3$), respectively.

Figure 12

Similar to Fig. 14, Morlet transformations of the spatial distribution of the incident fields, the reflected fields, and the transmitted fields with femtosecond pulse of $T_{\mathrm{fs}}=7\mathrm{fs}$ and $T_{\mathrm{fs}}=9\mathrm{fs}$ and the peak intensity of ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 13

The spatial distribution of electric field ($E_{\text{Z,as}}$) of diamond film with $d=29.988$ nm under the attosecond light pulse of $T_{\text{WZ}}=0.3\mathrm{fs}$ and different laser intensity. The electric fields of lower intensities are rescaled.

Figure 14

The spatial distribution of electric field ($E_{\text{Z,fs}}$) of diamond film with $d=29.988$ nm under the femtosecond light pulse of $T_{\mathrm{fs}}=9\mathrm{fs}$ and different laser intensity. The electric fields of lower intensities are rescaled.

Figure 15

Reflection, transmission, and absorption rates as a function of diamond film thickness with the peak intensity of ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ and three different types of laser pulses ($T_{\text{W}}=0.1\mathrm{fs}, T_{\text{WZ}}=0.3\mathrm{fs}$, and $T_{\text{Z}}=0.5\mathrm{fs}$). The gray dotted line represents the total reflectivity of the linear response.