Strong spectral broadening of Cherenkov-type terahertz radiation by free carrier generation

Free carrier generation is commonly viewed as detrimental to the optical-to-terahertz conversion efficiency in electro-optic crystals due to free carrier absorption of terahertz radiation. Contrary to this view, we show by numerical simulation that free carrier generation can have a positive effect on the Cherenkov-type terahertz emission from ultrashort laser pulses by strongly broadening the radiation bandwidth. The broadening is produced by terahertz emission from a surge current of the optically generated carriers, which are accelerated by the rectified electric field. Specific results are obtained for GaP pumped at a $1.7\text{−}\mu \mathrm{m}$ wavelength.

Figure 1

Geometry of the problem. An ultrashort laser pulse propagates in an electro-optic (EO) medium as a two-dimensional beam, induces nonlinear polarization, and generates free carriers. A trapezoidal Si prism is fixed at the exit boundary of the medium to couple the Cherenkov radiation to free space.

Figure 2

Snapshots of the electric field $E_y$ (normalized to $P_0$) and plasma density $N$ for (a) $I_0=1$ GW/${\mathrm{cm}}^2$, (b) $I_0=30$ GW/${\mathrm{cm}}^2$, and (c) $I_0=50$ GW/${\mathrm{cm}}^2$. (d) Oscillograms of $E_y$ (normalized to $P_0$) at $x=1$ mm for the same values of $I_0$. (e) Corresponding amplitude spectra.

Figure 3

The maximal (at $x=0$ and $\xi \to \infty$) plasma density $N_{\max }$, terahertz pulse energy $W_{\mathrm{THz}}$, and terahertz pulse spectral bandwidth (at the 0.1 level) as functions of the peak optical intensity.

Figure 4

Distributions of the normalized optical intensity $I/I_0$, the plasma density $N$ (bound of the shaded region), the free carrier current $J_y$ (normalized to $P_0{\omega }_p^{\max }$), and the electric field $E_y$ (normalized to $P_0$) along the plasma channel axis ($x=0$) for $I_0=50$ GW/${\mathrm{cm}}^2$.

Figure 5

(a) Snapshots of $E_y$ at three moments of time for $I_0=1$ GW/${\mathrm{cm}}^2$. (b) Oscillograms $E_y\left(t\right)$ at four points in free space near the surface of the Si prism. (c) Corresponding amplitude spectra. The crystal (green-shaded region) is 0.5 mm thick. The Si prism is shaded gray.

Figure 6

The same as in Fig. 5 but for $I_0=50$ GW/${\mathrm{cm}}^2$.

Figure 7

(a) The averaged oscillograms $E_y\left(t\right)$ (normalized to $P_0$) and (b) corresponding amplitude spectra for $I_0=1$, 30, and 50 GW/${\mathrm{cm}}^2$ The crystal thickness is 0.5 mm.

Figure 8

The terahertz radiation (a) energy and (b) bandwidth as functions of the crystal thickness for different $I_0$. The dashed lines in panel (a) show the linear energy scaling with the crystal thickness.

Figure 9

Snapshots of $E_y(x,\xi )$ (normalized to $P_0$) in the absence of free carrier generation obtained (a) numerically and (b) analytically [45]. (c) Numerical and analytical oscillograms of $E_y$ (normalized to $P_0$) at $x=1$ mm. (d) Corresponding amplitude spectra. In panels (c) and (d), the analytical curves are slightly shifted rightwards for clarity (otherwise they coincide with the numerical curves).

Figure 10

Numerically calculated amplitude transmission coefficient $T$ for a rectangular terahertz pulse (200-ps pulse duration, 1-THz central frequency) normally incident on the vacuum-plasma boundary as a function of the plasma frequency (blue solid line) in comparison to the analytical dependence for a 1-THz monochromatic wave (red dotted line).

Figure 11

(a) Oscillograms $E_y\left(t\right)$ (normalized to $P_0$) at $x=0.6$ mm in free space near the output surface of the Si prism for three different resolutions (the multiplication factor indicates an increase in the number of grid cells and time steps with respect to the steady-state case). (b) Corresponding amplitude spectra. The crystal thickness is 2 mm.

Figure 12

The terahertz pulse bandwidth and energy as functions of the peak optical intensity, with the corresponding fitting curves $\alpha +\beta I_0^4$ and $\gamma I_0^2$ ($\alpha , \beta$, and $\gamma$ are the fitting coefficients). The intensity dependencies of the terahertz spectral peak frequency ${\omega }_m$ and the maximal plasma frequency ${\omega }_p^{\max }$ are shown for reference. The vertical line marks the intensity ($\approx 27$ GW/${\mathrm{cm}}^2$) at which ${\omega }_p^{\max }$ equals the terahertz spectral peak frequency in the absence of free carrier generation ($\approx 2$ THz, shown by the lower horizontal line).