Three-dimensional modeling of intense unipolar THz pulses formation during their amplification in nonequilibrium extended Xe plasma channel

We develop a three-dimensional (3D) fully self-consistent model for analysis of an ultrashort THz pulse propagation and amplification in a nonequilibrium plasma channel formed in xenon by a femtosecond UV laser pulse. The model is based on the self-consistent solution of a second order wave equation in the cylindrical geometry and the kinetic Boltzmann equation for the electron velocity distribution function (EVDF) at different points of the spatially inhomogeneous nonequilibrium plasma channel. We analyze the wide range of plasma and seed pulse parameters and reveal the optimal regimes for producing high intensity outgoing THz fields as well as highly unipolar THz pulses within the proposed mechanism. It is demonstrated that the process of EVDF relaxation in plasma limits the amplification of THz pulses at the level of $\sim {10}^7\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. Both focusing features of nonequilibrium plasma and the possibility of producing THz pulses with a high degree of unipolarity are confirmed for the case of 3D geometry.

Figure 1

On-axis distribution of the electric field strength in the initial THz pulse normalized to unity, $\ell =0.18\mathrm{cm}$.

Figure 2

Spatial distribution of the absolute value of the electric field strength in the THz pulse: initial distribution (a), after the 30-cm length propagation in free space (b), in the nonequilibrium xenon plasma channel of pressure $\sim 4\mathrm{atm}$ with Gaussian profile of electron densities with $N_e^{\left(0\right)}=3\times {10}^{13}\mathrm{c}{\mathrm{m}}^{-3}$ (c), and ${10}^{14}\mathrm{c}{\mathrm{m}}^{–3}$ (d). Radial sizes of channel and THz pulse are $R_0={\rho }_0=0.5\mathrm{cm}$. The level lines indicate the certain values of pulse electric field strength. The femtosecond UV pulse is located at the point $z-ct=0$. Initial THz pulse intensity is $1\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 3

The transverse size of THz pulse in dependence on propagation time for different electron densities in the plasma channel. Electron densities $\left(\mathrm{in}\mathrm{c}{\mathrm{m}}^{–3}\right)$ are given in the plots. Initial pulse parameters are ${\rho }_0=0.5$ cm (a) and ${\rho }_0=1.5$ cm (b). Initial peak intensity is $1\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$.

Figure 4

The gain factor [see Eq. (13)] in dependence on the seed pulse peak intensity for initial channel radii $1.5\mathrm{cm}$ (1) and $0.5\mathrm{cm}$ (2).

Figure 5

Electron velocity distribution functions in dependence on propagation length in a spatial point behind the UV pulse ($z-ct=-0.2$ cm) for ${\rho }_0=0.5$ cm, $I_0={10}^5\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ (a),(b) and for ${\rho }_0=1.5$ cm, $I_0={10}^4\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ (c),(d). Radial coordinates $\rho =0$ (a),(c) and $\rho ={\rho }_0$ (b),(d). The propagation lengths (in cm) are given in the inset.

Figure 6

Normalized to the unity spatial distribution of the absolute value of electric field strength in the THz pulse after the 30-cm propagation in xenon plasma channel of pressure $\sim 4\mathrm{atm}$ with Gaussian profile with $N_e^{\left(0\right)}={10}^{14}\mathrm{c}{\mathrm{m}}^{-3}$. Radial sizes of channel and seed THz pulse are $R_0={\rho }_0=1.5\mathrm{cm}$. The level lines indicate the certain values of pulse electric field strength. The femtosecond UV pulse is located the point $z-ct=0$. Initial intensity of the THz pulses is ${10}^4\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ (a) and ${10}^5\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ (b).

Figure 7

On-axis distribution of the electric field strength in the THz pulse for different propagation lengths [see the lengths (in cm) in the inset]: all the parameters of plasma channel and initial pulse correspond to those given in Fig. 6. The femtosecond UV pulse is located at the point $z-ct=0$. Initial intensities of the THz pulse are ${10}^4\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ (a) and ${10}^5\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ (b).

Figure 8

Spatial distribution of the absolute value of electric field strength in the THz pulse (normalized to unity) after the 30-cm propagation in the nonequilibrium xenon plasma channel of pressure $\sim 4\mathrm{atm}$ with Gaussian profile of electron density with $N_e^{\left(0\right)}={10}^{14}\mathrm{c}{\mathrm{m}}^{-3}$ for the initial intensity ${10}^7\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The level lines indicate the certain values of pulse electric field strength. The femtosecond UV pulse is located at the point $z-ct=0$. Radial sizes of channel and seed THz pulse are $R_0={\rho }_0=0.5\mathrm{cm}$ (a) and 1.5 cm (b).

Figure 9

On-axis distribution of the electric field strength in the THz pulse for different propagation lengths [see the lengths (in cm) in the inset]: all the parameters of the plasma channel and of the initial pulse correspond to those given in Fig. 8. The femtosecond UV pulse is located at the point $z-ct=0$. Radial sizes of channel and seed THz pulse are $R_0={\rho }_0=0.5\mathrm{cm}$ (a) and $1.5\mathrm{cm}$ (b).

Figure 10

On-axis THz pulse spectrum for different propagation lengths in the plasma channel. Plasma channel parameters are $N_e^{\left(0\right)}={10}^{14}\mathrm{c}{\mathrm{m}}^{-3}, N={10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$, initial pulse intensity is ${10}^7\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. Radial sizes of channel and initial THz pulse are $R_0={\rho }_0=0.5\mathrm{cm}$ (a) and 1.5 cm (b). Propagation lengths (in cm) are given in the inset.

Figure 11

The $U$ factor of THz pulse depending on the initial pulse intensity at a propagation length of 30 cm in xenon plasma channel with ${\rho }_0=R_0=1.5$ cm and $N_e^{\left(0\right)}={10}^{14}\mathrm{c}{\mathrm{m}}^{-3}, N={10}^{20}\mathrm{c}{\mathrm{m}}^{-3}$.