Terahertz wave amplification by a laser-modulated relativistic electron beam

Generation of tunable terahertz radiation based on the interaction of a frequency-chirped low power terahertz wave with a relativistic electron beam is proposed. The electron beam is first modulated temporally due to the ponderomotive force induced by the beat wave of two copropagating intense laser beams of slightly different frequencies. Then the electron beam interacts with a low-amplitude driver wave at terahertz frequency with a linear frequency chirping. A nonlinear transverse current density is driven that emits terahertz radiation at an up-shifted frequency with a relatively enhanced amplitude. The modulation process is analyzed theoretically by a complete set of fluid equations and considering the effects of both the electrons space-charge potential and the beat wave ponderomotive force. The initial density and energy of the electron beam are both optimized in order to improve the terahertz amplification process. The effect of the driver’s frequency chirping, as well as the effects of the initial electron beam density and energy on the emitted terahertz radiation are investigated numerically. It is shown that the frequency chirping of the driver wave plays a key role in terahertz amplification. It is shown that there is an optimum chirp value for which the terahertz radiation is amplified significantly compared with the case without chirping. Moreover, transverse effects of the laser beams and the driver wave on the emitted terahertz radiation are also investigated.

Figure 1

The proposed layout of the interaction. The electron beam is modulated by the ponderomotive force induced by the lasers beat wave. Whereafter, the modulated electron beam interacts with a chirped-frequency low-amplitude driver wave at terahertz frequency that drives a nonlinear transverse current of electrons. The nonlinear oscillations of electrons will then emit high-intensity terahertz radiation.

Figure 2

Terahertz amplification gain versus its frequency for different chirp parameters, i.e., optimum chirp, $b_{\mathrm{d}}^{(\pm )}=b_{\mathrm{d}}^{\mathrm{opt}}\pm {10}^{-4}$ and the case without frequency chirping. The upper horizontal axis shows the driver wave’s frequency. All parameters are the same as in Table 1.

Figure 3

Terahertz amplification gain (a), and the optimum frequency chirp parameter of the driver wave (b) versus frequency for different initial electron beam densities. All parameters are the same as in Table 1.

Figure 4

Terahertz amplification gain versus the initial electron beam densities lower than the critical density for terahertz frequency $f_{\mathrm{T}}=30\mathrm{THz}$. Other parameters are the same as in Table 1.

Figure 5

Terahertz amplification gain (a), and the optimum frequency chirp parameter of the driver wave (b) versus frequency for different electron beam energies. All parameters are the same as in Table 1.

Figure 6

Terahertz amplitude dependency on the transverse dimensions.