Coherent Terahertz Polarization Control through Manipulation of Electron Trajectories

The dynamics of ionized electrons in a plasma can be controlled by synthetic optical fields composed of the fundamental and the second harmonic of femtosecond optical pulses with an arbitrary phase and polarization. We show here that the plasma-emitted half-cycle THz radiation directly reflects the two-dimensional trajectories of the electrons through polarization sensitive THz emission spectroscopy. As a result, we find that the THz polarization smoothly rotates through $2\pi$ radians as the relative phase between the two pulses is adjusted, providing a new means of coherently controlling the polarization of light at THz frequencies.

Figure 1

The experimental setup: An 800 nm beam is focused through a BBO crystal to create a plasma that radiates THz fields. Also shown are THz waveforms measured by electro-optical sampling with BBO position at $d=0\mathrm{mm}$ (purple or light gray) and $d=13\mathrm{mm}$ (red or gray), corresponding to $\pi /2$ relative phase difference, with half-cycle THz field polarization close to $E_x$ and $E_y$ respectively.

Figure 2

(a) The transmitted THz intensity through a horizontally (solid blue or dark gray) or vertically (solid cyan or gray) oriented THz polarizer as a function of the BBO crystal position, indicating polarization rotation of the THz field when the relative phase changes by $\pi /2$. Also shown are corresponding electro-optic sampling measurements (dots, see text). (b) The ratio (blue or dark gray) of minimum to maximum THz intensities during $2\pi$ radian change of the relative phase as a function of the BBO tilt angle, $\beta$. The measured ellipticity (orange or light gray) of the 800 nm pulse shows a similar dependence on $\beta$. (inset) THz intensity as a function of relative phase for two different tilt angles. (c),(d) Transmitted THz intensity as a function of the BBO position and the THz polarizer angle at tilt angles $\beta =1.2°$ and $\beta =0°$, respectively. (e),(f) The simulation of (c),(d), considering the change of the second harmonic doubling efficiency when translating the BBO crystal.

Figure 3

(a) and (b) are the wave fronts of the two-color field at relative phase $\phi =0$ and $\phi =\pi /2$, respectively, with 55° relative polarization with $\Gamma =0$. The color shows the carrier phase of the fundamental optical field. (c) and (d) show the calculated THz polarization dependence on the relative phase for $\beta =1.2°$ and $\beta =0$, respectively.

Figure 4

(a) The THz polarization angle (squares) with respect to the fundamental optical polarization as a function of the BBO crystal rotation angle $\alpha$. The solid line is calculated based on the $2\mathrm{\text{−}}d$ photocurrent model. The inset shows the THz transmission (dots) as a function of the THz polarizer angle ${\theta }_p$ at $\alpha =80°$ with the sinusoidal fit (solid line). (b) The total THz intensity (dots) as a function of BBO rotation angle $\alpha$. The solid line represents the calculation. (c) The transmitted THz intensity (dots) through a polarizer as a function of the polarizer angle at various pump energies with sinusoidal fits (solid lines). The measurements and calculations in Fig. 4 are obtained at $d=0\mathrm{mm}$ and $\beta =0$.