Coherent Control of THz Wave Generation in Ambient Air

Our study of THz wave generation in the pulsed laser induced air plasma with individually controlled phase, polarization, and amplitude of the optical fundamental wave ($\omega$) and its second harmonic ($2\omega$) indicates that the third-order nonlinear optical process mixing the $\omega$ and $2\omega$ beams in the ionized plasma is the main mechanism of the efficient THz wave generation. The polarity and the strength of the emitted THz field are completely controlled by the relative phase between the $\omega$ and $2\omega$ waves. The measured THz field amplitude is proportional to the pulse energy of the fundamental beam and to the square root of the pulse energy of the second-harmonic beam once the total optical pulse energy exceeds the plasma formation threshold. The optimal THz field is achieved when all waves ($\omega$, $2\omega$, and THz waves) are at the same polarization in the four-wave-mixing process.

Figure 1

Three schematic illustrations of the experimental setups. (a) A single optical beam excitation ($\omega$ or $2\omega$), in which the THz wave generation is assigned to the ponderomotive force to drive electrons and ions. (b) The common setup for the FWM which assuming the third-order nonlinear optical process. (c) A dichroic mirror combines the second harmonic beam with the fundamental beam. Phase, amplitude, and polarization of both beams can be controlled individually.

Figure 2

THz waveforms obtained by (a) focusing the $\omega$ and $2\omega$ beams in air, (b) and (c) by focusing a single beam in air ($\omega$ or $2\omega$), respectively. The detection is standard electro-optic sampling method with a 3 mm thick ZnTe crystal.

Figure 3

Interference pattern of rectified field measured by THz pulse peak amplitude from different combinations of polarization of the $\omega$ and $2\omega$ beams. The four letters in ${\chi }^{(3)}$ subscripts represent the polarization of THz wave, the $2\omega$ wave, and the two of $\omega$ waves, respectively, in which $x$ corresponds to $p$ polarized and $y$ corresponds to $s$ polarized.

Figure 4

(a) The interference pattern with a fine temporal resolution. The curve is a fit by $\cos (k_{2\omega }\Delta l)=\cos ({\omega }_{400}\tau )$ with 400 nm wavelength. (b) The relative phase between the $\omega$ and $2\omega$ beams is changed by $\pi$ ($\Delta l=200\mathrm{nm}$), and thus the waveforms show opposite polarity. The THz peak signal is extremely sensitive to the phase; the noise of the peak signal is from the phase fluctuation.

Figure 5

Dependence of THz amplitude on the power of the (a) $\omega$ and (b) $2\omega$ beams. The solid line and curve are the linear fit and the square-root fit, respectively. Once the plasma is created, the THz wave signal follows the equation $E_{\mathrm{THz}}\propto {\chi }^{(3)}\sqrt{I_{2\omega }}{I}_{\omega }\cos (\phi )$.