# Nonlinear Interaction of Intense THz and Optical Pulses in Air

We are investigating the effects of the nonlinear interaction between THz and optical pulses in air.  The experimental layout follows the scheme proposed by Dai and coworkers [1]: the THz pulse is overlapped, in air, with a probe, 800 nm pulse. The electric field of the THz pulse breaks the isotropy of the air medium and creates an effective second order nonlinearity, (\chi^{(3)}_{eff}\propto\chi^{(3)}E_{THz}\),  with ETHz being the THz electric field. The probe pulse therefore generates an “Electric-Field-Induced” Second Harmonic (EFISH) signal. Differently from the standard Air-Biased Coherent Detection (ABCD) technique [1,2] where the Second Harmonic (SH) of the probe beam is measured with a photodiode, we spectrally resolved the wave-mixing signal. The EFISH spectrum as a function of the delay between the THz and probe pulses generates a spectrogram similar to that used in standard FROG (Frequency Resolved Optical Gating) measurements. The nonlinear wave-mixing produces two SH sidebands spectrally located at $$\omega + \omega \pm \Omega$$, where $$\omega$$ is the probe frequency and $$\Omega$$ is the THz pulse frequency. The higher frequency product is strongly suppressed by mode-matching constraints [3]. For increasing probe pulse energies a shift of the SH spectrum appears and an increase of the energy transfer on the high-frequency sideband allows for the observation of the beating in the  region where the two sidebands overlap. We show that such beating is proportional to the instantaneous THz electric field squared (see Fig. 1). By further increasing the optical field intensity, an extremely narrowband signal appears in proximity of the absorption lines associated to excited N2+ [4–6]. We show that such a coherent signal is triggered by the THz pulse and follows the THz electric field profile, as a consequence of the above-mentioned beating. Possibilities of enhancing the detection of THz pulses are discussed.

Fig. 1 (a) Spectrogram of the wave mixing between a THz and an 800 nm pulse in air. (b) Lineout of the spectrogram at the wavelength for which the SH sidebands beating has maximum visibility, overlapped with the ABCD trace.

### References

1. J. Dai, X. Xie, and X. C. Zhang, Phys. Rev. Lett. 97, 103903 (2006).
2. N. Karpowicz et al., Appl. Phys. Lett. 92, 011131 (2008).
3. X. Lu, N. Karpowicz, and X. C. Zhang, J. Opt. Soc. Am. B 26, A66 (2009).
4. Q. Luo, W. Liu, and S. L. Chin, Applied Physics B: Lasers and Optics 76, 337 (2003).
5. Q. Luo, S. A. Hosseini, W. Liu, and S. L. Chin, Optics & Photonics News 0 (2004).
6. J. Yao et al., Phys. Rev. A 84, 051802(R) (2011).