Extreme-Ultraviolet Nonlinear Wave Mixing and Waveform Control

In the past three decades, nonlinear optics has revolutionized laser spectroscopy and made tremendousimpact in optical communication, material processing, optical measurement technique, etc. It usuallyoperates from near infrared (NIR) to visible region due to the limitation of material transmittance. Recently,several kinds of coherent extreme-ultraviolet (EUV) sources have been developed with ultrashort durationsand ultrahigh intensities, such as EUV free electron laser and high-harmonic generation (HHG). By usingsuch kind of ultrashort EUV sources, it is possible to extend the nonlinear optical techniques to shorterwavelengths. Then better spatial and temporal resolutions, and even the capability of elemental selectivitycan be obtained. However, due to the fact that most materials absorb EUV strongly, it is hard to find suitableinteracting medium.In this project, we propose to use rare gas ions as the interacting medium for EUV nonlinear wavemixing. The ions can be prepared by an intense near-infrared (NIR) pulse focused onto a rare gas jet. Theintense NIR pulse ionizes the gas atoms to a proper ionization stage through optical-field ionization at itsfront edge, then mixes with the following EUV pulse by the ions. If the ionization potentials of the remainingelectrons in the ion are larger than the EUV photon energy, photoionization will not occur and absorption ofthe EUV wave can be greatly reduced. The remaining electrons provide the required response for nonlinearwave mixing. Since the third-order nonlinearity is the dominant nonlinear response for such kind of isotropicsystem, we focus on the four-wave-mixing (FWM) process. Firstly we calculate the third-order nonlinearpolarizability of Ar2+ and Ar3+ ions by using R. D. Cowan’s atomic structure code and Wigner-Eckarttheorem. The result ranges from 10–65 to 10–60 coul-m4/volt3 for the wave mixing of one EUV (20–50 nm)photon plus two NIR (810 nm) photons to a second EUV photon. We propose the experiment of one 1-μJEUV pulse and one 16-mJ NIR pulse mixed in a 2-mm Ar gas jet. A conversion efficiency of 24% isexpected. After that, we plan to develop a single-shot cross-correlation frequency-resolved optical gating(FROG) for EUV waveform measurement, and demonstrate the EUV waveform control based on theproposed FWM process.