From Non-Linear to Extremely Non-Linear
Non-Linear Optical Spectroscopy is commonly used to study ultrafast dynamics in matter. In general, one or several pump pulses first excite a sample; a delayed probe pulse then interacts with this sample, resulting in the emission of light through a low (second or third) order nonlinear process. The emitted light carries structural information on the sample which is used to retrieve the dynamics.
The principle of Extreme Non-Linear Optical Spectroscopy is similar but the nonlinear process that is used is then High-order Harmonic Generation. At first sight, the extremely high nonlinearity of the process seems to be an obstacle to the retrieval of structural information from spectra. However, the simplicity of the HHG mechanism makes this retrieval quite straightforward. Tunnel ionization splits the molecule's wavefunction in two parts; the light emission is then produced by the interference of strong-field driven attosecond electron wavepackets and the electrons that stayed in the neutral. Since the strong-field driven electrons have a typical de Broglie wavelength in the Ansgtröm domain, they constitute a perfect probe of the molecular structure.
Getting faster electrons
The faster the strong field driven electrons are, the shorter their de Broglie wavelength is and the more accurate the measurement is. To get faster electrons, there are two possibility: increasing the laser intensity or increasing the laser wavelength. Since we want to keep reasonable intensities to avoid strong nonadiabatic effects, fragmentation or complete ionization of the molecules under study, we use long wavelength laser pulses to generate high harmonics.
Harmonic spectra produced in low-Ip polyatomic molecules at 800nm and at 1800nm. Even though the laser intensity was lower in the 1800nm case, higher harmonics are produced, which means that faster electrons are at play.
Revealing the dynamics
The molecular structural information is not only encoded in the spectrum of the emitted light but also in its polarization state and phase. We have developed optical tools to characterize all these parameters and have recently used them to study rotational wavepackets in simple molecules. Additional tricks adapted from conventional nonlinear optical spectroscopy were also developed to increase the contrast of pump-probe measurements [1,2].
 Y. Mairesse et al. New J. Phys. 10, 025028 (2008)
 Y. Mairesse et al., Phys. Rev. Lett. 100, 143903 (2008)