MIR laser CEP estimation using machine learning concepts in bulk high harmonic generation

Monitoring the carrier-envelope phase (CEP) is of paramount importance for experiments involving few cycle intense laser fields. Common measurement techniques include f-2f interferometry or stereo-ATI setups. These approaches are adequate, but are challenging to implement on demand, at different locations as additional metrology tools, in intense few cycle laser-matter interaction experiments, such as those prevalent in sophisticated user beamlines. In addition there are inherent difficulties for CEP measured at non-conventional laser wavelengths (like e.g. mid infrared) and measurements above 10 kHz laser repetition rates, on single shot basis. Here we demonstrate both by simulations and by experiments a machine learning (ML) driven method for CEP estimation in the mid infrared, which is readily generalizable for any laser wavelength and possibly up to MHz repetition rates. The concept relies on the observation of the spectrum of high harmonic generation (HHG) in bulk material and the use of ML techniques to estimate the CEP of the laser. Once the ML model is trained, the method provides a way for cheap and compact real-time CEP tagging. This technique can complement the otherwise sophisticated monitoring of CEP, and is able to capture the complex correlation between the CEP and the observable HHG spectra.