Researchers in the group of Robert Alfano at the Institute of Ultrafast Spectroscopy and Lasers at the City College of New York, with collaborators from the University of California, San Diego, have introduced an approach to explain higher harmonic generation (HHG). The method is an alternative to the electronic cloud distortion model proposed in 1970. The Alfano-led team modulated the phase by nonlinear Kerr effect at optical cycles by the electronic self-phase modulation (ESPM) for gases and condensed matter for compact tabletop UUV and x-ray microscopes. The 1970 model is based on the Kerr nonlinear index on the carrier-envelope phase and envelope of light at the optical cycle response for noble gases and solids. In the current work, HHG is coherently driven by the laser field. The odd HHG has the potential to be used as a compact UV light microscope or as an x-ray tabletop microscope. ESPM is produced from electronic phase modulation, from the instantaneous response of the refraction index via the nonlinear Kerr index. The electron cloud explains the experimental HHG and supercontinuum generation from the interaction of high-intensity ultrafast pulses in three states of matter. The theory reveals the salient experimental features observed from the HHG in the form of the three characteristic intensity regimes and cutoff for different states of matter. The electronic self-phase modulation model from nonlinear Kerr index reveals salient features of the HHG: decreasing harmonics generation followed by a plateau to descending HHG signals to the cutoff frequency using the method of the stationary phase on ESPM. According to the team, its ESPM model itself represents an alternative model to the quantum mechanical three-step model interpretation of HHG — the quantum three-step model struggles to explain generation in solids, and the ESPM model gives additional features of spectral broadening about the N odd harmonics. The team used a 50-fs laser pulse at intensities of 1012 to 1015 W/cm2 to simulate and experimentally compare the salient features of HHG and supercontinuum about each harmonic from various materials such as gases and solids supporting the Kerr ESPM model. The ESPM model yielded a supercontinuum background superimposed with the sharp odd HHG, which had been experimentally observed in various forms of matter. In addition to the results, such a source of HHG from various matters will help to chart a course for the development of a compact UV x-ray microscope, the researchers said. The research was published in Optik (www.doi.org/10.1016/j.ijleo.2021.167872).