Chirp and carrier-envelope-phase effects in the multiphoton regime: measurements and analytical modeling of strong-field ionization of sodium

Abstract

We investigate the influence of chirp on carrier-envelope-phase (CEP)-dependent strong-field few-cycle laser-induced photoelectron spectra of sodium, well within the multiphoton regime. Our measurements and analytical model of this process reveal a simple chirp-dependence, which has the potential to be utilized as an online monitor of laser chirp. Moreover, this effect could extend single-shot measurements of the CEP using above-threshold ionization to longer, chirped pulses, and significantly lower the required pulse energies. Specifically, at a wavelength of 775 nm and an intensity of $6.5\times {10}^{12}\,{\rm{W}}/{\mathrm{cm}}^{2}$ the CEP- and energy-dependent left-right asymmetries of emitted electrons are measured in a time-of-flight spectrometer. In these asymmetry maps, inclined stripe-like structures emerge, where the inclination is tunable with the chirp of the pulse. We report a simple analytical model, explaining the effect as the interference of electrons with even and odd angular momenta, located at energies in between adjacent above-threshold ionization peaks. As we demonstrate, the analytical model is in good agreement with the measurement, as well as with solutions of the three-dimensional time-dependent Schrödinger equation. Further, the analytical model, which can easily be extended to other atoms, allows us to derive an equation, describing the relation between the slope of the inclined stripes and the chirp of the laser.

Keywords

• multiphoton ionization
• ultrashort pulses
• Sodium
• chirp
• CEP effects
• above-threshold ionization