Three-dimensional carrier-envelope-phase map of focused few-cycle pulsed Gaussian beams

We derive an analytical expression that describes the complete three-dimensional carrier-envelope-phase (CEP) distribution in the focal volume of ultrashort pulsed Gaussian beams focused by spherical mirrors or lenses. The focal CEP map depends on the so-called factor g specifying the frequency dependence of the beam width of the source few-cycle pulse, on its chirp, and on the small chromatic aberration introduced by a lens without appreciably distorting or broadening the few-cycle pulse. We show how to tailor the CEP map of mirror-focused and lens-focused few-cycle pulses in order to produce negligible transversal and axial CEP variations in specific regions of the focal volume for phase-sensitive interactions of light with matter taking place in a volume or on a surface. We propose a quasiachromatic doublet lens that can implement in practice these tailored CEP distributions. © 2018 American Physical Society