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

TL;DR

This paper derives an analytical model for the three-dimensional carrier-envelope phase distribution in focused ultrashort Gaussian laser beams, enabling precise control of CEP variations for phase-sensitive light-matter interactions.

Contribution

It introduces a comprehensive analytical expression for the CEP map in the focal volume of focused few-cycle pulses, accounting for beam parameters and aberrations, and proposes a practical lens design for tailored CEP control.

Findings

Derived an analytical CEP distribution model for focused Gaussian beams.

Identified how to tailor CEP maps to minimize variations in specific regions.

Proposed a doublet lens design for practical implementation of tailored CEP distributions.

Abstract

We derive an analytical expression that describes the complete three-dimensional carrier-envelope phase (CEP) distribution of 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 quasi-achromatic doublet lens that can implement in practice these tailored CEP distributions.