Carrier-envelope phase shift of few-cycle pulses along the focus of lenses and mirrors beyond the nonreshaping pulse approximation: the effect of pulse chirp

Abstract

The carrier-envelope phase (CEP) shift of few-cycle pulses along a focal region is evaluated without neglecting the pulse reshaping inherent to any focusing process. The CEP shift is then found to strongly depend on the chirp of the focused pulse. Based on this effect, realistic optical systems for focusing few-cycle pulses are proposed to control their focal CEP shift for their phase-sensitive interactions with matter.

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

“…The second contribution includes the effect of the small pulse reshaping, and depends on the pulse shape itself. For on-axis points only, it has been shown that any small amount of chirp in the focused pulse drastically alters the CEP map [20]. Here we evaluate the two contributions for off-axis points with chirped or unchirped Gaussian pulses, providing thus a complete description of the CEP map about the focus.…”

“…Of particular interest is the situation in which the CEP is constant transversally and axially. Equating (20) and (21), this effect is seen to be possible in the focal region only with an input beam with g ≥ 1.15 at a certain position ζ in [−1, 1] (where the curves in FIG. 1(d) and FIG.…”

“…In Ref. [20], it has been shown that irrespective of the value of g, a small chromatic aberration γ in [−1, 0] or in [0, 1] flattens the axial CEP variation in the first or second half of the focus, respectively, and a small chirp enhances further the flatness of the axial CEP variation. Following this criterion, it is easy in practice, and faster than deriving particular expressions, to adopt a inspection procedure by directly plotting the 3D CEP map given by Eq.…”

Upper Bound to the Orbital Angular Momentum Carried by an Ultrashort Pulse

“…Figure 1 illustrates the situation with the usual model with factorized field in space and time at the focus or waist z = 0, in which the Gaussian waist width s ω ≡ s is independent of frequency [16]. While for a few-cycle pulsed Gaussian beam (l = 0) the pulse shape on its maximum (at r = 0) is substantially unaltered [22,23], the same few-cycle pulse on the bright ring of a RPB widens and distorts, particularly for high |l|, as seen in Fig. 1.…”

Propagation-induced changes in the instantaneous polarization state, phase, and carrier–envelope phase of few-cycle pulsed beams

“…(24). For linearly polarized pulses, the term with a 0 0 ∕a 0 describes spectral filtering due to diffraction, and results in red-or blueshift of the carrier oscillations [12], or in reshaping of the real amplitude for chirped pulses [21]. These effects depend not only on the space-dependent filtering factor a 0 0 ∕a 0 but also on the temporal shape of the source pulse through dA x;y τ∕dτ∕A x;y , and are therefore generally different for the two components of the source pulse.…”