Attosecond Pulse Shaping around a Cooper Minimum

High harmonic generation (HHG) is used to measure the spectral phase of the recombination dipole matrix element (RDM) in argon over a broad frequency range that includes the $3p$ Cooper minimum (CM). The measured RDM phase agrees well with predictions based on the scattering phases and amplitudes of the interfering $s$- and $d$-channel contributions to the complementary photoionization process. The reconstructed attosecond bursts that underlie the HHG process show that the derivative of the RDM spectral phase, the group delay, does not have a straightforward interpretation as an emission time, in contrast to the usual attochirp group delay. Instead, the rapid RDM phase variation caused by the CM reshapes the attosecond bursts.

Figure 1

Energy level diagram and time-domain picture of EWPs and broadband XUV pulses in (a) photoionization and (b) photorecombination in HHG in the vicinity of a Cooper minimum. See text for the discussion of paths (1), (2), and (3).

Figure 2

(a) Raw experimental HHG yield for $1.3\mu \mathrm{m}$ (open squares) and $2\mu \mathrm{m}$ (solid circles), with estimated transmission of $0.2\mu \mathrm{m}$ thick Al filter (dashed line), and time-dependent Schrödinger equation (TDSE)-Maxwell’s wave equation (MWE) calculation yield (solid line) for $1.3\mu \mathrm{m}$. (b) Raw experimental GD measurements [same symbols as (a)] with estimated GD contributions (offset for clarity) from the Ne atomic phase delay (dash-dotted line), Al filter dispersion (dashed line), and neutral Ar dispersion for a gas density-length product of $2.5\times {10}^{17}{\mathrm{cm}}^{-2}$ (dotted line). (c) TDSE-MWE calculations of the total GD (diamonds) for $1.3\mu \mathrm{m}$, along with the individual $s$ (left triangles) and $d$ contributions (right triangles) to the GD. The numbered regions are discussed in the text. In (b),(c) the attochirp GD (solid lines) is shown for reference.

Figure 3

Argon measurements for $1.3\mu \mathrm{m}$ (open squares) and $2\mu \mathrm{m}$ (solid circles), and TDSE-MWE calculation (solid lines) of the RDM (a) group delay and (b) phase. (b) also plots the RDM phase (dashed line) calculated with the simple model, Eq. (1). The horizontal line in (a) is the relative calibration error of the harmonic energy at the different drive wavelengths.

Figure 4

Dipole (a) phase and (b) GD, calculated from the simple model in Eq. (1) for argon $3p$ with $\mathrm{\Delta }\omega =6.6\mathrm{eV}$ (dashed lines), compared with an atom that has a larger or smaller relative amplitude strength, for example, $\mathrm{\Delta }\omega =2.2\mathrm{eV}$ (solid lines) or $\mathrm{\Delta }\omega =13.2\mathrm{eV}$ (dotted lines). Note that a small (large) $\mathrm{\Delta }\omega$ means that the $s$ contribution is relatively weak (strong) compared to the $d$ contribution.

Figure 5

Attosecond XUV time profiles reconstructed from a 24 eV spectral bandwidth centered on the CM feature, using the amplitude and phase results of the (a) $1.3\mu \mathrm{m}$ (solid line) and $2\mu \mathrm{m}$ (dashed line) experiments, (b) $1.3\mu \mathrm{m}$ TDSE-MWE calculations, and (c) $1.3\mu \mathrm{m}$ (solid line) and $2\mu \mathrm{m}$ (dashed line) simple model, Eq. (1), including the classical wave packet phase to match the attochirp of the experiment.