3 Bichromatic Control of Free Electron Wave Packets
51
sufficient to retrieve the full 3D information via Abel inversion [39]. However, in
general PMDs created by polarization-shaped pulses exhibit no such symmetry. In
this case, tomographic techniques, adapted from medical applications, are employed
to reconstruct the 3D PMD [40, 41]. The working principle of photoelectron tomography is illustrated in Fig. 3.4b. Numerous 2D projections of the PMD are measured
under different projection angles by rotating the ionizing laser pulse about its propagation axis using a superachromatic half wave plate (HWP). From the acquired set
of 2D images, the 3D PMD is reconstructed using tomographic procedures such as
the Fourier slice algorithm [40, 42, 43] or the backprojection algorithm [41, 42, 44].
Recent applications of the tomographic method comprise the imaging of molecular
orbitals [43], the creation and measurement of designer free electron wave packets
[45], the discrimination of chiral molecules via the multi-photon photoelectron circular dichroism [46–48], the characterization of elliptically polarized high-harmonic
radiation and the time-resolved investigation of laser-matter interaction inside transparent materials [44]. Further applications are reported in this chapter, including
the generation and detection of unusual angular momentum superposition states
[22] (Sect. 3.3.1), free electron wave packets with odd rotational symmetries [49]
(Sect. 3.3.4), photoelectron vortices [21, 50] (Sect. 3.3.3) and the spatial imaging of
spin-orbit wave packet dynamics [51] (Sect. 3.3.6).
3.3 Control of Free Electron Wave Packets
In this section, we present various applications of the experimental techniques introduced above. First we discuss different control scenarios to sculpture free electron wave packets from MPI of atomic systems employing the shaper-generated
polarization-tailored bichromatic fields. Subsequently, we describe two time-resolved
studies in which the bichromatic optical scheme was utilized for the observation of
atomic Rydberg and spin-orbit wave packet dynamics, respectively.
3.3.1 Control by Frequency Mixing
In the first control scenario, we use bichromatic fields with incommensurable center
frequencies ω 1 and ω 2 to control the 3D PMD from atomic MPI. Specifically we
employ temporally overlapping OLP pulses as prototypes for polarization-shaped
bichromatic fields. The OLP pulses consist of an s-polarized red band centered
around ω 1 = 2.28 rad/fs (826 nm) and a p-polarized blue band centered around ω 2 =
2.45 rad/fs (769 nm). Both colors have the same temporal shape E 1 (t) = E 2 (t) ≡ E(t)
with a spectral width of ω = 0.035 rad/fs which corresponds to a pulse duration
of t = 80 fs. By setting τ = 0 and decomposing each linearly polarized field into
a superposition of two counter-rotating circularly polarized components, the laser
field in (3.1) is rewritten as
51
sufficient to retrieve the full 3D information via Abel inversion [39]. However, in
general PMDs created by polarization-shaped pulses exhibit no such symmetry. In
this case, tomographic techniques, adapted from medical applications, are employed
to reconstruct the 3D PMD [40, 41]. The working principle of photoelectron tomography is illustrated in Fig. 3.4b. Numerous 2D projections of the PMD are measured
under different projection angles by rotating the ionizing laser pulse about its propagation axis using a superachromatic half wave plate (HWP). From the acquired set
of 2D images, the 3D PMD is reconstructed using tomographic procedures such as
the Fourier slice algorithm [40, 42, 43] or the backprojection algorithm [41, 42, 44].
Recent applications of the tomographic method comprise the imaging of molecular
orbitals [43], the creation and measurement of designer free electron wave packets
[45], the discrimination of chiral molecules via the multi-photon photoelectron circular dichroism [46–48], the characterization of elliptically polarized high-harmonic
radiation and the time-resolved investigation of laser-matter interaction inside transparent materials [44]. Further applications are reported in this chapter, including
the generation and detection of unusual angular momentum superposition states
[22] (Sect. 3.3.1), free electron wave packets with odd rotational symmetries [49]
(Sect. 3.3.4), photoelectron vortices [21, 50] (Sect. 3.3.3) and the spatial imaging of
spin-orbit wave packet dynamics [51] (Sect. 3.3.6).
3.3 Control of Free Electron Wave Packets
In this section, we present various applications of the experimental techniques introduced above. First we discuss different control scenarios to sculpture free electron wave packets from MPI of atomic systems employing the shaper-generated
polarization-tailored bichromatic fields. Subsequently, we describe two time-resolved
studies in which the bichromatic optical scheme was utilized for the observation of
atomic Rydberg and spin-orbit wave packet dynamics, respectively.
3.3.1 Control by Frequency Mixing
In the first control scenario, we use bichromatic fields with incommensurable center
frequencies ω 1 and ω 2 to control the 3D PMD from atomic MPI. Specifically we
employ temporally overlapping OLP pulses as prototypes for polarization-shaped
bichromatic fields. The OLP pulses consist of an s-polarized red band centered
around ω 1 = 2.28 rad/fs (826 nm) and a p-polarized blue band centered around ω 2 =
2.45 rad/fs (769 nm). Both colors have the same temporal shape E 1 (t) = E 2 (t) ≡ E(t)
with a spectral width of ω = 0.035 rad/fs which corresponds to a pulse duration
of t = 80 fs. By setting τ = 0 and decomposing each linearly polarized field into
a superposition of two counter-rotating circularly polarized components, the laser
field in (3.1) is rewritten as