1. INTRODUCTION
Studies of high harmonic generation (HHG) have become a very active
domain in high-field physics. Together with above threshold ionization,
this spectacular nonlinear process is exemplary of the
atom–high-field interaction in the tunneling regime, defined by
the Keldysh parameter γ < 1. Besides its fundamental interest,
HHG has demonstrated unique properties as a XUV source. Microjoule
energies per pulse in the range 80–30 nm to a few nanojoules at
shorter wavelengths have been obtained (Hergott
et al., 2002; Takahashi et
al., 2002). The ultrashort pulse duration of ∼10 fs to
subfemtoseconds, together with the high spatial coherence and wave
front quality, lead to high peak brightness. Now available terawatt
laser sources with kilohertz repetition rates make possible high
average power and brightness that actually compare with those of
third-generation synchrotron sources in the 10–100 eV range. This
opens considerable perspectives for the dynamical studies at an
unprecedented subfemtosecond time scale in a variety of fields, from
atomic and molecular physics, chemistry, and biology to solid-state or
plasma physics (Larsson et al.,
1995; Gisselbrecht et al.,
1999; Descamps et al., 2000;
Quéré et al., 2000;
Merdji et al., 2000a,
2000b; Hergott
et al., 2001).
High-order harmonic radiation presents unique properties of intrinsic
spatial and spectral coherence allowing the transposition of many
infrared techniques to the XUV range. Interferometry is a widely used
technique offering a variety of possibilities as a tool for probing but
also manipulating and controlling ultrafast phenomena. The
demonstration of the generation of two temporally separated
phase-locked harmonic pulses has been recently reported (Salières et al., 1999; Hergott et al., 2003). This XUV
frequency-domain interferometer has been applied to the study of the
temporal evolution of a dense laser plasma at the femtosecond time
scale. Recently Ramsey-like spectroscopy has been demonstrated using
the coherence properties of high order harmonic generation (Cavalieri et al., 2002). If you now
generate N temporally separated phase-locked XUV pulses
separated in time you will observe in the spectral domain fringes that
are becoming narrower and brighter (scaling as N2).
This technique can be applied to perform high resolution spectroscopy
in the XUV range. The control of the phase on these time scales offers
a powerful tool to perform Fourier transform spectroscopy with an
unprecedented resolution. Another exciting application could be to use
multiple time-delayed beams to perform Ramsey-like spectroscopy in the
XUV range. Frequency-domain interferometry is a widely used technique
offering a variety of possibilities as a tool for probing but also
manipulating and controlling ultrafast phenomena, for instance, in
solid-state and plasma physics. The extension of the technique
considering two temporally separated harmonic pulses to multiple
phase-locked harmonic pulses will lead to highly contrasted spectral
fringe patterns and an increased phase sensitivity. In this article we
will describe the extension to four phase-locked XUV pulses and will
show the extreme sensitivity of this method to a change of the relative
phase on an attosecond time scale.
2. EXPERIMENTAL RESULTS AND DISCUSSION
The experiment has been performed on the LUCA laser facility in
Saclay. This Ti:Sa system delivers 800-nm pulses with 50-fs pulse
duration at 20 Hz with an energy up to 100 mJ. We studied the 11th
harmonic generated in xenon at an estimated intensity of 4 ×
1013 W/cm2. The four phase-locked harmonic
pulses have been generated using four IR laser pulses separated in time
as shown in Figure 1. The first double laser
pulse is created by using the group velocity difference on the two axes
of a birefringent plate rotated at 45° from the laser polarization.
A polarizer placed after the plate projects both components on the same
axis. The calibrated thickness of the plate fixes the time delay τ
between the two pulses at 120 fs. This couple of laser pulses is sent
into a Michelson interferometer where two replicas (C1 and
C2) are produced with the same time delay τ between the
pulses. The length of the first arm of the interferometer is controlled
by a stepping motor, whereas the second one is moved by a piezoelectric
translation with nanometric precision. It is then possible to control
very precisely the optical paths of (and thus the time delay
ΔT between) the two laser pulse couples C1 and
C2. These four IR laser pulses (500 μJ each) are focused
in a pulsed xenon jet where they generate four harmonic pulses that are
sent into a spectrometer. The spectral fringe pattern obtained after
dispersion by the grating is recorded on microchannel plates mounted in
the focal plane of the spectrometer at grazing incidence (12°) in
order to increase the resolution to 0.1 Å. The signal level is
high enough to perform a single shot of the power spectrum of the four
pulses.
Diagram of the setup used for the generation of four laser pulses
delayed in time.
When the two arms of the Michelson are slightly misaligned, the two
couples are not spatially superposed and we observe two identical
spectral fringe patterns corresponding to the interference between the
two pulses of each couple, with a fringe period fixed by the same time
separation τ (Fig. 2a). In this case the
observed fringe patterns are independent of the time delay
ΔT between C1 and C2. A realignment
of the Michelson allows a spatial superposition of the harmonic
couples. A dramatic change of the fringe pattern is observed (as shown
in Fig. 2b), which gives evidence for the
generation of four phase-locked harmonic pulses separated in time. The
delay ΔT between C1 and C2 was
chosen to be 2τ, corresponding to an equal separation of the four
pulses of τ. Due to this regular time separation, an effective
fringe narrowing is obtained (factor 2 with respect to the 2 × 2
sources case). By slightly varying the delay to ΔT =
2τ + Tq
/2(Tq /2 is the harmonic half
period, ∼120 as for the 11th harmonic, corresponding to a mirror
displacement of 18 nm), we observe a clear change of the fringe pattern
that becomes more regular with a fringe period twice as small as in
Figure 2a (Fig.
2c).
Fringe patterns for the 11th harmonic generated in xenon by two laser
pulse couples separated by τ = 120 fs. a: The Michelson is
misaligned. b, c: The Michelson is aligned and the delay
ΔT between the two couples is set, respectively, to 2τ
and 2τ + Tq /2.
In Figure 3, we show the corresponding
spectral profiles. In the case of a single couple, the modulation of
the harmonic spectrum follows cos2(ωτ/2). When
the two couples interfere, an additional modulation comes into play in
cos2(ωΔT/2). When ΔT
∼ 2τ, the same periodicity as in the case of a single couple is
observed, with a significantly narrowed central peak surrounded by
satellite structures (Fig. 3a). When
ΔT ∼ 2τ + Tq /2,
the periodicity seems to decrease to half the former value, with
regular peaks of equal intensity (Fig. 3b).
In both cases, there is a good agreement with the results of the fit
using the theoretical formula of interference between four phase-locked
pulses with the corresponding delays (dashed lines). This demonstrates
the high sensitivity of our experimental setup to a change of the
relative phase on an attosecond time scale: A phase shift between the
two couples of a half harmonic period (∼120 as) results in a strong
modification of the whole fringe pattern, whereas for the simple
two-pulse case (variation of τ), there is only a general shift of
the whole fringe pattern in the envelope, which is much more difficult
to diagnose unambiguously due to the experimental fluctuations.
Spectral profiles (solid lines) obtained from the interference of two
couples (H11) delayed by about 2τ (a) and 2τ +
Tq /2 (b). Dashed lines indicate the
fits from the theoretical formula. a: The spectral profile obtained in
the case of a single couple.
3. CONCLUSIONS
We have performed the generation of four phase-locked harmonic pulses
separated in time. The spectral profiles obtained from frequency-domain
interferometry present a high sensitivity to a change of the relative
phase on an attosecond time scale, indicating that such a control is
achieved on the harmonic emission. Interesting perspectives arise from
the application of this technique. The sensitivity of this technique
could be useful for, for example, the precise diagnostic of dense
plasmas. Moreover, pump probe experiments with two spatially separated
harmonic couples (see Fig. 2a) would benefit
from an absolute reference pattern or the possibility to probe large
plasmas with relative density measurements.
