Spectral redshifts in the intense laser-cluster interaction
K. Y. Kim,
1
I. Alexeev,
1
T. M. Antonsen,
2
A. Gupta,
2
V. Kumarappan,
1
and H. M. Milchberg
1
1
Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
2
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
(Received 21 September 2004; published 4 January 2005)
We study spectral shifts in intense ultrashort laser pulses propagating in clustered gas jets. Forward- and
side-scattered laser pulse spectra were measured as a function of pulse width for chirped pulses, and the
forward spectrum and absorption were measured for variably delayed colinear 2 probe pulses. The observa-
tion of redshifts is consistent with our model of rapidly increasing cluster polarizability early in the laser-
heated cluster explosion. In addition, there is a blueshift contribution implying the presence of unclustered
atoms in the jet. Simulations of intense pulse propagation in cluster jets are in reasonable agreement with the
chirped pulse experiment.
DOI: 10.1103/PhysRevA.71.011201 PACS number(s): 36.40.Vz, 36.40.Gk, 52.50.Jm
The interaction of intense laser pulses with atomic clus-
ters is an area of research receiving increasing interest [1–3].
The coupling of intense laser pulses to clustered gases is
unusual in that it combines features of high-energy density
physics, corresponding to strong laser heating at locally solid
density, with laser propagation through low-volume average
density material.
In recent work, we have shown how the details of the
cluster explosion under an intense laser field are expressed
through the evolution of its transient complex polarizability
[4]. In general
r
=Re initially increases in time as the
cluster expands, and it can be enhanced by resonant laser-
cluster coupling at critical density [5] or, at higher intensity,
by a nonlinear resonance [6]. The hydrodynamic model of
Ref. [5] is appropriate for larger clusters and/or moderate
laser intensity, the conditions of the present experiment. The
polarizability remains positive as long as the cluster response
is dominated by plasma that is above critical density. After
sufficient cluster expansion, when the dominant response is
by the subcritical plasma,
r
becomes negative. At the same
time,
i
=Im is increasing and reaches its peak near the
zero crossing of
r
. The refractive index of a gas of clusters
is n = 1+4N
c
¯
1/2
1+2N
c
¯ , where N
c
is the cluster
number density and ¯ is the polarizability averaged over an
ensemble of cluster sizes (typically N
c
¯ 1 [5]). As the ini-
tial increase in ¯
r
occurs fastest at the beam center due to the
greater cluster heating rate there, self-focusing of the laser
pulse is expected. This has been observed in our recent ex-
periments [7].
In the frequency domain, the transient behavior of polar-
izability is seen as self-phase modulation and frequency
shifts in the laser spectrum. Assuming a uniform medium,
and allowing for a fraction of the gas to be unclustered, the
transient spectral shift can be expressed as
t =-2L
-1
d
dt
n
r
t
=-2L
-1
d
dt
2N
c
¯
r
t -
1
2
N
e
t/N
cr
, 1
where is the laser central wavelength, L is the propagation
path length through the heated cluster plasma, N
e
t is the
electron density arising from ionization of the unclustered
atoms (monomers), and N
cr
= m
2
/4e
2
is the critical plasma
density, where m and e are the electron mass and charge, and
is the laser frequency. If the cluster response is dominant,
spectral redshifts 0 are expected when ¯
r
increases
with time as the clusters ionize and expand [5] in the pres-
ence of the laser pulse. The observation of redshifts due to
the propagation of intense pulses in plasmas has been previ-
ously restricted to the case of ultra-intense pulses in the rela-
tivistic regime, where the refractive index change due to the
relativistic mass increase can lead to self-focusing and red-
shifts [8,9]. In this paper, we show that in a clustered gas jet,
redshifts are observed at intensities four orders of magnitude
lower, and that these shifts are consistent with our moderate
intensity model of exploding cluster polarizability. We note
that at similar intensities in nonclustered gas jets, only blue-
shifts from ionization are observed [10], given by the second
term in Eq. (1).
The experimental setup is shown in Fig. 1. Positively and
negatively chirped Ti:sapphire laser pulses (1.5 mJ, 798 nm),
of adjustable width in the range 80 fs to 1.5 ps, were focused
to 5 10
13
–10
15
W/cm
2
in a gas jet of argon clusters. The
pulse width was controlled by adjusting the grating separa-
tion in the laser’s pulse compressor. The average radius of
clusters was estimated to be 300 Å at a backing pressure of
FIG. 1. Experimental layout for the measurement of forward-
and side-scattered spectra of intense femtosecond laser pulses
propagating through a gas of clusters.
PHYSICAL REVIEW A 71, 011201(R)(2005)
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