Plasma Waveguides: Addition of End Funnels
and Generation in Clustered Gases
K.Y. Kirn, I. Alexeev, J. Fan, E. Parra, and H.M. Milchberg
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742
Abstract. We present results from some recent experiments: the generation of a plasma funnel for
improved pump pulse input coupling to plasma waveguides, and the development of a single shot
transient phase diagnostic with 15 fs temporal resolution. The phase diagnostic is used in two
experiments. We first demonstrate that short pulse heated clustered gases can act as an optical
guiding medium and are highly absorbing. We show that this leads to a method for plasma
waveguide generation at densities substantially lower than current typical values. Second, we
measure transient phase shifts generated by intense pump pulses injected into plasma waveguides.
1. PLASMA WAVEGUIDES WITH END FUNNELS
One of the major problems associated with the use of laser-generated preformed
plasma waveguides for laser-driven accelerators is reduced pump pulse coupling that
occurs owing to excessive waveguide taper at the end [1]. This taper results from the
sharp falloff in line-focused waveguide generation laser intensity near the end of the
focus. The plasma near the end is less ionized and heated and consequently the radial
shock development and radial propagation lags that of axial sections closer to the line
focus center. This problem can be exacerbated with gas jets, where a sharp drop off in
gas density occurs at the jet edge [1].
A promising solution to this problem is to use an auxiliary laser pulse to generate a
short length of strongly heated plasma near the end of the line focus. The goal is to
produce a local plasma lens or 'funnel', grafted onto the end of the plasma
waveguide, which can focus and match an injected intense pump pulse into the main
waveguide. Favourable conditions for this occur either when the funnel plasma
expands radially at a rate faster than the waveguide end, or when it starts its
expansion at a time earlier than the waveguide.
Control of the funnel plasma in time and space independent from the waveguide
generation should allow greatly improved coupling. Figure 1 shows our setup to
explore this idea. The line focus is generated by focusing a pulse (500 mJ, 100 ps,
1064 nm from a mode-locked Nd:YAG laser system [2]) through an axicon lens. The
funnel plasma is produced by focusing a 100 mJ portion of the 100 ps Nd:YAG pulse
through the same lens used to inject intense ultrashort Ti:Sapphire laser pulses into
the plasma waveguide. The funnel generation pulse and injection pulse
counterpropagate with respect to the axicon-focused waveguide generation pulse. The
axial and transverse positioning of the funnel plasma with respect to the axicongenerated plasma waveguide is controlled by an external negative-positive lens pair
in the funnel generation beam. By means of a long optical delay line, the funnel
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
646
plasma can
can be
be generated
–10 ns
plasma
generated with
with aa negative
negative through
through positive
positive delay
delay of
of-10
ns to
to ++ 3ns
3ns
with respect
respect to
to the
the plasma
plasma waveguide.
waveguide.
with
ref.
ref.
Lb
CCD 1
pump
pumpA
/
Waveguide 500 mJ
Waveguide
100 ps
gen. beam
1064 nm
gen.
beam 1064nm
probe
JllL Iprobe
I Funnel
Funnel generation
generation beam
beam
100
100mJ,
rnJ, 100ps,
100ps, 1064
1084 nm
nm
-10
ns -^ +3
-10ns
+3 ns
ns w.r.t.
w.r.t. waveguide
waveguide
Pump
Pump pulse
pulse
50 mJ, 70 fs
50 mJ, 70 fs
800
nm
800 nm
La
Frequency domain
Frequency domain
interferometer
interferometer
FDI
B
IF filter
800 nm
C
C
D
2
L2
He 640 torr
N20 10 torr
L1
DL1
Transverse probe
,_ beam
,_
Transverse probe beam
DL2
FDI reference
FDI reference
and probe
and probe
Beams
Beams
λ0=700 nm
/L=700nm
°
FIGURE 1. Experimental setup for generation of a plasma funnel at the end of a plasma waveguide.
FIGURE 1. Experimental setup for generation of a plasma funnel at the end of a plasma waveguide.
The funnel generation pulse is directed through the Ti:Sapphire pump pulse lens, and it is
The funnel generation pulse is directed through the Ti: Sapphire pump pulse lens, and it is
independently adjustable in time and space with respect to both the waveguide generation pulse
independently adjustable in time and space with respect to both the waveguide generation pulse
(axicon pulse) and the injected pump pulse.
(axicon pulse) and the injected pump pulse.
Figure 2 shows shadowgram images of the end region of a plasma waveguide with
Figure
2 shows shadowgram images of the end region of a plasma waveguide with
and without funnels generated at its end. In this experiment, a backfill target gas of
and without funnels generated at its end. In this experiment, a backfill target gas of
640 torr of helium plus 10 torr of N2O was used. Transverse interferometry shows
640 torr of helium plus 10 torr of N2O
was used. Transverse interferometry shows
that beyond the entrance, the waveguides are fully ionized. The times in the figure
that beyond the entrance, the waveguides are fully ionized. The times in the figure
refer to funnel pulse delay with respect to the waveguide generation pulse. The
refer to funnel pulse delay with respect to the waveguide generation pulse. The
funnel-free waveguide is seen to have a significant taper, as seen in previous work.
funnel-free waveguide is seen to have a significant taper, as seen in previous work.
The addition of the funnel pulse is seen to remove the taper and widen the end region.
The addition of the funnel pulse is seen to remove the taper and widen the end region.
For the cases where the funnel pulse arrives in advance of the waveguide pulse
For the cases where the funnel pulse arrives in advance of the waveguide pulse
(negative delays), the waveguide end is significantly fatter than for the reverse
(negative delays), the waveguide end is significantly fatter than for the reverse
situation. Coupling of an intense Ti:Sapphire pump pulse to the waveguide with and
situation. Coupling of an intense Ti: Sapphire pump pulse to the waveguide with and
without the funnel is shown in waveguide exit mode images of Fig. 3. As usual, the
without the funnel is shown in waveguide exit mode images of Fig. 3. As usual, the
waveguide-free case shows a very large beam at the guide exit, which here overfills
waveguide-free
case shows a very large beam at the guide exit, which here overfills
the imaging optics aperture. The funnel-free waveguide case shows a bright lowest
the imaging optics aperture. The funnel-free waveguide case shows a bright lowest
order exit mode surrounded by rings, which are due to far field interference of the
order
exit mode surrounded by rings, which are due to far field interference of the
portion of the injected beam which is refractively ‘scraped’ off by the taper at the
portion
of theThe
injected
is refractively
by thelowest
taper at
the
guide end.
funnelbeam
plus which
waveguide
case shows'scraped'
an even off
brighter
order
guide end. The funnel plus waveguide case shows an even brighter lowest order
mode of the same size, without rings. The focal spot FWHM is 20µm and the peak
mode
the sameis size,
rings.non-appearance
The focal spotofFWHM
is 20jum
guidedofintensity
1017 without
W/cm2. The
the rings
shows and
thatthe
thepeak
end
guided intensity is 1017 W/cm2. The non-appearance of the rings shows that the end
647
coupling has improved. The mode profile is determined by the main extent of the
waveguide, which is unaffected by the presence of the funnel.
No f.mn-1 m.le-
No funnel pulse
200 (.im
Funnel pulse precedes
.
waveguide gen pulse
-3.5 ns
-2.5 ns
-0.5 ns
Funnel pulse follows
waveguide gen. pulse
0.5 ns
2.5 ns
|2-5
FIGURE 2. Shadowgram images of waveguide end region showing typical taper for case of no funnel
pulse, and taper removed for cases of funnel pulse at various delays before and after the waveguidegeneration pulse.
lOjimCFWHM)
nliunnel
with funnel
FIGURE 3. Top image: image of waveguide exit plane location when no waveguide present.
Overfilling of imaging aperture results in fringes. Bottom images: end mode images from waveguides
with and without funnel at injection end.
648
2. SINGLE-SHOT SUPERCONTINUUM SPECTRAL
INTERFEROMETRY AND PLASMA WAVEGUIDE
GENERATION IN CLUSTERED GASES
In order to measure wakefields generated by intense guided pump pulses in plasma
waveguides, we developed an ultrafast, single shot transient phase diagnostic
technique, which we call 'single-shot supercontinuum spectral interferometry'.
Spectral interferometry [3] is a well-known technique for measuring refractive index
transients in materials. In our setup (see Fig. 4), [4], approximately 1 mJ was split
from the main Ti: Sapphire pulse and was focused in 1 atm air to produce a broad,
150nm FWHM supercontinuum (SC) extending mainly to the short wavelength side
of the pump pulse, with central wavelength 700 nm. After spatial filtering, the ~ 0.1
mJ continuum pulse was recollimated and split by a Michelson interferometer delay
line into equal energy probe and reference pulses. Temporal chirp to -1.5 ps was
imposed on the pulses by a 25.4 mm thick SF4 glass window, allowing single shot
measurement of refractive index transients up to 1.5 ps long. The twin chirped SC
pulses were recombined with the pump and collinearly focused with it into the
interaction region, with the reference pulse leading the pump, and the probe
superimposed on the pump. The SC beam was focused to a -IVOjum FWHM spot
size, overfilling the pump spot. After the interaction region, the pump pulse was
removed by a high reflectivity 800 nm mirror, and the SC pulses were imaged (from
the end of the plasma) onto the entrance slit of a spectrometer, providing ID
transverse space resolution of the interaction region exit plane. An 8-bit CCD camera
in the spectrometer's focal plane recorded the frequency domain interferogram
generated by interference of the reference and probe pulses, from which the timedependent real and imaginary refractive index changes induced by the pump and
encoded on the probe were extracted using Fourier techniques [3,4]. As the pump
and SC probe and reference beams travel in collinear geometry, there is negligible
geometric limitation to the time resolution; the ultimate limit (here -15 fs [4]) is
imposed by the SC bandwidth.
As one of the preliminary experiments to test this diagnostic, we wished to measure
the transient complex refractive index of a gas of exploding laser-heated clusters.
Clusters are van der Waals-bonded agglomerations of up to ~107 atoms that are
produced in supersonic nozzle flows [5]. The density in an individual cluster is solidlike, while the volume average density can be variable up to that of typical gas at
several atmospheres. Even for low volume average densities, an intense laser pulse
can strongly couple to individual clusters owing to their high local density. This
suggests the possibility of producing preformed plasma waveguides in a lower range
of average density than is possible in the usual case of laser-heated unclustered gas.
The need for lower densities is motivated by the fact that the best-matched laser
pulsewidth for resonant wakefield generation scales as T ~ cop"1 oc Ne~1/2, which
requires densities of a few times 1017 cm"3 and below for -100 fs pump pulses pulses.
Such low densities are not easily accessible with standard avalanche breakdown of
..
.
1 8 " }
unclustered gas, which favour densities of a few times 10 cm" and higher [6].
649
space (µm)
We
schemes such
such as
as short
short pulse
pulse field
field
We note
note here
here that
that avalanche
avalanche pre-ionization
pre-ionization schemes
ionization
[7]
or
electrical
discharges
[8]
in
unclustered
gas
targets
do
not
help
in
ionization [7] or electrical discharges [8] in unclustered
gas
18
3 targets do not help in
18 cm"
-3 . At early times in the
cases
when
desired
electron
density
is
below
~10
cases when desired electron density is below ~10 cm . At early times in the
avalanche
density grows
grows as
as N
NGe(f)
Ne0
whereNTVe0eo
GQGxp(SNot),
avalanche breakdown,
breakdown, the
the electron
electron density
(t) ~~ N
exp(SN0t), where
isis the
seed
electron
density,
S
is
the
collisional
ionization
rate,
and
TVo
is
the
initialgas
gas
the seed electron density, S is the collisional ionization rate, and N0 is the initial
density.
The
most
important
factor
by
far
is
TVo,
since
it
appears
in
the
exponent.
The
density. The most important factor by far is N0, since it appears in the exponent. The
initial
and sensitivity
sensitivity to
to its
its value
value isis lost
lost after
after
eo is
initial electron
electron density
density TV
Ne0
is aa prefactor,
prefactor, and
several
e-folding
times
of
the
avalanche
process
as
saturation
is
approached.
The
several e-folding times of the avalanche process as saturation is approached. The
solid
density
values
for
TVo
in
clusters
favours
strong
local
avalanche
ionization,
solid density values for N0 in clusters favours strong local avalanche ionization,
independent
per unit
unit volume.
volume.
independent of
of the
the number
number of
of clusters
clusters per
(+) fringe shift
time
time
(-)
shift
(-) fringe
fringe shift
':"X"W'"
Pumpbeam
beam
Pump
wavelength (nm)
(nm)
Imaging
Imaging
Spectrometer
Spectrometer
CCD|
CCD
L2
4
Cluster
gas jet
gas
LI
L1
i
Ref.
Ref.
Probe
Probe
FIGURE
interferometry. AA typical
typical spectral
spectral
FIGURE 4.
4. Setup
Setup for single-shot
single-shot supercontinuum spectral interferometry.
interferogram is
is shown.
shown.
interferogram
A gas
gas of
of argon clusters from
A
from aa pulsed
pulsed supersonic
supersonic gas
gas jet
jet was
was heated
heated by
by aa 100
100 fs,
fs,
15
800 nm,
nm, 10
1015
W/cm22 pump
pump laser
laser pulse.
pulse. The
jet backing
800
W/cm
The gas
gas jet
backing pressure
pressure was
was in
in the
the range
range
150-400 psi,
psi, producing
producing average
average cluster
150-400
cluster sizes
sizes in
in the
the range
range 150-300
150-300 Å
A [9].
[9]. As
As described
described
above, the
the twin
twin SC
SC pulses
pulses were
were co-propagated
above,
co-propagated with
with the
the pump
pump pulse.
pulse. The
The first
first SC
SC
pulse preceded
preceded the
the pump
pump and
and the
the second
second SC
pulse
SC pulse
pulse was
was superimposed
superimposed on
on it.
it. Figure
Figure44
shows aa raw
raw spectral
spectral interferogram
interferogram from
shows
from which
which the
the pump-induced
pump-induced transient
transient phase
phase
shift A<fi(x,i)
∆φ(x,t) and
and absorption
absorption A(x,f)=l-Qxp(-rj(x,i))
A(x,t)=1−exp(−η(x,t)) are
shift
are extracted.
extracted. Here
Here xx isis the
the
transverse dimension,
dimension, and
and η
transverse
77is
is the
the small
small signal
signal absorption
absorption coefficient.
coefficient. These
These are
are
related to
to the
the real
real and
and imaginary
imaginary refractive
(x,t)= k(n
related
refractive indices
indices nwrr and
and nn\i by
by ∆φ
A$x,f)=
k(nrr(x,t)-1)d
(x,f)-l)d
η(x,t)=kni(x,t)d, assuming
assuming gas
jet uniformity
uniformity along
and rj(x,f)=kni(x,f)d,
and
gas jet
along the
the d=1
d=\ mm
mm interaction
interaction length
length
(only the
the edge
edge of
of the
the L=3mm
L=3mm wide
wide jet
jet is
(only
is sampled
sampled for
for reasons
reasons given
given below),
below), where
where
k=ω/c is
is the
the vacuum
vacuum wavenumber.
wavenumber. We
k=a>/c
We note
note that
that10 the
the short
short jet
jet3 interaction
interaction length
length of
of11
mm was
was used,
used, at
at aa low
low cluster
cluster density
mm
density (N~3x10
(N~3xl010 clusters/cm
clusters/cm3),), in
in order
order to
to eliminate
eliminate
the effect
effect of
of SC
SC beam
beam lensing
lensing in
pump pulse-ionized
the
in the
the pump
pulse-ionized cluster
cluster plasma.
plasma. Ionizationlonizationinduced refraction
refraction of
of the
the SC
SC beam
beam would
induced
would have
have obscured
obscured the
the correct
correct phase
phase extraction
extraction
from the
the raw
raw interferogram.
interferogram. Figure
Figure 55 shows,
from
shows, for
for the
the range
range of
of backing
backing pressures,
pressures, the
the
extracted A<ftx=Q,f)
∆φ(x=0,t) and
and η
(x=0,t), with
extracted
rj(x=Q,i),
with the
the scale
scale on
on the
the left
left hand
hand axis.
axis. The
The right
righthand
hand
and ni, obtained by dividing by d=1mm and
axis shows
shows these
these results
results scaled
scaled to
to nwr −1
axis
r -1 and n\, obtained by dividing by d=lmm and
650
Q where >lprobe =700nm is the SC central wavelength. Also shown is a 2D
k=2π/λprobe where λprobe
=700nm is the SC central wavelength. Also shown is a 2D
grayscale plot of A(fi(x,i) for the 350 psi case. Note that the positive-going spatial
grayscale plot of ∆φ(x,t) for the 350 psi case. Note that the positive-going spatial
profile for A$ at early times shows that ultrafast laser-heated cluster gas can be used
for ∆φ at early times shows that ultrafast laser-heated cluster gas can be used
asprofile
an optical
guiding medium [10]. In fact, this effect is likely the reason it has been
as an optical guiding medium [10]. In fact, this effect is likely the reason it has been
observed in many experiments on laser-cluster interactions, that focused -100 fs
observed in many experiments on laser-cluster interactions, that focused ~100 fs
pulses
which end-pump cluster jets do not appear to suffer ionization-induced
pulses which end-pump cluster jets do not appear to suffer ionization-induced
refraction.
This is so even though the volume average electron density from laserrefraction. This is so even though the volume average electron density from laserheated
cluster
even greater
greater than
than in
in unclustered
unclustered gas
gasjet
jet targets,
targets,
heated clusterjets
jets is
is comparable
comparable to
to or
or even
where
ionization-induced
refraction
is
always
observed
[11].
where ionization-induced refraction is always observed [11].
We
generation method
method which
which combines
combines the
the selfselfWe propose
propose here
here aa plasma
plasma waveguide
waveguide generation
guiding
of
short
laser
pulses
in
cluster
jets
with
their
strong
absorption
in
the
clusters.
guiding of short laser pulses in cluster jets with their strong absorption in the clusters.
The
initial density
density requirement
requirement imposed
imposed by
by efficient
efficient
The idea
idea isis to
to circumvent
circumvent the
the high
high initial
inverse
bremsstrahlung
breakdown
in
unclustered
gas
targets,
and
to
achieve
tight,
inverse bremsstrahlung breakdown in unclustered gas targets, and to achieve aatight,
elongated
line
focus
in
an
end-injected
geometry.
Some
typical
numbers
can
be
elongated line focus in an end-injected geometry. Some typical numbers can be
worked
out.
worked out.
Examination
where ∆φ
A(/> ∝oc nnrT −1
-1 isis atat peak
peak positive
positive
Examination of
of Fig.
Fig. 55 shows
shows that
that the
the times
times where
values
(where
guiding
can
occur)
corresponds
to
values
of
n\
that
are
at
more
than
values (where guiding can occur) corresponds to values of ni that are at more than
half
their
maximum
value
(the
maximum
in
n\
occurs
near
the
zero
crossing
point
for
half their maximum value (the maximum in ni occurs near the zero crossing point for
nnT r -1).
So
guiding
is
accompanied
by
strong
absorption.
How
strong
is
the
−1). So guiding is accompanied by strong absorption.
How strong is the
11
absorption?
clusters/cm33 (such
(such as
as in
in the
the
absorption? For
For higher
higher density
density cluster
cluster jets
jets with
with N-10
N~1011 clusters/cm
center
of
our
jet),
the
measured
value
of
n\
from
Fig.
5
would
be
scaled
linearly
with
center of our jet), the measured value of ni from Fig. 5 would
be scaled linearly with
the
~5xlO"-44 (for
(for the
the 350
350 psi
psi case,
case,
the cluster
cluster number
number density
density increase,
increase, giving
giving nn\i ~5x10
corresponding
clusters). The
The corresponding
corresponding damping
damping length
length
corresponding to
to 300
300 A
Å average radius clusters).
l
isis (kn\)~
8 //m
essentially complete
complete absorption
absorption
250 //m
µm for
for aa AM).
λ=0.8
µm pump pulse. So essentially
(kni)−1 ~~ 250
can
cantake
takeplace
place in
in less
less than
than 1 mm.
(nr-1) x10-4
ni x10-4
50
500
1000
1500
transient guiding profile
1000
1500
time (fs)
time (fs)
Figure 5.5. Left:
Left: extracted
extracted transient
transient real
real and
and imaginary
imaginary refractive
Figure
refractive indices
indices of
of laser-heated
laser-heated cluster
cluster gas.
gas.
Right:2D
2D grayscale
grayscale phase
phase plot
plot (A(/>
(∆φ ∝
nrT-l)
−1) showing
showing that
Right:
oc n
that early
early in
in time,
time, the
the clustered
clustered gas
gas acts
acts as
as an
an
opticalguiding
guidingmedium.
medium.
optical
Reducing the
the number
number of
of clusters
clusters per
per unit
unit volume
volume would
Reducing
would extend
extend the
the damping
damping length
length
to
distances
of
interest
for
wake-field
applications.
In
the
unsaturated
absorption
to distances of interest
for
wake-field
applications.
In
the
unsaturated
absorption
−5
regime, ifif (Ar^)"
(kni)−11 ~~ 11 cm,
cm, then
then that
that requires
requires nn\i ~1.3x10
regime,
~1.3xlO~5,, which
which in
in turn
turn requires
requires
651
N~3xl09 clusters/cm3. This cluster number density is too low for self-guiding, so very
large f/# focusing should be used. For 300 A argon clusters, this N corresponds to
~7xl015 atoms/cm3. If the argon atoms in the clusters are ionized to Z~10, as has been
observed using moderate intensity pump pulses [9], resulting volume average electron
density is ~1017 cm"3. After the laser pulse passes, the strongly heated clusters
disassemble on a few picosecond timescale [11,12] to generate a smooth local
electron density of ~1017 cm"3 . Simultaneously, the laser-heated heated zone within
the cluster jet expands radially on a few hundred picosecond timescale and a plasma
waveguide is formed in the usual manner [6]. The electron density of ~1017 cm"3 is
well within the resonant wakefield regime for waveguide-injected -100 fs pump laser
pulses. Note that in the saturated absorption regime, sufficiently higher values of N
could be used to promote self-guiding of the waveguide-generation pulse.
3. TRANSIENT PHASE SHIFTS GENERATED BY INTENSE
PUMP PULSES INJECTED INTO PLASMA WAVEGUIDES
For the experimental setup of Sec. 1, we employed our spectral interferometry
diagnostic to measure phase shifts induced by intense pump pulses injected into
plasma waveguides. Preliminary results are for waveguides without funnels. Figure 6
shows three interferograms. The swept frequency of the chirped SC pulses
corresponds to the time interval shown in the images. Panel (a) is for the case of no
waveguide, panel (b) is for the waveguide present but no pump, and panel (c) is for
the waveguide and a guided pump. Obviously, there is no time-dependent fringe shift
for case (a). In case (b), the waveguide is seen to trap the SC pulses. The injected SC
pulses transversely overfill the waveguide. The bright region in the center is the
trapped light. Above and below that is spatial interference (manifested by wide
horizontal fringes) between light refracted away from the outside of the guide, and
light that does not encounter the guide. In case (c), it is clear that guided pumpinduced transient fringe bending is imposed on the guided SC light, here
corresponding to a transient negative phase shift. At this point, without having used
the funnel, we attribute this phase shift to pump-induced ionization at the waveguide
entrance (as noted in Sec. 1, interferometry shows that downstream, the waveguide is
fully ionized). This is suggested by the negative sign of the phase shift, which
corresponds to ionization, and by the temporal location of the shift beginning near the
center of the chirped SC pulse time window, where the pump pulse is located. It is
also seen that the bright strip of guided SC light widens at the same time that the
fringe shift (phase shift) begins. The reason for this is not clear, and further
experiments will elucidate the origin of this effect.
652
(a)
wavepiide + pump
(c)
FIGURE 6. Single-shot spectral interferograms for cases of (a) no waveguide, (b) waveguide but no
guided pump pulse, and (c) waveguide plus guided pump pulse.
ACKNOWLEDGEMENTS
The authors thank T. Antonsen for useful discussions. This work is supported by
the US Department of Energy and the National Science Foundation.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
S. P. Nikitin, I. Alexeev, J. Fan, and H.M. Milchberg, Phys. Rev. E 59, R3839 (1999)
T.R. Clark, PhD dissertation, University of Maryland, 1998
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