Appl. Phys. B 64, 323—330 (1997)
Harmonic generation in an ionized gas medium with a 100-femtosecond,
high repetition rate laser source at intermediate intensities
C. de Lisio1, C. Altucci1, R. Bruzzese1, F. De Filippo1, S. Solimeno1, M. Bellini2, P. Foggi2
1Dipartimento di Scienze Fisiche, Universitá di Napoli ‘‘Federico II’’ and Istituto Nazionale di Fisica della Materia (INFM), Padiglione 20,
Mostra d’ Oltremare, 80125 — Napoli, Italy
(Fax: #39-81/239-508, E-mail: [email protected])
2European Laboratory for Nonlinear Spectroscopy (LENS), Largo E. Fermi, 2, 50125-Firenze, Italy
Received: 29 March 1996/Revised version: 25 July 1996
Abstract. We report the realization of a vacuum-ultraviolet radiation source based on high-order harmonic
generation in noble-gas samples, operating at high repetition rate. In particular, we observed up to the 13th harmonic (j"61 nm) of the fundamental frequency of
a short pulse, high repetition rate titanium—sapphire laser
after its interaction with a Xe gas jet. The effects of the
propagation of the fundamental and harmonic beams
through an ionized medium are studied by analysing the
spectral profile of the 9th and 7th harmonics. Finally, we
report a study of the dependence of the harmonic conversion efficiency on relative position of the focus and the gas
target.
PACS: 42.65.Ky; 32.80.Rm
In recent years, high-order harmonic generation in noble
gases has become one of the most promising ways for
realizing coherent radiation sources in the VUV—XUV
region [1]. It is well known that by irradiating a noble gas
sample of finite extension with a very intense laser pulse,
odd harmonics of the fundamental laser frequency are
generated with considerable efficiency [2, 3]. For instance,
harmonics as high as the 143rd [4] and wavelengths as
short as 7 nm [5] have been observed. Some interesting
characteristics of the harmonic radiation are temporal
and spatial coherence, low divergence, short time duration, which result in an extremely high brightness [typically 1017—1018 photons/(As s mrad2) in the 20—200 nm
VUV spectral region]. This is several orders of magnitude
higher than the typical brightness of a synchrotron radiation source in the same spectral region.
So far, the shortest wavelengths observed have been
obtained with laser sources delivering pulses of high energy
(E K0.5 J) and short duration (q K100 fs). These perfor1
1
mances can be obtained only with table-top-terawatt laser
sources operating at very low repetition rate (typically
10 Hz) compared with that of a synchrotron (K100 MHz).
In spite of the extremely high peak power available
with table-top-terawatt lasers, most of the results
published so far in the field of harmonic generation,
have been obtained at intensities between 1012 and
1016 W/cm2, thus employing a weak focusing geometry.
There are at least two reasons for this. First, it is
well known that the laser intensity dependence
of the photon yield of a given harmonic lying in the
plateau region follows a power law with a quite high
exponent (typically between 5 and 7) until saturation
due to ionization occurs [6]. Thus, increasing the laser
intensity well above the saturation intensity does
not result in a strong enhancement in the harmonic
photon yield and only a minor increase in the plateau
extent can be observed. This means that only a small
fraction of the laser pulse energy is efficiently used for
harmonic generation.
As an example, the 15th harmonic of a 250 fs Titanium—Sapphire (Ti:S) laser generated in xenon saturates
at I"I +1.5]1014 W cm~2, which corresponds (in
4!5
the experimental conditions of [6]) to a laser pulse energy
of a few mJ, i.e. a very small fraction of the maximum pulse
energy the laser can deliver. According to [6], the 15th
harmonic photon yield remains almost constant by increasing the laser intensity by a factor of 5 above the
saturation intensity.
Secondly, due to the coherence of the harmonic generation process, the harmonic photon yield depends quadratically on the number of atoms involved in the generation
process, and, hence, in a weak focussing geometry, on
the confocal parameter b"2pw2 /j [7, 8], where w is the
0
0
laser beam radius in the focal region and j the laser
wavelength.
Thus, an alternative and interesting way to considerably increase the average flux of harmonic photons is to
use moderate pulse energies (corresponding approximately to the saturation intensity), but at much higher
repetition rates. After suitable focusing, intensities in excess of 1015 W/cm2 are now available also with commercial lasers operating at high repetition rate (1 kHz) and
with low energy pulses (1 mJ). The above intensity is
sufficient for efficient generation of harmonics lying in the
324
spectral range 50—200 nm, a region of interest for several
experiments of atomic and molecular physics.
The usefulness of harmonic generation in gases has
been demonstrated by Eikema et al. [9] who observed the
4He 11S P 21P resonance line at 58.4 nm with the fifth
harmonic generated in C H of a nanosecond frequency2 2
doubled tunable dye laser ( j"584 nm). In spite of the
low laser intensity, a sufficient number of fifth-harmonic
photons (104/shot) were generated although at low repetition rate (few Hertz).
High repetition rate, high-intensity regenerative amplifiers have been rapidly developing in the last few years
[10, 11].
Salin et al. [12] demonstrated the advantages of kilo
Hertz laser sources in intense-field physics experiments.
They employed a chirped-pulse-amplified (CPA) Ti:S laser
operating at high repetition rate (1 kHz) with pulse energies of the order of 1 mJ and duration shorter than 100 fs.
After focusing the laser beam with a very short focal
length lens close to the diffraction limit, intensities in
excess of 1016 W/cm2 were readily obtained. In particular,
the authors of [12] reproduced multiphoton and abovethreshold ionization experiments previously realized only
with very large table-top-terawatt laser systems.
Taking advantage of the unique features of short-pulse
kilo Hertz laser systems and of harmonic radiation,
Haight and Peale [13, 14] analyzed the energy bands of
semiconductors by means of tunable photoemission. They
employed a sub-picosecond dye laser amplified at 600 Hz
and then focused on a noble gas sample where odd harmonics of the laser fundamental (j"610 nm) were generated up to the 25th. Tunability of the pump laser source is
of fundamental importance in angle-resolved photoemission studies for the observation of critical points within
the bulk Brillouin zone of crystalline materials.
In this paper we describe a sub-picosecond source
of coherent, partially tunable, VUV radiation based on
the generation of harmonics of a Ti:S pump laser
(j"800 nm) delivering 1 mJ, 100 fs pulses at 1kHz repetition rate. Harmonics are efficiently produced during the
interaction of the intense laser field with a pulsed Xe gas
jet operating at 500 Hz. In spite of the low pulse energy,
intensities slightly smaller than 1015 W/cm2 are achievable due to the short pulse duration and good optical
quality of the laser beam. Such an intensity level lies well
above the saturation intensity of Xe for 100 fs, 800 nm
pulses (namely I "1.5]1014 W/cm2).
4
We observed odd harmonics from the 3rd
(j"267 nm) to the 13th (j"61 nm) order (plateau). For
this spectral range, of great interest for applications in
VUV ultrafast spectroscopy, we report a spectral analysis
of some harmonics, with evidence of blue-shift and
broadening of the harmonic spectral profile due to the
time-dependent photoelectron density. Moreover, we
have studied the optimization of harmonic conversion
efficiency with respect to the position of the laser beam
focus relative to the gas jet. We report measurements for
several harmonics at different laser intensities. Our results
seem difficult to interpret, since neither phase-matching
effects nor optical-field-induced ionization appear to satisfactorily account for them. A deeper study of the observed
phenomena will be the goal of our future work.
The paper is organized as follows: in Sect. 1 we describe the experimental apparatus with its main performances and characteristics. Section 2 is devoted to the
presentation of the results and their interpretation, together with a comparison with other available data obtained in similar experimental conditions. Finally, we
conclude by exposing in Section 3 a summary of our main
results and the limits of our experimental apparatus and
its possible improvement.
1 Experimental setup
A block diagram of our experimental layout is shown in
Fig. 1.
The light source of our experiment is a Ti:S laser based
on chirped pulse amplification. An argon-ion laser pumps
a Ti:S self-mode-locked oscillator. Its output consists of
a 82 MHz pulse train with 800 nm wavelength, 60 fs time
duration and about 1 W average power. The laser
wavelength can be tuned in the interval 750—830 nm. The
wavelength range can be further extended by employing
different sets of optics properly designed for the desired
spectral output.
The laser beam is then driven into the grating stretcher
at the output of which the pulse duration is of the order of
300 ps.
A fast photodiode converts the 82 MHz light signal
into an electric pulse train. An electronic frequency divider
converts the photodiode signal to a 1 kHz signal which
triggers both the laser pumping of the regenerative amplifier and a Pockels’ cell. The latter picks up one of the laser
pulses, injects it into the regenerative amplifier and extracts it after amplification.
The regenerative amplifier consists of a Ti:S rod
pumped by a Q-switched doubled Nd:YLF laser. The
nanojoule input energy is increased to about 2 mJ before
the beam enters the grating compressor. The final output
consists of 800 nm, K100 fs, 1 mJ pulses at 1 kHz repetition rate.
A 200 mm focal length lens focuses the laser beam on
the Xe gas jet. We monitored the laser beam cross-section
in the vicinity of the waist with a CCD camera. In particular, the beam radius, w , at the waist position was about
0
19 lm, only slightly greater than the diffraction limited
value of 17 lm. Moreover, the beam area is SK1150 lm2
and the confocal parameter b"2S/jK2.8 mm.
The intensity in the focal region was, then, estimated to be around 1015 W/cm2. In the following, we
shall refer to the laser intensity as that of an unperturbed
beam.
The gaseous sample was injected in the interaction
chamber by a piezoelectric valve (Laser Technics, mod.
LPV) with a maximum repetition rate of 750 Hz, according to the manufacturer specification. In order to synchronize valve and laser pulses, we operated the valve at
500 Hz. The valve repetition rate is the only present limitation preventing from obtaining a true 1 kHz VUV
radiation source. The valve performances and the gas
jet characteristics were extensively studied in a previous
paper [15]. By employing a tunable differential interferometer, detailed information on the spatial behaviour
325
Fig. 1a, b. Experimental apparatus:
a Ti:Sapphire laser system; b monochromator
and detection system: L: focusing lens; C:
interaction chamber; J: gas jet; DG: spherical
diffraction grating; S: monochromator exit slit;
Ph: TPB phosphor; PMT: photomultiplier tube.
of the gas density profile were obtained. In particular, we
observed an exponential decay of the local gas density as
a function of the distance from the valve nozzle. The decay
length, approximately 0.5 mm, remained almost constant
with the valve backing pressure. On the other hand, the
gas jet transverse profile showed a nearly Lorentzian
shape with a full width at half maximum linearly dependent on the distance from the nozzle. Thus, the gas jet had
the shape of a cone with a measured apex full angle of
about 32°.
In the experimental conditions of the present paper,
the gas jet width was estimated to be about 0.7 mm and
the average pressure experienced by the laser beam was
approximately 20 Torr. The latter is defined as the integral of the local pressure along the laser beam path
divided by the gas jet width.
The interaction chamber and the monochromator
were evacuated by two turbomolecular pumps to a background pressure of 10~6 Torr.
Harmonic radiation was analyzed by a nearly normal
incidence (15°) monochromator equipped with a 2160
grooves/mm, holographic grating with a spherical surface
of 1 m radius of curvature. The spectral resolution was
about 0.5 As . The VUV monochromator was described in
more details in a previous paper [16].
VUV radiation was then down converted to visible by
a fluorescent layer of TetraPhenyl Butadiene (TPB) [17]
and detected with a Photo-Multiplier Tube (PMT; ThornEMI, mod. 9250). Electrical signals of the PMT were
recorded with a digital oscilloscope and converted to
absolute numbers of photons by taking into account the
PMT gain and the overall efficiency of the analysis and
detection systems.
In particular, the PMT signal is integrated over a time
window of about 50 ns; the result of this integration, A , is
4
proportional to the number of electrons, N , produced at
%
the photocathode:
GN e
% ,
A"
4
R
(1)
where G is the gain of the PMT dinode chain, e the
electron charge and R the oscilloscope input resistance. In
order to extend the dynamical range of our detection
system, we had to vary the PMT high voltage. Hence, we
also determined experimentally the voltage dependence of
326
the gain G. We found G-values of 1.4]104 and 1.2]106
for applied voltages of 500 and 900 V, respectively, in
excellent agreement with the manufacturer specification.
The number of harmonic photons, N , reaching the
1
TPB phosphor is given by N "N /g, where g is the
1
%
product of the quantum efficiencies of the photocathode
and the TPB phosphor, and the geometrical collection
efficiency of the system phosphor-photocathode. The
photocathode quantum efficiency as given by the manufacturer is approximately 28% at the wavelength emitted
by the phosphor. The TPB phosphor efficiency has been
experimentally determined by Naletto et al. together with
the spatial emission pattern [17], which allowed us to
estimate the geometrical collection efficiency. In particular, the TPB quantum efficiency ranges between 45% and
95%, depending on the harmonic wavelength, whereas the
geometrical collection efficiency is about 50%.
The number of harmonic photons, N produced dur)
ing the laser—gas interaction is simply N "N /g , where
)
1 '
g is the diffraction efficiency of the grating, also given by
'
the manufacturer and ranging between 13% and 28% in
the investigated wavelength interval.
Obviously, all the results reported in the following
section account for the different wavelengths involved in
the experiment.
It is worth stressing here that the uncertainty in the
absolute number of photons is quite high (almost one
order of magnitude), due to uncertainty in the various
efficiencies involved in the computation. Nevertheless,
all discussions on relative variations of the number of
photons remain valid.
Fig. 2. Spectrum of VUV radiation for a laser intensity of
4]1014 W/cm2 and a gas pressure of 30 Torr
2 Results and discussion
From the point of view of a user of a VUV radiation
source based on high-order harmonic generation, there
are some parameters of fundamental importance, namely,
number of photons per laser shot, spectral width of the
harmonics, brightness of the source, pulse duration and
pulse repetition rate. In this paper, we have tried to address some of these points.
A preliminary comment concerns the possibility of
partial wavelength tunability of the harmonic output of
the VUV source. This can be achieved by varying the Ti:S
pump laser wavelength within its 750—830 nm amplification band width. However, in the present experiment we
have operated the Ti:S laser at a fixed wavelength of
about 800 nm.
In order to test the performances of our detection
apparatus, we have recorded a spectrum of the UV radiation emerging from the interaction of the laser beam with
the gas jet. Figure 2 shows the absolute number of photons in the region 60—180 nm generated during the laser—gas
interaction for an intensity of 4]1014 W/cm2 and an
average local xenon pressure of 20 Torr. We can clearly
distinguish odd harmonics from the 5th to the 13th of the
fundamental laser frequency. Harmonic peaks are overlapped to a large background, which is mainly due to
incoherent emission from the laser-created plasma (in the
long wavelength region) and to stray laser light (at shorter
wavelengths). The broad peak at jK140 nm is due to the
Fig. 3. Intensity dependence of the harmonic photon yield for the
3rd, 5th and 9th harmonics
transition 6s P 5p in neutral xenon. The limit of our
detection system is due to the rapid decrease of the grating
efficiency in the short wavelength region.
In Fig. 3 we report a log—log plot of the number of
photons generated per each laser shot vs the laser intensity for the 3rd, 5th and 9th harmonics.
The intensity dependence of the 9th harmonic is substantially different from those of the 3rd and 5th ones: in
fact, the behaviour of the 3rd and 5th harmonics shows
only two regions, one at low laser intensity with a slope of
3 and 5, respectively, and another at intensities above
6]1013 W/cm2 with a smaller slope. On the other hand,
we can clearly distinguish three regions in the intensity
dependence of the 9th harmonic photon yield: in the first
region (intensities below 8]1013 W/cm2), the slope is
about 9, in agreement with the lowest order perturbation
theory (LOPT); in the second region, the slope decreases
to approximately 6; in the third region, starting at
I"3]1014 W/cm2 the slope reduces to about 3.
Such a different behaviour can be explained by considering that 3rd and 5th harmonics never lie in the plateau
327
region. In other words, they are generated in a perturbative regime until, by increasing the laser intensity, saturation of the optical-field-induced ionization occurs. For
intensities higher than the saturation intensity, the nonlinear medium consists mainly of ions, whose nonlinear
susceptibility is believed to be at least one order of magnitude smaller than that of neutral atoms [7]. Nevertheless,
a slower increase in the photon yield is still present due to
a growth of the effective interaction volume.
Higher order harmonics differ from the first two or
three, since they can be generated also in the so-called
plateau regime (for instance, see [3] and references cited
therein). In this case, the intensity dependence of the
harmonic photon yield still follows a power law, but
the exponent strongly deviates from that predicted by the
LOPT. Typically, it is smaller and almost independent on
the harmonic order. The value 6 found in our case for the
9th harmonic is in good agreement with the other published results [6].
When an intense femtosecond laser pulse propagates
through a gas sample, optical-field-induced ionization can
cause a rapid variation in the electron density, and, in
turn, in the refractive index. Transverse spatial variations
of the refractive index originate due to the laser beam
intensity profile and give rise to defocusing of the fundamental as well as harmonic beams [18, 19]. On the other
hand, a rapid time variation of the refractive index leads to
spectral broadening and, in the case of femtosecond
pulses, to a blue-shift of the fundamental and harmonic
wavelengths [6, 20—22]. A simple expression of the
plasma-induced spectral blue-shift, dj, for an initial radiation wavelength j can be obtained by assuming propagation in a homogeneous medium and a radiation frequency
u"c/j much greater than the plasma frequency u :
1
dj
1 u2j2 ¸ dZ
1
"!
(S.I. units)
(2)
j
2 4n2c2 c dt
Here u "Je2N /e m is the plasma frequency when
1
% 0 %
all the atoms are ionized, N the corresponding electron
%
density, ¸ the medium length, and Z the degree of ionization. From Eq. (2), it is evident that the blue-shift of
harmonic wavelengths is mainly due to the blue-shift of
the fundamental radiation, rather than to direct self-phase
modulation of the harmonic beam. In fact, for the q-th
harmonic, the former contribution is dj "dj /q, whereas
q
1
the latter is dj "dj /q3, with q'1.
q
1
In case of complete ionization, we can assume that
N (dZ/dt)+N/q, where N is the neutral atom density
%
and q"100 fs laser pulse duration. In our experimental
conditions (i.e. j "800 nm, ¸"0.7 mm, N"0.8]
1
1018 cm~3), dj "5.6 nm. Thus, for the 7th and 9th har1
monics, we obtain, respectively, dj "0.8 nm and dj "
7
9
0.6 nm.
We determined the spectral profile of the 7th and 9th
harmonics at different laser intensities (Fig. 4) and measured both the broadening and the blue-shift by assuming
that the wavelength corresponding to the lowest laser
intensity was the unshifted one.
In this case we obtain dj "0.1 nm and dj "0.4 nm.
7
9
The great discrepancy of the result for the 7th harmonic is
attributed to the fact that the spectral region around
Fig. 4. Spectral profile of the 7th (a) and 9th (b) harmonics at
different laser intensities
115 nm (where the 7th harmonic lies) is rather noisy because of the vicinity of the transition 6s P 5p (see Fig. 2),
as one can deduce from the irregular shape of the 7th
harmonic spectral profile.
On the other hand, the experimental value of the 9th
harmonic blue-shift is much closer to the theoretical one;
we attribute the small difference to the assumption that
the wavelength measured at the lowest laser intensity
(namely 2.2]1014 W/cm2) corresponds to the unshifted
one. Obviously, this is not true, since such a laser intensity,
corresponding to a deep plateau region (see Fig. 3), cannot
be considered low. On the other hand, we could not
acquire the 9th harmonic spectral profile at lower laser
intensities since, in order to maximize the monochromator
resolution, we had to reduce the width of its exit slit which,
in turn, caused a dramatic reduction of the overall
throughput. Thus, it is reasonable to believe that the
unperturbed wavelength is greater than that measured
from the data of Fig. 4b and this statement is in agreement
with the expected 9th harmonic wavelength, namely
j "j /9K88.9 nm.
9
1
Finally, both 7th and 9th harmonics show intensity
broadening of the order of 50% in the investigated intensity range.
Further evidence of the effects of gas ionization on the
harmonic generation process results from z-scan measurements of harmonic photon yield. The focal plane is moved
328
across the gas jet by translating the focusing lens along the
laser axis. In our case, the confocal parameter of 2.8 mm
and the gas jet length of 0.7 mm correspond to a moderately loose focusing geometry. The focus position is varied
in steps of 0.1 mm.
The general trend of the harmonic photon yield as
a function of the lens position consists of a double-peak
structure which is more pronounced for low order harmonics and high intensities (Figs. 5 and 6; the first (left)
maximum corresponds to the experimental condition
where the laser beam is focused before the gas jet). Moreover, the first (left) peak is generally higher than the
second (right) one.
In Fig. 5 we report plots of the relative number of
photons of the 5th, 9th and 13th harmonics as a function
of the focus position at a laser intensity of 5.3]
1014 W/cm2. In all cases we observe two peaks at a distance of approximately 4 mm. However, such a distance
slightly decreases for increasing harmonic order.
Figure 6 shows the harmonic photon yield versus the
focus position for the 5th, 9th and 13th harmonics at three
different laser intensities. We notice that the distance
between the two peaks slightly increases with the laser
intensity.
Several authors [23—27] observed structures with multiple maxima in quite different experimental conditions.
Balcou and L’Huillier [24] interpreted the oscillations
of the harmonic yield vs the position of the laser beam
focus in the atomic jet as a phase-matching effect due to
the tight focussing geometry of their experiment. In particular, with a confocal parameter of 1.5 mm and a gas jet
length of 1 mm, they observed oscillations separated by
a coherence length [22], defined as
b n
¸(q) +
,
#0) 2 q!1
(3)
Fig. 5. 5th, 9th and 13th harmonic photon yield as a function
of the focus position. The horizontal ticks mark the zero for each
data set. The laser intensity is 5.3]1014 W/cm2. The left maximum
corresponds to the laser being focused before the gas jet
where b is the confocal parameter of the laser beam and
q the harmonic order.
Similar considerations follow from theoretical predictions based both on the weak-field approximation and on
a non-perturbative approach [24]. Nevertheless, in many
cases the oscillations reduce to only two peaks. It is worth
noticing that both the theoretical and experimental works
Fig. 6. Same as Fig. 5, but for three different laser intensities. The intensity is indicated for each curve in units of 1014 W/cm2.
329
of [24] refer to Nd: YAG (j"1064 nm) long (K35 ps),
low intensity (few 1013 W/cm2) laser pulses. In particular,
the laser intensity range was typically below the saturation regime.
L’Huillier and co-workers [23] also observed a considerable enhancement of the harmonic photon yield
when very intense (1015 W/cm2) and short (1 ps) laser
pulses were defocused with respect to the gas target.
On the other hand, Sakai and Miyazaki [27] performed similar measurements with a dye laser
(j"616 nm) delivering 2 mJ, 800 fs pulses. Intensities as
high as 2]1014 W/cm2 were obtained with a focusing
lens length of 15 cm. Their confocal parameter was about
8 mm and the gas jet width 1 mm (loose focusing geometry). In spite of the quite different experimental conditions with respect to [23, 24], they also observed a focus
position dependence of the harmonic photon yield characterized basically by two peaks, sometime collapsing into
a single one. The origin of the dip between the two peaks
was attributed to the depletion of neutral atoms due to
optical-field-ionization, which is more important when
the laser beam is focused on the symmetry axis of the gas
jet. Such an interpretation was confirmed by simultaneous
measurements of the ion yield, whose maximum occurred
in correspondence of the central dip in the harmonic yield.
Moreover, Salières et al. and Lewenstein et al. [25, 26]
performed numerical calculations based on the theory
described in [28], which show that the harmonic photon
yield strongly depends on the phase of the nonlinear
polarization field. There are two terms contributing to
such a phase, both depending on the relative distance, z,
between the laser focus position and the gas jet: the first
one is a purely geometrical term due to the phase shift of
the Gaussian fundamental beam; the second one, which
takes into account the induced-dipole phase, depends on
z through the laser intensity. As a conclusion, the harmonic photon yield versus z exhibits a behavior similar to
Figs. 5 and 6. However, it must be pointed out that
[25, 26] refer to very high-order harmonics, for which the
geometrical term in the polarization field phase is much
more important than for low order harmonics. Furthermore, they study harmonic generation in neon whose
ionization potential is higher than that of xenon. This
implies that the influence of ionization is smaller than in
our case.
A possible explanation of our results is more likely
connected to the ionization of the gas medium rather than
to phase matching effects. In fact, in our experimental
conditions, the coherence length is 1.4 mm for the 5th
harmonic, and becomes smaller for higher order harmonics [Eq. (3)]. Hence, it cannot account for the 4 mm
distance between the two observed peaks. On the other
hand, the saturation intensity in xenon for the 800 nm,
100 fs pulses is I +1.5]1014 W/cm2, [6]. For the max4
imum nominal laser intensity of our experiment
(+7.5]1014 W/cm2), such an intensity is reached also
away from the laser beam waist. In our case, the intensity
remains higher than I up to a distance from the laser
4
beam waist equal to the laser confocal parameter b. Then,
by moving the laser focus across the gas jet, one should
observe production of harmonics for a distance of twice
the confocal parameter b plus the gas jet width ¸, namely
2b#¸K6.3 mm. Moreover, complete ionization of the
gas medium should correspond to strong reduction in the
harmonic photon yield [27].
This is confirmed by the curve of Fig. 6a corresponding to the highest laser intensity: in this case the distance
between the two peaks is about 6.2 mm, in good agreement with the value 2b#¸"6.3 mm. A decrease in the
peak distance for lower intensities is also expected; in fact,
it reduces to 4.4 mm for an intensity of 3.2]1014 W/cm2.
The distance between the two peaks also decreases by
increasing the harmonic order (for a given laser intensity),
probably due to the fact that the generation of higher
order harmonics requires higher intensities that can be
reached closer to the laser beam waist.
Another interesting aspect of our result is the height of
the first peak which is always larger than the height of the
second one. The explanation is based on the consideration
that intense laser pulses propagating in strongly ionized
media are subject to self-defocusing. Thus, for a given laser
pulse energy, the highest effective intensity on the gas
sample can be obtained only when the laser beam is
focused on the front edge of the gas target: if one tries to
focus it on the rear edge, self-defocusing prevents from
reaching the smallest transverse dimension of the laser
cross-section, and, in turn, the highest intensity.
The effect is more pronounced the higher the harmonic order, as one can deduce from Fig. 6. In particular,
the curve of Fig. 6c relative to an intensity of 2.6
]1014 W/cm2 shows only one peak, as a result of the fact
that the intensity in correspondence of the second peak
position does not reach a value sufficient for efficient
generation of 13th harmonic photons.
Moreover, we notice that the left peak shifts towards
right as the laser intensity decreases. This is in agreement
with our interpretation: in fact, when the intensity at best
focus becomes too small, the degree of ionization in the
gas medium also decreases and the maximum of the harmonic photon production occurs when the laser beam
waist position coincides with the highest gas density, i.e.,
the position 5.5 mm in Figs. 5 and 6.
By increasing the laser intensity, the second (right)
peak begins to appear, although some additional modulations on the harmonic yield profile also become evident.
The origin of such modulations is not completely clear
and is presently under study.
3 Conclusions
We have realized an experimental apparatus for high
order harmonic generation in gases. The primary light
source is a Ti:S laser with chirped pulse amplification at
1 kHz repetition rate. The main feature of such a system is
the high repetition rate of harmonic pulses, that can be of
great interest in view of the application of VUV harmonic
radiation in ultrafast spectroscopy of atoms and molecules.
In order to address requirements of possible users, we
measured the absolute number of harmonic photons generated in various experimental conditions: depending on
the harmonic order, laser intensity, focus position and
other parameters, such as gas pressure and confocal parameter, it can vary from 104 to 108 photons per laser shot.
330
Multiplying such numbers by the valve repetition rate
(namely, 500 Hz) one obtains 5]1015—5]1010 photons/s.
The considerable average harmonic photon flux and the
high repetition rate are of great interest in applications of
harmonics since they greatly reduce the data acquisition
time.
Moreover, our results confirm that the conversion
efficiency can be improved by modifying the focusing
geometry. In fact, we find a strong dependence of the
harmonic photon yield on the distance between the laser
beam waist and the center of the gas target.
The main features of our experimental data can be
explained by taking into account the optical-field-induced
ionization occurring in the gas sample irradiated by a very
intense light pulse.
Finally, it is worth recalling that partial wavelength
tunability of the harmonic output can be achieved by
varying the Ti:S pump laser wavelength, operated at
a fixed wavelength of about 800 nm in our experiment,
within its 750—830 nm oscillating range. This possibility is
obviously of great interest for applications.
Acknowledgements. We acknowledge Prof. G. Tondello and his coworkers at the University of Padova for providing the VUV sensitive
TPB phosphor, and for their useful suggestions. This work was supported by the European Community under contract GE1*CT92-0046.
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