Download Get PDF - OSA Publishing

Resonantly-enhanced harmonic generation in
Argon
P. Ackermann,* H. Münch, and T. Halfmann
Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstraße 6, D-64289 Darmstadt, Germany
*
[email protected]
Abstract: We present systematic investigations of harmonic generation in
Argon, driven in the vicinity of a five-photon resonance by intense, tunable
picosecond radiation pulses. When properly matching the laser frequency
with the Stark-shifted multi-photon resonance, we observe a pronounced
enhancement not only of the 5th, but also the 7th and 9th harmonic of the
driving laser (i.e. at orders higher than the involved multi-photon resonance). We study the harmonic yield at different intensities and wavelengths
of the driving laser to determine optimal conditions for resonantlyenhanced harmonic generation.
(c) 2012 Optical Society of America
OCIS codes: (320.7110) Ultrafast nonlinear optics; (020.6580) Stark effect; (020.2649) Strong
field laser physics.
References and links
1.
E. Mevel, P. Breger, R. Trainham, G. Petite, P. Agostini, A. Migus, J.-P. Chambaret, and A. Antonetti, “Atoms
in strong optical fields: Evolution from multiphoton to tunnel ionization,” Phys. Rev. Lett. 70(4), 406–409
(1993).
2. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307 (1965).
3. A. L’Huillier, P. Balcou, and L. A. Lompré, “Coherence and resonance effects in high-order harmonic generation,” Phys. Rev. Lett. 68(2), 166–169 (1992).
4. E. S. Toma, P. Antoine, A. Bohan, and H. G. Muller, “Resonance-enhanced high-harmonic generation,” J. Phys.
At. Mol. Opt. Phys. 32(24), 5843–5852 (1999).
5. M. Barkauskas, F. Brandi, F. Giammanco, D. Neshev, A. Pirri, and W. Ubachs, “A novel-type tunable and
narrowband extreme ultraviolet radiation source based on high-harmonic conversion of picosecond laser
pulses,” J. Electron Spectrosc. Relat. Phenom. 144-147, 1151–1155 (2005).
6. R. Ganeev, “Generation of high-order harmonics of high-power lasers in plasmas produced under irradiation of
solid target surfaces by a prepulse,“Phys.- Usp. 52(1), 55–77 (2009).
7. R. Taïeb, V. Véniard, J. Wassaf, and A. Maquet, “Roles of resonances and recollisions in strong-field atomic
phenomena. II. High-order harmonic generation,” Phys. Rev. A 68(3), 033403 (2003).
8. M. Plummer and C. J. Noble, “Resonant enhancement of harmonic generation in argon at 248 nm,” J. Phys. At.
Mol. Opt. Phys. 35(2), L51–L58 (2002).
9. M. Gaarde and K. Schafer, “Enhancement of many high-order harmonics via a single multiphoton resonance,”
Phys. Rev. A 64(1), 013820 (2001).
10. C. de Morisson Faria, R. Kopold, W. Becker, and J. Rost, “Resonant enhancements of high-order harmonic
generation,” Phys. Rev. A 65(2), 023404 (2002).
11. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990).
1. Introduction
Frequency conversion processes significantly extend the spectral region accessible by lasers.
This holds in particular true for short wavelengths towards the regime of vacuum-ultraviolet
(VUV) or even extreme-ultraviolet (XUV) radiation. Such short wavelengths find a large
number of applications, e.g. in spectroscopy, microscopy, lithography or the generation of
ultra-short radiation pulses in the sub-femtosecond domain. Typically, highly nonlinear interactions of gaseous atomic media with intense ultra-short laser pulses are applied to generate
XUV radiation. However, the efficiency of harmonic generation in low density gaseous media is rather small, rarely exceeding the regime of 10−8 to 10−4.
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13824
Excitation of atomic resonances exhibits a simple way to enhance conversion efficiencies.
The basic idea is straightforward: The driving laser is tuned to an atomic resonance (usually a
multi-photon resonance, e.g. with n photons from the driving laser involved). The resonance
enhances the nonlinear susceptibility χ(n) of order n. If permitted by selection rules, this supports generation of the n-th harmonics of the driving laser or frequency mixing processes
with m additional photons from the same laser field, e.g. generating harmonics of order (n +
m). Such resonantly-enhanced frequency conversion is well known from low-order frequency
conversion processes, driven by lasers of moderate intensities. As a simple example, we note
resonantly-enhanced four-wave mixing in atomic gases. Here, a first laser pulse drives a twophoton transition, which serves to resonantly enhance a sum or difference frequency mixing
process with a second laser pulse. However, it is not obvious, that resonance-enhancement
also works for (higher) harmonic generation, driven by high-intensity ultra-short laser pulses.
The strong electric field of the laser significantly perturbs the level structure of the medium
and may destroy any resonance effect in conversion processes.
From this simple consideration it becomes clear, that resonantly-enhanced harmonic generation with ultra-short pulses may be efficient, if the driving radiation field is on one hand
sufficiently strong to drive (higher) harmonic generation – and on the other hand the field is
still not too strong to destroy the resonance structure of the medium. In the terminology of
high intensity laser-matter interactions and photoionization, we require operation in the regime of “multi-photon ionization” rather than “tunneling ionization” [1,2]. This choice provides appropriate conditions to observe pronounced resonance effect. The restriction towards
not too strong laser intensities still enables a large range of applications – and the possibility
to exploit resonances for efficient harmonic generation. We note, that proper investigation
and application of resonance effects also requires tunable lasers and moderate frequency
bandwidth (i.e. not too short pulse durations) to properly address isolated atomic resonances.
In recent years there already have been some (but still quite few) experimental investigations of resonance enhancements in harmonic generation via bound atomic states. As early
examples, we note the work by L’Huillier et al. [3] and Toma et al. [4]. The authors observed
enhancement of particular harmonics for specific laser intensities, e.g. an increase in the yield
of the n-th harmonic by exciting a dynamically shifted n-photon resonance. We also note
work by Barkauskas et al. [5], aiming at the development of a sophisticated laser system to
provide intense, rather long laser pulses (duration 300 ps) with small frequency bandwidth
and spectral tunability in the near infrared. In an application of the laser system for high harmonic generation, the authors found enhancement of harmonics for appropriate choice of the
driving laser wavelength. The authors suggest, that phase matching effects or multi-photon
resonances may lead to these enhancements. However, no definite explanation was given.
Finally we mention a sequence of experiments by Ganeev et al. on pronounced enhancement
of single harmonics in laser-driven plasmas (for a summary of these experiments see ref [6].).
The authors explain the enhancement by dynamically-shifted ionic resonances close to specific harmonics. However, in most of the above experiments resonance effects were scarcely
investigated systematically nor fully understood in detail. Moreover, in most cases only single harmonics were enhanced, while excitation of n-photon resonances should also affect
harmonics with order larger than n [7–10].
In the following, we present systematic investigations of resonantly-enhanced harmonic
generation, involving observations of dynamic (Stark) shifts, and simultaneous enhancement
of several harmonics with order higher than the resonantly-driven multi-photon transition. To
address single atomic resonances, in our experiments we apply intense pulses with quite short
pulse duration in the regime of 1 ps, sufficient spectral resolution (small bandwidth) well
below 1 nm, as well as center wavelength in the visible regime. The latter permits us to proceed already with lower-order frequency conversion processes quickly towards the XUV.
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13825
2. Coupling scheme and experimental setup
Figure 1 shows the coupling scheme and relevant energy levels in a jet of Argon atoms. We
tune intense, picosecond laser pulses in the vicinity of the five-photon resonance 3p6 1S0 →
4s’ [1/2]1 at 95400 cm−1, corresponding to a fundamental laser wavelength of 524 nm. In the
experiment we observe resonantly-enhanced fifth harmonic generation of the driving laser
radiation as well as harmonics of higher order (indicated by dashed arrows in the figure).
Fig. 1. Coupling scheme in Argon atoms with relevant energy levels. The short designation
(5p/5p’) indicates the manifold of closely spaced states 5p’ [3/2]2, 5p [1/2]0, 5p [3/2]2 and 5p
[5/2]2. Full arrows depict the driving laser at 524 nm, dashed arrows indicate the 5th, 7th and
9th harmonics, as investigated in the experiment.
The experimental setup is as follows (see Fig. 2): A titanium:sapphire oscillator (MIRA
900P, Coherent), pumped by a frequency doubled, continuous-wave Nd:YAG laser (VERDI
V18, Coherent), generates laser pulses with a pulse duration of 1.2 ps (full width at halfmaximum, FWHM). The pulse train synchronously pumps an optical parametric oscillator
(OPO) with intracavity frequency doubling (OPO automatic, APE GmbH). The setup provides tunable (ps) radiation pulses in the visible regime, with linear polarization, pulse duration of approximately 1.4 ps (FWHM), and spectral bandwidth close to the Fourier transform
limit. The average output power of the OPO is 100 - 200 mW, corresponding to pulse energies around 2 nJ, at a repetition rate of 76 MHz.
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13826
Fig. 2. Schematic representation of the experimental setup with some details of the homemade, four stage (S1-S4) dye amplifier chain. (BS: beam sampler, VBS: variable beam splitter, CL: cylindrical lens, PM: power meter).
The picosecond pulse train propagates into a home-made four-stage dye amplifier chain
(see Fig. 2), pumped by the third-harmonic frequency of a pulsed, injection-seeded Nd:YAG
laser (Pro 230-20, QuantaRay). The pump laser provides pulse energies of approximately 350
mJ at 355 nm, with pulse duration of 8 ns at a repetition rate of 20 Hz. The dye amplifier
chain essentially consists of two transversally and two longitudinally pumped dye amplifier
stages. For the experiments discussed below, we operated the first and second stage of the
dye amplifier with Coumarin 540, solved in a mixture of dioxane and ethylene glycol. In the
third and fourth stage we used Coumarin 504, solved in methanol. The four-stage dye amplifier chain permits amplification of tunable, visible picoseconds pulses with output pulse
energies up to 2 mJ. The duration of the amplified pulses is (1.45 ± 0.25) ps (FWHM) with a
bandwidth close to the Fourier-transform limit (as determined by measurements in a homemade setup for frequency-resolved optical gating (FROG)). In the experiment, we focus the
laser beam by an achromatic doublet (focal length f = 150 mm) into a pulsed gas jet of Argon
atoms. The diameter of the picosecond laser beam in the interaction region is approximately
(18 ± 4) µm (FWHM). This yields intensities up to 100 TW/cm2 (peak intensity, assuming a
spatial Gaussian and a temporal sech2 intensity envelope).
The harmonics, generated in the gas jet propagate into an evacuated monochromator
(VM502, Acton Research, maximal resolution ∆λ = 0.1 nm). The monochromator separates
the harmonics and directs them onto an electron multiplier tube (EMT R595, Hamamatsu) for
detection. In parallel to acquisition of harmonic spectra, we carefully monitor the laser pulse
energy and the spatial beam profile to guarantee stable conditions in the interaction volume.
3. Experimental data and discussion
To spectroscopically identify the relevant multi-photon transition 3p6 1S0 → 4s’ [1/2]1 at
95400 cm−1 in Argon, we monitored the intensity of the fifth harmonic frequency when tuning the wavelength of the driving picosecond laser pulse. Figure 3 shows such spectra, obtained for different laser intensities. For rather small intensity of approximately 5 TW/cm2,
the obtained signal intensity at the fifth harmonic is still quite low. The spectrum shows an
isolated peak (i.e. resonantly-enhanced fifth harmonic generation) at a laser wavelength of
525 nm (marked by an arrow in Fig. 3), corresponding to a fifth harmonic wavelength of 105
nm.
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13827
Fig. 3. Yield of the fifth harmonic vs. driving laser wavelength for different laser intensities.
Raw data after averaging 20 laser shots and low pass filtering. For better visibility, the harmonic yields for laser intensities at 5 TW/cm2 and 20 TW/cm2 are scaled up by factors of 80
and 10, respectively. The arrow in the graph for lowest intensity at 5 TW/cm2 indicates the
spectral position of the five-photon resonance 3p6 1S0 → 4s’ [1/2]1.
This fits well with the expected transition wavelength at 104.8 nm – in particular taking
the resolution of our spectrometer, the laser bandwidth of (0.6 ± 0.1) nm and AC Stark shifts
(which we ignored for this “small” intensity) into account. Thus, we can clearly assign the
observed feature at 525 nm to the five-photon resonance 3p6 1S0 → 4s’ [1/2]1. However, we
also observe quite strong fifth harmonic signal in a broad wavelength regime around 510 nm.
We attribute this to a resonantly-enhanced difference frequency mixing process via highly
excited states. In the photon picture this can be understood as a six-photon transition up from
the ground state 3p6 1S0 to the closely spaced set of four highly excited states 5p’ [3/2]2, 5p
[1/2]0, 5p [3/2]2 and 5p [5/2]2 and down with another photon from the same laser pulse. Also
this “six minus one” mixing process yields signal at the fifth harmonic frequency. The spectral positions of the six-photon transitions to states 5p’ [3/2]2, 5p [1/2]0, 5p [3/2]2 and 5p
[5/2]2 are expected at 506 nm, 510.4 nm, 512.0 nm and 512.8 nm. This fits well with the
observed broad feature around 510 nm in the spectrum.
When we increase the laser intensity, the signal of the fifth harmonic quickly grows – as
expected. Moreover, we also observe systematic shifts in the spectrum. At a laser intensity of
(20 ± 9) TW/cm2, the five-photon resonance 3p6 1S0 → 4s’ [1/2]1 experiences a stronger Stark
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13828
shift, moves towards shorter wavelengths and shows a line broadening. Moreover, the line
seems to be slightly asymmetric now, with a longer tail towards shorter wavelengths. The
shift, the line broadening and the asymmetry are all typical for the AC Stark effect. We note,
that the Stark shifts are due to off-resonant couplings to all bound and continuum states in
Argon, i.e. beyond the simplified two-level picture of states 3p6 1S0 and 4s’ [1/2]1 only. As
another interesting feature in the spectrum for an intensity of 20 TW/cm2, we do not observe
the difference-mixing process via six-photon resonances around 510 nm anymore. We also
attribute this to an AC Stark effect, which shifts the six-photon transitions to shorter wavelength, i.e. outside the spectral region of observation. We note, that the five-photon resonance
is energetically lower than the six-photon resonances. Thus, the Stark shifts should be even
stronger for the latter. We could not further investigate the shifts of the six-photon resonances
with our laser setup, as the OPO permits output wavelengths longer than 505 nm only. However, this did not matter for our experiment, which deals with the clearly visible five-photon
resonance.
When we further increase the intensity to (41 ± 18) TW/cm2 and (61 ± 26) TW/cm2, the
shift and line broadening of the five-photon resonance becomes very pronounced. For the
strongest intensity at 61 TW/cm2 the five-photon resonance shifted by more than 15 nm. If
we take the right shoulder of the spectral lines as an indicator for the strength of the shift and
the peak of the line at lowest intensity of I = 5 TW/cm2 as a reference (see arrow in Fig. 3),
we roughly estimate Stark shifts in the range of 0.25 THz per TW/cm2 laser intensity.
As already briefly indicated above, our experimental conditions are closer to the multiphoton regime than the tunneling regime. In this case, we can estimate the total Stark shift of
level 4s’ [1/2]1 by adding up contributions from off-resonant couplings to all other states. The
relevant expression for the Stark shift of a state |i〉 is [11]: S = − Σ j Ωij2 / 2∆ij , with the coupling Rabi frequency Ωij between state |i〉 and the manifold of all other states |j〉, as well as the
detuning of the laser from the transition frequency ωij. We note, that the sum in the expression for the Stark shift is infinite and also includes continuum states. For a first estimation,
we calculated the Stark shift of level 4s’ [1/2]1 by taking off-resonant couplings to the 18
closest states in the 4p, 4p’, 5p, 5p’ manifold into account. The calculation yields the strongest contributions by off-resonant couplings to states 4p’. The latter off-resonant couplings
push the level 4s’ [1/2]1 to higher energy (i.e. shorter wavelength), as also observed in our
experiment. The strength of the calculated Stark shift is about an order of magnitude larger
than observed in the experiment. We expect this deviation, as in our simplified calculation we
ignored contributions from excited states beyond the 5p, 5p’ shells. The higher states (all of
them with positive detuning) will reduce the estimated Stark shift. Moreover, we must be
careful with interpretations of level shifts in the simple multi-photon picture. At our laser
intensities of several 10 TW/cm2 we already operate towards the tunneling regime. Nevertheless, our simplified estimations in the multi-photon picture at least confirm the correct direction of the observed Stark shift.”
To investigate resonantly-enhanced harmonic generation, we tune now the laser on and
off the Stark-shifted resonances and compare the obtained harmonic spectra. Figure 4 shows
harmonic spectra for a laser intensity of 20 TW/cm2. In this case, we expect the Stark-shifted
five-photon resonance 3p6 1S0 → 4s’ [1/2]1 at a wavelength of 522 nm (compare Fig. 3). If we
tune the laser to a wavelength of 524 nm (i.e. off the Stark-shifted five-photon resonance),
the harmonic spectrum shows a weak 5th harmonic and a very weak 7th harmonic of the
driving laser (see Fig. 4(a)). If we tune the laser now on the Stark-shifted five-photon resonance at 522 nm, the intensities of both the 5th and 7th harmonic increase by an order of magnitude due to resonance enhancement (see Fig. 4(b), red line).
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13829
Fig. 4. Harmonic spectra at different wavelengths of the driving laser, tuned in the vicinity of
the Stark-shifted five-photon resonance 3p6 1S0 → 4s’ [1/2]1. Raw data after averaging 20 laser
shots, but without filtering.
Thus, the five-photon resonance also enhances generation of a higher harmonic, i.e. with
an order larger than the five-photon transition. If we tune the laser further to a shorter wavelength around 510 nm (i.e. again off the five-photon resonance), both the 5th and 7th harmonics decrease significantly (see Fig. 4(c)). However, both harmonics are still slightly stronger
than the harmonics, driven with the laser wavelength at 524 nm, i.e. at the other side of the
resonance (compare Fig. 4(a)). We attribute this to the long tail of the Stark-shifted resonance
towards shorter wavelength (compare Fig. 3). Thus, at a wavelength of 510 nm, we operate
still in the tail of the resonance and get some (though weaker) resonance enhancement.
The effect of resonantly-enhanced harmonic generation becomes even better visible when
more observation channels (i.e. harmonics) appear in the spectrum, e.g. at better signal-tonoise ratio or larger laser intensity. Figure 5 shows harmonic spectra for a laser intensity of
61 TW/cm2. In this case, we expect the Stark-shifted five-photon resonance 3p6 1S0 → 4s’
[1/2]1 at a wavelength of 510 nm (compare Fig. 3). If we tune the laser to wavelengths of 524
nm and 522 nm (i.e. off the Stark-shifted resonance), besides the 5th harmonic only rather
weak 7th and 9th harmonics show up in the spectrum (see Figs. 5(a,b)). If we tune the laser to
a wavelength of 510 nm (i.e. onto the Stark-shifted five-photon resonance), we resonantly
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13830
Fig. 5. Harmonic spectra at different wavelengths of the driving laser, tuned in the vicinity of
the Stark-shifted five-photon resonance 3p6 1S0 → 4s’ [1/2]1.
enhance 5th, 7th and 9th harmonics (see Fig. 5(c)). The enhancement factor is now between 3
and 10 (depending on which of the harmonics in Fig. 5 we take as reference). As comparison
of Figs. 4 and 5 shows, the maximal resonance-enhancement occurs at different wavelengths
– obviously depending on the Stark shift (respectively the laser intensity).
We note, that the harmonic signals for off-resonant excitation with a laser wavelength of
524 nm (see Fig. 5(a)) are slightly stronger compared to the harmonic signals obtained with a
laser wavelength of 522 nm (see Fig. 5(b)). This is a bit surprising, as 524 nm is further away
from the Stark-shifted resonance at 510 nm. Also the spectroscopic data on resonantlyenhanced fifth harmonic generation (see Fig. 3) provided some similar evidence: At a laser
intensity of 61 TW/cm2, the yield in the 5th harmonic smoothly decreases from the maximum
around 510 nm towards 522 nm. However, for longer wavelengths the 5th harmonic yield
seems to slightly increase again. We attribute this to a lower lying five-photon resonance 3p6
1
S0 → 4s [3/2]1, (see Fig. 1) which is pushed and broadened by Stark shifts from the original
position around 533 nm towards the region of 524 nm – and also enhances the harmonic
yield.
The experimental data clearly demonstrate the effect of resonant multi-photon excitation
to enhance harmonic generation at higher orders than the involved multi-photon transition –
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13831
provided we take Stark shifts into account and match our laser wavelength to the shifted
resonances.
4. Conclusion
We investigated harmonic generation in a dense jet of Argon atoms, driven in the vicinity of
the five-photon resonance 3p6 1S0 → 4s’ [1/2]1 by intense, tunable picosecond radiation
pulses. As a major optical component for the experiment, we implemented a laser setup with
a home-made four-stage dye amplifier system to provide picosecond pulses with appropriate
specifications. The laser system combines sufficient intensity (i.e. up to 100 TW/cm2) to
approach the regime of higher harmonic generation with still fine spectral resolution to address and exploit single atomic resonances.
In a first experiment on resonantly-enhanced fifth harmonic generation, we determined
pronounced AC Stark shifts and line broadenings of the five-photon resonance. Moreover, we
found evidence for an additional difference frequency mixing process “six minus one photon” via a set of highly excited states in Argon – which also generates radiation at the fifth
harmonic of the driving laser. In a second experiment, we investigated the effect of resonant
multi-photon excitation on the generation of harmonics (i.e. with higher order than the involved multi-photon transition). When we tuned the laser frequency to the Stark-shifted fivephoton resonance, we found a pronounced resonance-enhancement not only of the 5th, but
also of the 7th and 9th harmonic. As an important feature of resonance enhancement, the
laser wavelength must be matched to the position of the Stark shifted atomic resonance –
which depends upon the applied laser intensity. The experimental data clearly demonstrate
the effect of resonant multi-photon excitation to enhance harmonic generation. The investigations may serve as another small step to determine appropriate mechanisms for efficient generation of XUV laser pulses.
Acknowledgement
We acknowledge most valuable comments by M. Lein (University of Hannover), as well as
financial support by the Deutsche Forschungsgemeinschaft.
#167644 - $15.00 USD
(C) 2012 OSA
Received 30 Apr 2012; revised 24 May 2012; accepted 24 May 2012; published 6 Jun 2012
18 June 2012 / Vol. 20, No. 13 / OPTICS EXPRESS 13832