Download attosecond light sources

Apr09-to-trigraphic.qxp
5/8/2009
12:28 PM
Page 63
ARTICLE DE FOND
ATTOSECOND LIGHT SOURCES
BY
DAVID VILLENEUVE
S
ince the invention of photography in the 19th century, scientists have been trying to freeze the
motion in fast-moving events. Motion pictures of
galloping horses were an early application of high
speed photography, see Fig. 1. Shutter speeds of cameras
are limited to about 1 millisecond, and scientists then
Fig. 1
Eadweard Muybridge was an English photographer
who moved to San Francisco. In 1877 he created a
series of photographs of a horse trotting for former
California governor and Stanford University founder
Leland Stanford. This is the earliest example of using
high speed photography to study moving objects.
Attosecond science is at the extreme limit of time resolution.
SUMMARY
The shortest-duration laser pulses now have
durations below 100 attoseconds. This is
less than the time it takes an electron to go
around a hydrogen atom. This article
describes how these new sources work.
turned to brief light flashes to illuminate the subject for
microseconds. The invention of the laser in the 1960s then
reduced the duration of the light flashes to nanoseconds.
Figure 2
shows
the
progress that
has
been
made
in
reducing the
pulse duration of laser
sources over
the past 40
years.
For
the
first
20 years, the
Fig. 2 Lasers produce the shortest manshortest pulse
made pulses of light. There has been
duration
steady progress in reducing the pulse
decreased
duration, using Q-switched and
exponentialmode-locked laser sources. A completely different approach was
ly, much like
required to break into the attosecond
Moore’s law
frontier.
in the semiconductor
industry. Then a floor of about 5 femtoseconds was
reached. The reason for this floor is illustrated in Fig. 3.
A pulse of light from a laser source is composed of two
components – the carrier frequency corresponding to the
optical wavelength of the laser, and the envelope that
defines the pulse duration. Figure 3(a) shows a 50 fsec
pulse containing many optical cycles, and Fig. 3(b) shows
the corresponding Fourier transform. The spectrum is
centered at the optical frequency of 375 THz corresponding to the 800 nm laser source.
The spectral width and the pulse duration go hand-inhand. A pulse of a certain duration requires at least the
spectral bandwidth of its Fourier transform. The converse
is not true – a broad spectrum does not guarantee that you
have a short pulse. The solar spectrum is very broad, yet
it is not composed of femtosecond pulses because the different frequencies are not coherent. To work as a laser, the
spectral bandwidth must be supported by the gain bandwidth of the laser source. This is the reason that titaniumdoped sapphire (Ti:Sapphire) is the laser medium of
choice for femtosecond lasers. It has a gain spectrum that
covers the range of 700-1000 nm. This is short enough to
support a 5 fsec pulse, as shown in Fig. 3(c,d).
D. Villeneuve
<david.villeneuve
@nrc.ca>, Program
Leader for attosecond science, National
Research Council of
Canada, 100 Sussex
Drive, Ottawa ON
K1A 0R6
LA PHYSIQUE AU CANADA / Vol. 65, No. 1 ( avril à juin 2009 ) C 63
Apr09-to-trigraphic.qxp
5/8/2009
12:29 PM
Page 64
ATTOSECOND LIGHT SOURCES (VILLENEUVE)
Fig. 4
Fig. 3
A laser pulse is composed of an optical carrier frequency and
a pulse envelope. The Fourier transform of a particular pulse
shape shows the spectral bandwidth required to produce that
pulse. The narrower the pulse is in time, the wider must be
its spectral bandwidth. The pulse duration limit for a particular optical frequency is one optical cycle.
spectrum onto a microchannel plate detector. The laser pulse
has an intensity of over 1014 W/cm2, sufficient to ionize the gas
sample.
The spectrum is seen to be composed of odd harmonics of the
laser frequency, in this case extending to a photon energy of
60 eV. This source is of interest for photoionization of molecules, and is fast enough to be able to time-resolve molecular
dynamics. It was also found that the xuv radiation is collimated into a few milliradian beam, and was coherent.
To break through the barrier of insufficient gain bandwidth to
support an even shorter pulse, it was realized that a shorter
wavelength carrier frequency was required. The practical limit
to this was around 200 nm, the point at which most materials
become absorbing. Physicists discussed coherently combining
the output of several lasers to cover a wider spectrum. The
lasers would operate at integer multiples of frequency. Figure 4 shows what happens if we add together
the electric fields from sources at 1, 3 and 5 times a
fundamental frequency. The sum of the fields is seen
to be localized into shorter and shorter times.
This approach was seen to be impractical and was
never seriously pursued. However, in an example of
serendipitous discovery that is so important to scientific breakthroughs, a completely different approach
was discovered. It was called high harmonic generation. It was first noticed [1] that an intense picosecond laser beam focused into a gas sample would produce odd harmonics of the laser frequency. This was
considered a bit of a scientific curiosity without any
application, until it was realized that it provided a
source of short wavelength radiation that had the
same duration as the laser pulse. An example of the
experimental setup is seen in Fig. 5. A 30 fsec
Ti:Sapphire laser pulse with a wavelength of 800 nm
is focused into a pulsed supersonic gas jet. In the forward direction, an xuv spectrometer disperses the
64 C PHYSICS
IN
Fig. 5
It is possible to create a shorter duration laser pulse by adding
together different frequencies. In fact this is how modelocked lasers produce short pulses, by coherently adding
together different cavity modes of an optical resonator. In
this example, we add together odd integer multiples of a
given frequency, and see that the sum is localized at short
times.
This is a sketch of how high harmonic generation is performed in the lab.
An intense femtosecond laser pulse is focused into a gas jet. The resulting
extreme ultraviolet (xuv) radiation is coherent and is collimated in the forward direction. The spectrum (bottom) is composed of odd multiples of the
laser frequency, leading to the name high harmonic generation.
CANADA / VOL. 65, NO. 1 ( April-June 2009 )
Apr09-to-trigraphic.qxp
5/8/2009
12:30 PM
Page 65
ATTOSECOND LIGHT SOURCES (VILLENEUVE)AA
The simple kinematics of the electron motion is described by
Corkum [2]. The maximum kinetic energy of the electron as it
returns is 3.17 Up, where the ponderomotive potential
Up = 9.3x10-14 Iλ2 (in eV) when the laser intensity I is in
W/cm2 and the laser wavelength λ is in microns. In addition to
the kinetic energy, the electron also acquires the ionization
potential Ip when it recombines. The highest energy photon
produced by this mechanism is thus Emax = 3.17 Up + Ip. By
using a very intense laser pulse and helium whose ionization
potential is 25 eV, high harmonic emission has been extended
to kilovolt photons [3].
Fig. 6
A semiclassical three-step model explains the process of high
harmonic generation. The entire process occurs during a single laser optical cycle, about 2 femtoseconds. An electron is
tunnel-ionized from an atom by a strong laser field. When
the optical field reverses direction a femtosecond later, the
electron can be driven back to the parent ion. It has a small
but finite probability to recombine, and in doing so it will liberate its kinetic energy in the form of a photon.
In 1993 the mechanism behind the xuv radiation was identified [2]. It was called the three-step process, and is illustrated
in Fig. 6. The time scale for these three steps is the period of a
single optical cycle, about 2 femtoseconds, not the duration of
the full laser pulse. An atom is exposed to the electric field of
an intense laser pulse, and an electron is detached from the
atom by the field. The freed electron is accelerated by the laser
field, first away from the ion, and then is driven back towards
the
ion
when
the
laser field
changes
direction.
Most of the
time
the
returning
electron will
simply miss
the ion, but
with a small
probability
the electron
can recombine with
the
ion.
Since it has
acquired
kinetic ener- Fig. 7 The quantum mechanical explanation of
high harmonic generation also includes
gy from the
three steps. The bound state electronic
laser field,
wave function can tunnel into the continuwhen
it
um if the laser field is strong enough. When
recombines
the laser field switches direction, this conit must give
tinuum wave function can return to the parup
this
ent, where it interferes with the bound state
kinetic enerwave function. The oscillation of the charge
gy in the
produced by this interference leads to emission of electromagnetic radiation in the xuv
form of a
spectral range.
photon.
This semiclassical description explains the presence of high
energy photons, but it does not explain the coherent nature of
the emission. A quantum mechanical model does [4]. Figure 7
shows the quantum equivalent of the three-step model for a
simple atom like hydrogen. The bound state wave function of
the electron is held by the -1/r potential of the nucleus. The
Fig. 8
The xuv electric field is shown along with the femtosecond
laser field that produces it. Within each optical half-cycle, an
attosecond pulse is produced. If the laser pulse has many
cycles, many attosecond pulses are produced. The interference of the different pulses in the spectral domain leads to the
creation of odd harmonics. If the laser pulse duration is very
short, then only a single electron recollision occurs, and only
a single attosecond pulse is produced. The shortest pulse currently produced is 80 attoseconds.
LA PHYSIQUE AU CANADA / Vol. 65, No. 1 ( avril à juin 2009 ) C 65
Apr09-to-trigraphic-revised.qxp
5/11/2009
10:28 AM
Page 66
ATTOSECOND LIGHT SOURCES (VILLENEUVE)
strong laser field E(t) adds an additional potential E(t)x. If the
field is strong enough, it causes some of the bound state wave
function to tunnel through the potential barrier and away from
the nucleus. When the laser field changes sign a femtosecond
later, some of this wave function is pushed back to the nucleus,
where it interferes with the remaining bound state wave function. The interference contains a high frequency term that is
the difference between the energy of the bound state (-Ip) and
the wave function in the continuum (p2/2). If the total wave
function is written as the sum of the bound part and the continuum part, the emission is due to an electric dipole transition
between the continuum and the bound parts.
most direct way is to make the laser pulse as short as possible,
under 5 fsec. This is seen in Fig. 8(b). There are other
approaches such as controlling the polarization of the laser
pulse, or adding the second harmonic, that also achieve a single attosecond pulse [5]. Single 130 attosecond duration pulses
have been measured [6], and the current record is 80 attoseconds.
This model also explains why the high harmonic spectrum contains only odd harmonics of the laser frequency. Figure 8
shows the electric field of the high harmonic emission that is
produced by a laser pulse. It is seen that an xuv pulse is produced during each half-cycle of the laser electric field. This is
because the ionization occurs preferentially near the peak of
the laser cycle, and recollision occurs within the same laser
cycle. The result is a train of xuv pulses, each with a duration
of less than a femtosecond, that repeats every half-cycle of the
laser field. The Fourier transform of this pulse train must have
a spectral periodicity of twice the laser frequency. The fact that
it is at odd multiples of the laser frequency is determined by the
alternating left-right parity of the recollision.
The process underlying attosecond xuv pulses is an electron
recolliding with a parent ion. This recollision electron is itself
an attosecond probe that can measure fast molecular motion [9].
Since the recombination process is a transition between the
continuum electron and the bound state wave function, the
emitted spectrum contains information on the bound state wave
function, and can be used to determine the shape of a molecular orbital [10] or observe molecular vibrations on the time scale
of the laser pulse duration [11] or on the time scale of the optical cycle [12].
The attosecond pulse train that is seen in Fig. 8 can be and is
used in experiments. But for true attosecond experiments, a
single xuv pulse must be selected. The trick is to choose a laser
electric field shape that results in only a single recollision. The
As the field of attosecond science is still young, we are still
learning about its potential. Attosecond science has been used
to observe decay processes in excited atoms [7], and to measure
the emission time of photoelectrons from a metal surface [8].
FURTHER READING
If you are interested in learning more about attosecond science,
there are some excellent review articles. For example the production of attosecond pulses is described in [13]; applications
are described in [14].
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
A. McPherson, G. Gibson, H. Jara, U. Johann, T.S. Luk, I.A. McIntyre, K. Boyer, and C.K. Rhodes, Studies of multiphoton production
of vacuum-ultraviolet radiation in the rare gases, J. Opt. Soc. Am. B 4, 595-601 (1987).
P.B. Corkum, Plasma perspective on strong-field multiphoton ionization, Phys. Rev. Lett. 71, 1994 (1993).
J. Seres, E. Seres, A.J. Verhoef, G. Tempea, C. Streli, P. Wobrauschek, V. Yakovlev, A. Scrinzi, C. Spielmann, F. Krausz, Laser technology: Source of coherent kiloelectronvolt X-rays, Nature 433, 596 (2005).
M. Lewenstein, P. Balcou, M. Yu. Ivanov, A. L'Huillier and P.B. Corkum, Theory of high-harmonic generation by low-frequency laser
fields, Phys. Rev. A 49, 2117 (1994).
H. Mashiko, S. Gilbertson, C. Li, S.D. Khan, M.M. Shakya, E. Moon and Z. Chang, Double Optical Gating of High-Order Harmonic
Generation with Carrier-Envelope Phase Stabilized Lasers, Phys. Rev. Lett. 100, 103906 (2008).
G. Sansone, E. Benedetti, F. Calegari, C. Vozzi, L. Avaldi, R. Flammini, L. Poletto, P. Villoresi, C. Altucci, R. Velotta, S. Stagira,
S. De Silvestri, M. Nisoli, Isolated Single-Cycle Attosecond Pulses, Science 314, 5798 (2006).
M. Uiberacker, Th. Uphues, M. Schultze, A.J. Verhoef, V. Yakovlev, M.F. Kling, J. Rauschenberger, N.M. Kabachnik, H. Schraeder,
M. Lezius, K.L. Kompa, H.-G. Muller, M.J.J. Vrakking, S. Hendel, U. Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, Attosecond
real-time observation of electron tunnelling in atoms, Nature 446, 627 (2007).
A.L. Cavalieri, N. Muller, Th. Uphues, V.S. Yakovlev, A. Baltuska, B. Horvath, B. Schmidt, L. Blumel, R. Holzwarth, S. Hendel,
M. Drescher, U. Kleineberg, P.M. Echenique, R. Kienberger, F. Krausz, U. Heinzmann, Attosecond spectroscopy in condensed matter,
Nature 449, 1029 (2007).
Hiromichi Niikura, F. Légaré, R. Hasbani, A.D. Bandrauk, Misha Yu Ivanov, D.M. Villeneuve and P.B. Corkum, Sub-laser-cycle electron pulses for probing molecular dynamics, Nature 417, 917-922 (2002).
J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J.C. Kieffer, P.B. Corkum and D.M. Villeneuve, Tomographic imaging of
molecular orbitals, Nature 432, 867-871 (2004).
Nicholas L. Wagner, Andrea Wüest, Ivan P. Christov, Tenio Popmintchev, Xibin Zhou, Margaret M. Murnane, and Henry C. Kapteyn,
Monitoring molecular dynamics using coherent electrons from high harmonic generation, Proc. Nat. Acad. Sci. 103, 13279 (2006).
S. Baker, J.S. Robinson, C.A. Haworth, H. Teng, R.A. Smith, C.C. Chirila, M. Lein, J.W.G. Tisch, and J.P. Marangos, Probing Proton
Dynamics in Molecules on an Attosecond Time Scale, Science 312. 424 (2006).
A. Scrinzi, M. Yu Ivanov, R. Kienberger and D.M. Villeneuve, Attosecond Physics, J. Phys. B 39, R1-R37 (2006)
F. Krausz and M. Yu. Ivanov, Attosecond Physics, Rev. Mod. Phys. 81, 163 (2009).
66 C PHYSICS
IN
CANADA / VOL. 65, NO. 1 ( April-June 2009 )