Phase-Coherent Frequency Combs in the Vacuum Ultraviolet via High-Harmonic Generation
inside a Femtosecond Enhancement Cavity
R. Jason Jones,*Kevin D. Moll, Michael J. Thorpe, and Jun Ye†
JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
(Received 7 April 2005; published 20 May 2005)
We demonstrate the generation of phase-coherent frequency combs in the vacuum utraviolet spectral
region. The output from a mode-locked laser is stabilized to a femtosecond enhancement cavity with a gas
jet at the intracavity focus. The resulting high-peak power of the intracavity pulse enables efficient high-
harmonic generation by utilizing the full repetition rate of the laser. Optical-heterodyne-based measure-
ments reveal that the coherent frequency comb structure of the original laser is fully preserved in the high-
harmonic generation process. These results open the door for precision frequency metrology at extreme
ultraviolet wavelengths and permit the efficient generation of phase-coherent high-order harmonics using
only a standard laser oscillator without active amplification of single pulses.
DOI: 10.1103/PhysRevLett.94.193201PACS numbers: 39.30.+w, 42.62.Eh, 42.65.Ky
Recent developments in short-wavelength light sources
have been rapid, with significant advances in temporal
resolution, spectral coverage, and brightness [1,2]. A num-
ber of approaches have been proposed and/or are under
active investigation, ranging from large scale systems such
as free-electron laser-based x-ray generation  to smaller
harmonic generation (HHG) via photo-ionization dynam-
ics, or extreme nonlinear optics [4,5]. However, the spec-
tral resolution (or the corresponding temporal coherence)
of these short-wavelength light sources remains poor in
comparison with laser sources in the visible. Furthermore,
system complexity and cost have prevented the widespread
use of these short-wavelength light sources. In this work
we address both issues using a standard femtosecond laser
coupled to a completely passive optical cavity. Phase sta-
bilization of a femtosecond optical frequency comb ena-
bles such a development.
Femtosecond laser-based optical frequency combs have
played a remarkable role in precision measurement and
ultrafast science . Phase control of wide-bandwidth
optical frequency combs has enabled numerous advances
in optical frequency measurement and synthesis , opti-
cal atomic clocks [7,8], direct frequency comb spectros-
copy , coherent pulse synthesis and manipulation ,
and deterministic studies in subcycle physics . Phase
stabilization offemtosecond pulses has also led to a certain
degree of control capability in the HHG process, allowing
generation of isolated, single attosecond pulses in the
extreme ultraviolet (XUV) region . However, the origi-
nal frequency comb structure is lost due to the reduction of
the pulse train repetition rate required to actively amplify
single pulses to the energies needed for the HHG process.
In this work we utilize phase stabilization of optical fre-
quency combs as the necessary technological base for
precise manipulation of femtosecond pulses such that
they are coherently added inside a ‘‘femtosecond (fs)
enhancement cavity’’ (Fig. 1). The enhanced intracavity
field provides the necessary peak intensity for ionization of
atoms or molecules for HHG where the liberated photo-
electron recollides with the parent ion resulting in coherent
light emission. The advances documented in this Letter
enable a unification of these research fields, generating a
high repetition rate (at the laser’s original 100 MHz repe-
tition frequency) and phase-controlled frequency comb in
the XUV region, which is shown to maintain a definitive
phase relationship with respect to the original comb in the
near infrared. The spectral resolution demonstrated here
can extend direct frequency comb spectroscopy  into the
FIG. 1 (color).
generation. The incident pulse train is stabilized to a high finesse
cavity, enhancing pulse energy nearly 3 orders of magnitude
while maintaining a high repetition frequency. A gas target at the
cavity focus enables phase-coherent HHG, resulting in a phase-
stable frequency comb in the vacuum utraviolet (VUV) spectral
region. The photo inset shows the actual spatial mode profile of
the 3rd harmonic coupled out of the cavity.
Schematic setup of intracavity high-harmonic
PRL 94, 193201 (2005)
20 MAY 2005
2005 The American Physical Society
XUV spectral region, advancing capabilities to perform
high resolution spectroscopy , precision measurement
, and coherent manipulation in the XUV. The ineffi-
ciency of the HHG process makes the fs enhancement
cavity ideally suited for efficient harmonic generation as
the driving pulse is continually ‘‘recycled’’ after each pass
through the interaction region, leading to a significant
improvement in the average power conversion efficiency
compared to amplifier-based systems, up to the ratio in
repetition rates (100’s MHz compared to kHz). In addition,
system cost and size are greatly simplified.
For successful implementation of this highly efficient
approach to HHG, the passive optical cavity needs to
demonstrate a number of important characteristics: (i) a
high finesse to build up the pulse power, (ii) low round-trip
group-delay dispersion to allow ultrashort pulses to be
coupled into and stored inside the cavity, and (iii) a robust
servo to stabilize the 2 degrees of freedom of the incident
pulse train (e.g., optical carrier frequency and repetition
frequency) to the corresponding cavity resonance modes.
We have been pushing towards these goals for the past
several years, investigating direct stabilization of femto-
second lasers to high finesse cavities , dispersion com-
pensation and characterization of mirror coating tech-
nology , and the nonlinear response of the cavity to
intracavity elements . The previous work resulted in
the demonstration of passive-cavity-based ‘‘amplifiers’’ in
both picosecond  and femtosecond  regimes by
periodically switching out the stored intracavity pulse.
A standard mode-locked femtosecond Ti:Sapphire laser
with a repetition frequency (fr) of 100 MHz, 48 fs pulse
duration, and 8 nJ pulse energy is used. The carrier-
envelope offset frequency (f0) and frset the pulse-to-pulse
(Fig. 1). The pulse train from the laser passes through a
prism-based compressor before incident on the passive
optical cavity. To couple the pulse train from the mode-
locked laser into the cavity, both f0and frof the laser are
adjusted such that the optical comb components are maxi-
mally aligned to a set of resonant cavity modes . For
short optical pulses (<100 fs) and high finesse cavities
(F > 1;000), the comb components need to overlap with
corresponding narrow cavity resonances across a large
spectral bandwidth. The power transmitted through the
cavity as the length of the laser is scanned therefore shows
a single sharp resonance only when both the laser carrier
frequency (average comb position) and spacing (fr) are
optimally aligned [Fig. 2(a)] .
To investigate the peak intensity that can be obtained
with this method, an empty fs enhancement cavity was
initially characterized. The passiveoptical cavity has a ring
geometry formed by six mirrors. All mirrors are high
reflectors except the input coupler, which has a transmis-
sion of 0.1%, nearly matching the net intracavity loss. The
center wavelength of the mirror coating is 800 nm, with a
bandwidth of 100 nm within which the net cavity group-
delay dispersion is compensated to <10 fs2. However,
?? ? 2?f0=fr
residual group-delay dispersion in the enhancement cavity
causes the cavity free-spectral-range (FSR) frequency to
vary as a function of wavelength, limiting the bandwidth of
the pulse that can be coupled into the cavity . To
measure the average cavity finesse, a ring-down measure-
ment of the cavity field decay is performed across the
bandwidth of the laser pulse. The ring-down signal is
measured in reflection from the cavity, in the form of an
optical heterodyne beat between the leakage field from the
cavity and the incident field reflected off of the input
coupler . The decay curve gives a cavity field decay
time of ? 8 ?s for the entire pulse bandwidth [Fig. 2(b)],
corresponding to an effective finesse of 2500. The ring-
down time of a few comb components centered at 800 nm
is ? 9 ?s, consistent with the predicted cavity finesse of
3000 at the center wavelength of the coating.
The average frequency of the laser is locked to the fs
enhancement cavity by adjusting the cavity length. A
second servo loop, actuated on the group delay inside the
laser cavity, keeps the transmission peak maximized by
controlling fr[14,20]. As we will show later, this phase
stabilization of the near-IR femtosecond comb directly
transfers the resultant phase stability to that of the HHG
light. The transmitted spectrum indicates the deleterious
effect of the cavity dispersion limiting the intracavity pulse
bandwidth [Fig. 2(c)]. By measuring the transmitted pulse
while adjusting the compressor, it is verified that the mini-
mumcompressable pulseduration insidethe cavityis 60fs.
The intracavity pulse energy is enhanced up to 4:8 ?J for
these short pulses, approximately a 600-fold increase from
the incident pulse energy of 8 nJ. Based on these measure-
ments we estimate a peak intracavity intensity of >3 ?
1013W=cm2is produced at the intracavity focus.
750 800 850
Transmitted spectrum (a.u.)
60 80 100120
Ringdown Signal (a.u.)
Full pulse spectrum
1/e field decay 8 µs
Ringdown at 800 nm
1/e field decay 9 µs
and fr of the comb
those of the cavity
Transmitted intensity (a.u.)
Scan of cavity length
FIG. 2 (color).
enhancement cavity. (a) Transmission through fs enhancement
cavity as the laser cavity length is scanned. The dominant peak
results from optimal alignment of frequency comb modes to
resonant modes of the fs enhancement cavity. (b) Cavity ring-
down measurements for the entire pulse spectrum (top trace) and
for a 5 nm region centered at 800 nm. (c) Incident and trans-
mitted spectrum of the pulse. The pulse durations measured by
frequency-resolved-optical gating are 48 fs (incident) and 60 fs
(transmitted). (d) Visible plasma generation at the cavity focus.
A pair of electrodes for ion collection is useful for signal
Characterization and measurement of the fs
PRL 94, 193201 (2005)
20 MAY 2005
We have verified experimentally that the ionization re-
quired in the HHG process does not degrade the effective
cavity finesse at the intensities and pressures used here.
Noble gas atoms, such as Xe or Kr, as well as N2mole-
cules, are introduced at the cavity focus (Fig. 1). A
?25 ?m beam waist is formed between the curved mir-
rors (radius of curvature 10 m), where peak intracavity in-
tensities exceed ionization thresholds of Xe and Kr, pro-
ducing a strong visible plasma [Fig. 2(d)]. For optimization
of the intracavity intensity, a pulse compressor is adjusted
to minimize the intracavity pulse duration by monitoring
the relative ionization strength via a pair of electrodes.
To couple the copropagating HHG light out of the cavity
without affecting the finesse for the 800 nm comb, a
?700 ?m-thick fused-silica or sapphire plate is placed at
Brewster’s angle for the IR inside the cavity (Fig. 1). This
additional optical element, while lowering the cavity fi-
nesse by <5%, requires a negative group-delay-dispersion
coated mirror to compensate for the additional material
dispersion. Higher order dispersion in the cavity still in-
creases slightly and the useful bandwidth of the cavity is
thus reduced by a small amount. However, it does not
produce a noticeable difference in the transmission spec-
trum shown in Fig. 2(c). The Fresnel reflection coefficient
of the intracavity plate risestowardsshorter wavelengths in
the XUV, with a maximum reflectivity of ?10% between
30 to 80 nm. For the coherent detection of the comb
structure of the HHG light at 266 nm (3rd harmonic)
discussed later, this intracavity plate is coated to provide
a reflectivity of ?40% at that wavelength.
The gas target is confined within a thin, hollow brass
cylinder, with a 150 ?m hole to allow the intracavity pulse
to pass through (Fig. 1). The 0.75 mm inner diameter of the
tube defines the effective interaction length of the gas tar-
get. The typical backing pressure is about 30 Torr, with
<1 mTorr of background pressure for the evacuated cham-
ber where the fs enhancement cavity is located. The posi-
tion of the gas target is adjusted to be slightly after the
cavity focus to maximize the HHG light. While Kr atoms
and N2molecules have both produced HHG light, Xe is
used for the data presented throughout this Letter. The
diffracted pattern of the HHG light, obtained with a
MgF2-coated aluminum grating, demonstrates that at least
the 7th order harmonic is generated (Fig. 3). While the low
detection efficiency of this system limits the harmonics
observed so far, we expect the spectrum should extend well
into the XUV spectral region considering recent results on
anomalous high-order harmonic generation obtained at
similar intensity levels . Similar work in Garching
has recently demonstrated HHG up to the 15th harmonic
. The average power of the 3rd harmonic light gener-
ated inside the cavity reaches nearly 10 ?W. The corre-
sponding intracavity single-shot efficiency (?10?8) is
comparable to traditional femtosecond-amplifier-based
systems at similar intensity levels. This demonstrates the
dramatic increase in high-harmonic power that can be
accessed using a high repetition rate (100 MHz). Clearly
there is significant potential to further improve this effi-
ciency and produce harmonics far into the XUV simply by
increasing the incident pulse energy, easily allowing access
to intensities >1014W=cm2at high repetition rates. A
number of attractive oscillators include an extended cavity
femtosecond Ti:sapphire laser  or Yb-doped yttrium
aluminum garnet (Yb:YAG) mode-locked laser that pro-
duce pulse energy above 1 ?J directly from the oscillator
. A potential limitation for scaling up the intracavity
intensity with this approach is the presence of an observed
nonlinear response of the intracavity plate, which has
been reported in previous experimental and numerical
work [14,16]. A possible configuration to overcome this
limitation is to use a higher order spatial mode of the cavity
and couple the generated XUV light out via a small hole
(?100 ?m diameter) drilled in the second curved mirror.
This separation of HHG light from the fundamental beam
via diffraction has already been demonstrated in amplified
systems with annular laser beams . This cavity con-
figuration can allow efficient output of all HHG orders and
permit scaling up the technique to greater intracavity
The fs enhancement cavity provides an ideal platform to
perform detailed studies of phase coherence of the HHG
process. First, the high repetition frequency makes it pos-
sible to have a well-separated frequency comb structure
that would allow a direct optical heterodyne detection of
the comb linewidth. Second, the fs cavity provides ideal
spatial filtering for the input fundamental pulses, as well as
phase and amplitude stabilization of the input pulses. One
strategy to determine the coherence properties of the HHG
process is to have a suitable narrow-linewidth continuous-
wave laser in the XUV region to heterodyne beat against
the XUV comb and produce a coherent beat signal, as is
normally done for the visible optical frequency comb
work. Another strategy is to use two sets of XUV combs
and bring them together for coherent interferometry by
detecting the heterodyne beat between them. To directly
measure any phase or frequency fluctuations in the har-
monic generation process, we allow the original comb to
drive two independent nonlinear processes, one through
the usual perturbative nonlinear optics based on second
harmonic and sum frequency generations via two beta-
barium-borate (BBO)optical crystals and the other through
the intracavity HHG process. Two sets of the frequency
FIG. 3 (color).
signals on a phosphor screen after diffraction from a grating.
Detection of the 3rd, 5th, and 7th harmonic
PRL 94, 193201 (2005)
20 MAY 2005
combs at 266 nm that represent the third harmonic of the Download full-text
fundamental IR comb are then brought together in a Mach-
Zehnder interferometer geometry [Fig. 4(a)] for beat de-
tection, after these two separate pulse trains are temporally
overlapped. A 90 MHz acousto-optic modulator is inserted
in one of the interferometer arms so that the beat detection
is shifted to a convenient nonzero frequency. Pairs of cor-
responding comb components from each spectrum produce
coherent optical beats, which collectively add together to
form the beat signal detected by a photomultiplier. The
radio frequency spectrum of the beat note shows the clear
presence of the comb structure in the UV[Fig. 4(b)], with a
repetition frequency signal at 100 MHz and coherent beat
signals both at 90 MHz and 10 MHz. The high frequency
roll-off is due to the response function of the photomulti-
plier amplifier. The resolution bandwidth-limited 1 Hz beat
signal [inset, Fig. 4(b)], influenced by slow, differential
path length fluctuations of the interferometer,demonstrates
that the full spectral resolution and temporal coherence of
the original near-IR comb has been faithfully transferred to
higher harmonics in the HHG process, limited only by the
observation time period of ?1 s.
This type of temporal coherent interferometry of the
HHG light opens the door for an exciting and unique set
of precision measurements on the HHG process. While the
present test relying partially on bound optical nonlineari-
ties is limited to the 3rd harmonic, two independent fs
enhancement cavities can be easily implemented and will
allow the same type of coherent optical heterodyne mea-
surements to be performed at any harmonic order in the
XUV spectral range. This ultrahigh spectral resolution
approach will allow precise, phase-sensitive measurements
of long and short quantum trajectories [26,27] associated
with freed electrons during the HHG process, as proposed
in the 3-step model [4,5]. A number of physical processes
that impact the phase coherence properties of HHG can be
studied in detail, including ionization dephasing, intensity-
dependent phase shifts, the effect of temporal chirp (spec-
tral phase) of the near-IR pulse on the HHG light, etc., In
the future, the presence of the frequency comb structure in
the VUV and XUV spectral regions will enable similar
advances in precision measurement, quantum control, and
ultrafast science as have been recently witnessed in the
We thank D. Dessau and J.L. Hall for equipment loans,
R.Lalezari (Advanced Thin Films)formirror coatings, and
J. Biegert for useful discussions. The work is supported by
AFOSR, ONR, NASA, NIST, and NSF.
*Electronic address: firstname.lastname@example.org
†Electronic address: Ye@jila.colorado.edu
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Ti:Sapphire laserTi:Sapphire laserTi:Sapphire laser
+ 90 MHz+ 90 MHz
+ 90 ΜΗz
+ 90 ΜΗz
2nd harmonic 2nd harmonic
Resolution Bandwidth 3 kHzResolution Bandwidth 3 kHz
1010 2020 3030 4040 50 5060 6070 7080 809090 100 100
Frequency (MHz) Frequency (MHz)
1 Hz 1 Hz
Frequency - 10,189,000 Hz (Hz) Frequency - 10,189,000 Hz (Hz)
- 20 -10 - 20 -100010 1020 20 30 30
FIG. 4 (color online).
tion between 3rd harmonic generated in Xe gas and that gen-
erated by bound optical nonlinearities in BBO. (b) Measurement
of the detected beat signal and repetition frequency. The line-
width shown in the inset is resolution bandwidth limited at 1 Hz.
(a) Setup for coherent heterodyne detec-
PRL 94, 193201 (2005)
20 MAY 2005