Femtosecond Laser Spectroscopy
The ability to use light sources with a sub-picosecond pulsewidth has greatly aided the
investigation of processes that occur on this time interval. Direct observation of the wave
packet dynamics of molecular states, the transfer of charge between a donor and acceptor
molecule, the coupling of vibrational states which allows for 2d IR, are just a few
examples of the new world that can be explored with ultra-fast laser spectroscopy.
To pursue spectroscopic studies on these timeframes the laser pulses have to be shortened
and in doing so we'll find that this has implications for the laser bandwidth as we run up
against the Heisenberg uncertainty principle. Additionally, we'll need special
components to generate these ultra-short laser pulses, to amplify them, and to detect
them.
Let's first discuss the bandwidth. Remember that the natural linewidth is governed by the
Heisenberg uncertainty principle
This suggests that if the uncertainty in the pulsewidth is on the order of 100 fs then 
will be around 100 fs although it depends somewhat on the profile of the beam pulse.
The beam could be Gaussian, Sech2 or another profile and so  might be slightly
different than 100fs but let's use 100 fs.
So one can calculate that E ≥ h / (4), where E is the bandwidth of the laser in
Joules.
For the case of  = 100fs one finds
in cm- 1 this would be
Therefore for a 10 fs pulse the bandwidth would be
And for a 1 fs pulse the bandwidth would be
For a Gaussian pulse and a sech2 pulse, the bandwidths are even larger and turn out to be
Heisenberg (cm- 1 )
Gaussian (cm- 1 )
sech2 (cm- 1 )
1000 fs
26.4
147
107
10 fs
264
1,470
1,070
1 fs
2640
14, 700
10,700
*Note that if you want the bandwidth in nm, you must know the central wavelength of
the laser.
As you can see the bandwidths of these ultra-fast pulsed lasers are very large and at 1fs
you are basically dealing with white light.
At first glance you might think that this is troublesome, and it can be, but it is also
advantageous in that when using an ultra-short pulse you are exciting the sample with a
broad spectrum of wavelengths, so in the case of CARS, for example, if this beam was
2, all of the vibrational resonance lines satisfying 1 - 2 = vib would be present during
the same pulse and an entire spectrum could be had in one pulse.
However there are other cases where one is interested in a particular transition and this
may prove difficult if you use sub-ps or sub-100fs pulses.
Now lets move onto how these short pulsewidths are generated and amplified.
One problem with generating and amplifying these pulses is due to the large powers that
are generated in each pulse.
For the case of a Nd:YAG operating at 10 ns pulsewidth with say 10mJ/pulse of energy,
that corresponds to a peak power of
0.010J/pulse x pulse/1 x 10- 8 sec =
if the ultra-fast laser with a pulsewidth of 100 fs had the same energy/pulse, then
0.010J/pulse x pulse/100 x 10- 1 5 sec =
Laser pulses on the order of 10GW/cm2 can cause damage to the stimulated gain medium
by nonlinear processes such as self focusing, so amplification must be done in a little bit
different way.
First let's look at how the very short laser pulses are generated.
Two ways of creating an ultra-short pulsewidth are called
1) Passive Mode Locking - passive mode-locking techniques are those that do not
require a signal external to the laser (such as the driving signal of a modulator) to produce
pulses. Rather, they use the light in the cavity to cause a change in some intracavity
element, which will then itself produce a change in the intracavity light. Usually this is
based on the presence of a saturable absorber inside the laser resonator.
2) Active Mode Locking - a technique of mode locking, based on active modulation of
the intracavity losses or the round-trip phase change
Both techniques rely on some type new element being placed in the resonance cavity of
the laser.
Passive Mode Locking to Create an Ultra-short Pulsewidth
Saturable
Absorber
Material
Stimulated Gain Medium
Fig 1
Fig 2
The laser first starts operation in a basically continuous way, but with significant
fluctuation of the laser power. The saturable absorber acts to cause short-pulsed
operation by absorbing the laser light in the cavity initially until the absorber is saturated
meaning that eventually light will pass through the absorber and cause the absorber to
relax back to the ground state in a short amount of time. Then the absorber will again
absorb until it has reached saturation and another intensity spike will be released, and so
on. Another way of looking at this is that in an un-mode locked laser, there are
somewhat intense spikes of light and these will be transmitted preferentially by the
standard absorber. As the light in the cavity oscillates, the process repeats leading to
selective amplification of the high intensity spikes and complete absorption of the lowintensity light. After many round trips, this leads to a train of narrow pulses and to
passive mode locking of the laser.
In "self-start mode locking" the pulse generation process begins automatically after
switching on the laser. Usually the laser first starts operation pretty much in a
continuous fashion, but with each round trip, the saturable absorber favors the light with
higher intensities and after many round trips winner takes all. Self-starting is not always
achieved. Sometimes the laser will run in continuous mode and reportedly will only start
mode locking when the user knocks against a resonator mirror.
There are two general types of saturable absorbers. One is a slow absorber and the other
a fast absorber. Generally speaking the fast absorber will give shorter pulse times as the
absorber recovery time is below the laser pulse duration. In this case the loss modulation
essentially follows the variation of the optical power.
For a slow absorber, the recovery time is longer than the pulse duration as there is a
temporal range with net gain just after the pulses, where the absorber is still in the
saturated state. The saturable absorber causes a loss modulation which is fast for the
leading wing of the pulse, whereas recovery of the absorber takes some longer time.
Figure: Temporal evolution of optical power and losses in a passively mode-locked
laser with a slow saturable absorber.
The crucial intracavity component for passive mode locking is a saturable absorber.
Saturable absorbers are commonly liquid organic dyes, but they can also be made from
doped crystals and semiconductors. Semiconductor absorbers tend to exhibit very fast
response times (~100 fs), which is one of the factors that determines the final duration of
the pulses in a passively mode-locked laser. Perhaps the most important type of absorber
for passive mode locking is the Semiconductor Saturable Aborber Mirror called SESAM.
This is a compact semiconductor device, the parameters of which can be adjusted in very
wide ranges, so that appropriately designed SESAMs can be used to mode-lock very
different kinds of solid state lasers including semiconductor lasers. Other absorbers for
mode locking include lead sulfide quantum dots suspended in glass and doped-insulator
saturable absorbers.
SESAM
Stimulated Gain Medium
.
The shortest pulses generated directly with a passively mode-locked laser have durations
around 10 fs and with further external compensation this can go somewhat shorter.
The shortest directly produced optical pulses are generally produced by Kerr-lens modelocked Ti-sapphire lasers, and are around 5 femtoseconds long. The minimum pulse
duration is limited by the period of the carrier frequency (which is about 2.7 fs for Ti:S
systems), therefore shorter pulses require moving to shorter wavelengths. Some advanced
techniques (involving high harmonic generation with amplified femtosecond laser pulses)
can be used to produce optical features with durations as short as 100 attoseconds in the
extreme ultraviolet spectral region (i.e. <30 nm).
Active Mode-Locking to Create a Short Pulsewidth
Active mode-locking involves the periodic modulation of the resonator losses or of the
round-trip phase change. This can be achieved in a few different ways including an
acousto- or electro-optic modulator or a semiconductor electroabsorption modulator. If
the modulation is synchronized with the resonator round trips, this leads to the generation
of ultrashort pulses.
The basic idea of active mode locking through modulating the resonator losses (AM
mode locking) is that a pulse with the “correct” timing can pass the modulator at times
where the losses are at a minimum. The wings of the pulse experience a little attenuation,
which effectively leads to (slight) pulse shortening in each round trip. This is shortening
on each trip is eventually balanced by other phenomenon such as gain narrowing that
broaden the pulse.
Figure: Temporal evolution of optical power and losses in an actively mode-locked laser.
The modulator causes increased losses for the pulse wings, effectively shortening the
pulses.
In simple cases, the pulse duration achieved in the steady state can be in the picosecond
range and is only weakly dependent on parameters such as the strength of the modulator
signal. This weak dependence arises from the fact that the pulse-shortening effect of the
modulator becomes less effective for shorter pulse durations, whereas other effects which
lengthen the pulse such as chromatic dispersion then become more effective. Chromatic
dispersion of an optical medium is where the phase velocity and group velocity of light
propagating in a transparent medium depend on the optical frequency.
Again amplification of the laser must be done carefully since there are many problems
with medium nonlinearities and optical components if the power gets in the GW/cm2
range.
CPA
.
CPA is a technique that was adapted from the amplification of Radar signals. The main
idea of this technique is that the ultra-fast pulse must be stretched-out temporally and
spectrally, THEN AMPLIFIED and then recompressed back together. CPA allows
ultra-short laser pulses to be amplified into the petawatt level.
Figure: Electric field of a strongly
instantaneous frequency grows with time.
, where the
Basically an ultrashort laser pulse is stretched out in time prior to introducing it to the
gain medium using a pair of gratings that are arranged so that the low-frequency
component of the laser pulse travels a shorter path than the high-frequency component
does. After going through the grating pair, the laser pulse is said to be positively chirped,
that is, the high-frequency component lags behind the low-frequency component, and the
pulse has a longer pulse duration than the original by a factor of 103 to 105. Then the
stretched pulse, whose intensity is sufficiently low compared with the intensity limit of
gigawatts per square centimeter, is safely introduced to the gain medium and amplified
by a factor 106 or more. Finally, the amplified laser pulse is recompressed back to the
original pulse width through the reversal process of stretching, achieving orders of
magnitude higher peak power than laser systems could generate before the invention of
CPA.
oscillator
In addition to the higher peak power, CPA makes it possible to miniaturize laser systems
and make terawatt tabletop laser systems.
Detection
We talked previously a bit about detector risetimes. For typical Si photodiodes and
photomultiplier tubes a detection risetime on the order of a nanosecond is reasonable.
Some detectors like a microchannel plates and some photodiodes are a bit faster, and
have risetimes slightly below 100 ps. Actually the detectors will detect an average signal
in the femtosecond range but they cannot measure the pulsewidth directly. They often
will become saturated.
For measuring the duration of ultrashort pulses one may use an optical autocorrelator.
They are used for various purposes including the measurement of the duration of
ultrashort pulses with picosecond or femtosecond durations, where an electronic
apparatus (based on a photodiode for example) would be too slow. The basic principle of
operation of an autocorrelator for a pulse duration measurement is explained in the
following. A beam splitter creates two copies of the incoming pulses. These copies are
superimposed in a nonlinear medium, where they interact on the basis of
some nonlinearity, provided that they overlap temporarily.
In an intensity autocorrelator as shown here a beam splitter splits an incoming pulse into
two pulses, which are then focused and sent into a crystal with a χ(2) nonlinearity. The
arm length difference and thus the relative timing of the pulses can be mechanically
adjusted via the variable delay line. (Different kinds of delay lines are used, e.g. using
rotating glass blocks or mirrors mounted on loudspeakers.) If the arm length difference is
made small, so that the pulses meet in the nonlinear crystal, the process of sum frequency
generation occurs, leading to an output with a shorter wavelength. If the relative time
delay is increased, so that the overlap of the two pulses in the crystal is reduced, the
mixing product becomes weaker.
For measuring the pulse duration, the power of the mixing product is recorded as a
function of the arm length difference. This can be done under computer control, using a
motorized translation stage to move the delay line. The dependence of the autocorrelation
signal on the temporal delay is given by:
Iac(
Note that very short pulse durations can be measured without requiring a fast
photodetector: the detector only has to measure an average power (assuming that a
regular pulse train is sent into the autocorrelator), rather than resolving the power. Also
for very short pulsewidths < 20 fs or so some other complications may begin to
arise: the beam splitter may have a limited bandwidth, and its substrate and the other
optical elements introduce chromatic dispersion.
Figure : Intensity autocorrelation of a sech2-shaped pulse with a duration of 150 fs. A
shift of the delay line by 15 μm corresponds to a change in the time delay by 100 fs.
For sech2 shaped pulses the pulse duration is ~ 0.65 times the width of the
autocorrelation signal, but this conversion factor depends on the pulse shape. A rough
evaluation is often based on some assumption concerning the pulse shape
The intensity autocorrelation is called background-free, since the signal vanishes for
large time delays. This is different for interferometric autocorrelators, as discussed below.
The setup of an interferometric autocorrelator contains a Michelson interferometer with a
variable arm length difference. The superimposed copies of the pulse are collinearly
propagating into the nonlinear crystal (after focusing with a lens or curved laser mirror)
and have the same polarization.
An interferometric autocorrelation is obtained by recording the average power of the
frequency-doubled signal:
Iac =
This kind of autocorrelation trace exhibits a fast oscillation with a period of half the
optical wavelength. The maximum signal is obtained when the two pulses after the beam
splitter undergo perfect constructive interference, leading to twice the amplitude
compared with a single pulse, and thus four times the intensity, and after frequency
doubling 16 times the intensity. For a large arm length difference, the pulses do not
overlap in the nonlinear crystal, and the intensity is only twice that generated by a single
pulse. Hence the peak signal is always eight times higher than the background, provided
that the interferometer is properly aligned.
Fig Interferometric autocorrelation of sech2-shaped unchirped pulse duration of 15 fs.
Fig : Interferometric autocorrelation of a sech2-shaped chirped pulse, duration of 15 fs.
Even though the pulse duration is the same as previous fig, the signal has a smaller width.
The interferometric autocorrelation is sensitive to chirps and thus in principle makes it
possible to extract more information on the pulses. However, the pulse duration of a
chirped pulse is underestimated if one simply uses the width of the autocorrelation signal
(see 2nd Figure above). An improved method called modified-spectrum autointerferometric correlation (MOSAIC) is based on an interferometric autocorrelation,
which is numerically post-processed such that the resulting trace makes it much easier to
diagnose a chirp.
For relatively long pulses, the many oscillations of the interferometric autocorrelation
trace can be averaged out. In that case, the peak signal is three times the background (not
four times, due to the non-sinusoidal oscillation). Owing to its simpler setup,
interferometric autocorrelators are more suitable than intensity autocorrelators for
measuring very small (few-femtosecond) pulse durations. In particular, the abovementioned geometric effect is avoided.
Other methods of pulse characterization (e.g. FROG (Frequency Resolved Optical
Gating) or SPIDER) are more precise in the regime below 10 fs. The choice of a
suitable nonlinear crystal and the crystal thickness involves various considerations, in the
femtosecond regime particularly concerning group velocity mismatch. Thin KDP crystals
are a good choice for pulse durations down to a few femtoseconds. Lithium iodate
(LiIO3) is also often used due to its particularly wide phase-matching bandwidth.