arXiv:0903.0168v1 [physics.optics] 1 Mar 2009
Broadband sensitive pump-probe setup for ultrafast optical
switching of photonic nanostructures and semiconductors
Tijmen G. Euser1,2,3, Philip J. Harding1,2, and Willem L. Vos1,2∗
1FOM Institute for Atomic and Molecular Physics (AMOLF),
Kruislaan 407, 1098 SJ Amsterdam, The Netherlands
2Complex Photonic Systems, MESA+Institute for Nanotechnology,
University of Twente, The Netherlands and
3Max Planck Institute for the Science of Light,
Gu¨ nther-Scharowsky-Str. 1, Bau 24 91058 Erlangen, Germany
We describe an ultrafast time resolved pump-probe spectroscopy setup aimed at studying the
switching of nanophotonic structures. Both fs pump and probe pulses can be independently
tuned over broad frequency range between 3850 and 21050 cm−1. A broad pump scan range
allows a large optical penetration depth, while a broad probe scan range is crucial to study
strongly photonic crystals. A new data acquisition method allows for sensitive pump-probe
measurements, and corrects for fluctuations in probe intensity and pump stray light. We observe
a tenfold improvement of the precision of the setup compared to laser fluctuations, allowing a
measurement accuracy of better than ∆R= 0.07% in a 1 s measurement time. Demonstrations of
the improved technique are presented for a bulk Si wafer, a 3D Si inverse opal photonic bandgap
crystal, and z-scan measurements of the two-photon absorption coefficient of Si, GaAs, and the
three-photon absorption coefficient of GaP in the infrared wavelength range.
PACS numbers: 42.70.Qs, 42.65.Pc, 42.79.-e
Optical pump-probe experiments1,2,3are a powerful tool to study the ultrafast optical
response of a wide range of effects in, for example, semiconductor physics,4high harmonic
generation,5and optics of biomembranes.6Recently, pump-probe techniques have also
been extended to study ultrafast switching of photonic nanostructures such as photonic
crystals7,8,9,10and photonic cavities.11,12,13In these studies, one literally attempts to catch
light with light. Therefore such switching processes are susceptible to perturbing effects
such as absorption or (induced) inhomogeneity,14and sensitive experimental methods are
In pump-probe experiments, high pump pulse intensities are often required to observe
small changes in probe reflection or transmission. This requirement has led to the de-
velopment of regenerative amplifiers, in which femtosecond (fs) pulses from Ti:Sapphire
lasers are amplified to pulse energies of up to several mJ. The amplification process comes
at a price of a strongly reduced repetition rate, typically from the MHz to the kHz range.
The amplification step is often followed by conversion to different wavelengths using opti-
cal parametric amplifiers (OPA). Amplification processes typically increase pulse-to-pulse
intensity variations of the laser.
There are two important issues that limit the speed and accuracy of pump-probe
experiments. First, since experiments intrinsically depend in the magnitude of the ir-
radiance, they are sensitive to pulse-to-pulse variations of the laser. The result is that
long integration times are required to sufficiently reduce the fluctuation-induced error in
probe reflectivity measurement. Secondly, scattered light from the intense pump pulses
contributes to the background signal of the probe detector. In particular for strongly
photonic samples, light is necessarily strongly scattered, therefore the background level
can be larger than the reflectivity changes of the samples under study. To circumvent
both potential issues, we have developed a versatile measurement scheme that allows for
compensation for pulse-to-pulse variations in the output of our laser, as well as a subtrac-
tion of the pump background from the probe signal. Our technique strongly reduces the
acquisition times required in pump-probe experiments, allowing for much more detailed
scans than previously possible. While this paper focuses on the application to switching
of semiconductors and nanophotonic structures through optical excitation of free carries,
our results are relevant to any pump-probe experiment with regeneratively amplified laser
II. PUMP-PROBE SETUP
A. Optical setup
Time-resolved optical measurements on photonic crystals were performed with a ded-
icated two-color pump-probe setup. Our laser system provides high power pulses at two
independently tunable frequencies, allowing us to adjust the pump frequency to optimize
the optical penetration depth14and the probe frequency to scan across broad photonic
gaps. The setup is based on a regeneratively amplified Titanium Sapphire laser that emits
short 120 fs pulses at λ= 800 nm with a pulse energy of 1 mJ at a repetition rate of 1 kHz
(Spectra Physics Hurricane). This laser drives two optical parametric amplifiers (OPA,
Topas 800-fs) shown schematically in Fig. 1, that serve as pump and probe. The output
frequencies of the OPAs are computer controlled, and can be continuously tuned between
3850 and 21050 cm−1. The excitation of carriers at pump frequencies near the two-photon
absorption edge of semiconductors requires a high pump irradiance in the range of 10 to
300 GWcm−2, depending on the material and the pump frequency chosen.14Since both
OPAs have a conversion efficiency that exceeds 30%, a pulse energy Epulseof at least 20
µJ is available over the entire frequency range. The output of our OPAs consists of pulses
with Gaussian pulse duration τp= 140±10 fs (measured at λ= 1300 nm). The spectral
shape of the output spectrum was measured to be Gaussian with a frequency indepen-
dent linewidth ∆ν/ν= 1.44±0.05%. We deduce the time-bandwidth product to be τp∆ν=
0.47±0.05, in good agreement with the Fourier limit for Gaussian pulses (τp∆ν= 0.44).2
To a good approximation, the temporal profile of the pulses has a Gaussian intensity
FIG. 1: (Color online) Schematic drawing of the setup. Pulses (Gaussian pulse duration τp=
120 fs, λ= 800 nm, E= 1 mJ) from a regeneratively amplified Ti:Saph laser (not shown) drive
two OPAs. The output frequency of both OPAs is computer controlled, and tunable from 3850
to 21050 cm−1. The pump pulse passes through an optical delay line with minimum time step
of 10 fs. Both pump and probe beam pass through a chopper wheel that is synchronized to
the laser output (see Fig. 2). Both pump and probe beam are focused on the same spot on
the sample. Two InGaAs photodiodes are used to monitor the output variation of the OPAs
as well as the reflected signal. The reflectivity from the sample is measured by a third InGaAs
photodiode. Three boxcar averagers are used to hold the short output pulses of each detector for
1 ms, allowing simultaneous acquisition of separate pulse events of all three detector channels.
P(t) = Pmaxe−2?
where Pmax= (Epulse/τp)(?2/π) is the peak power. Experimentally, we obtain the Pmax
inside the sample by subtracting the pump reflectivity at the sample interface:
Pmax= Pext(1 − R),(2)
where Pextis the external pump power, and R is the measured reflectivity of the pump
beam at the sample interface at λpump. Both pump and probe beams were focused onto
the sample at a small numerical aperture NA= 0.02. The pump intensity profile was
confirmed to be Gaussian with a radius wpump= 113±5 µm. We can therefore describe
the spatial irradiance distribution in the focus as Gaussian:
I(x,y) = I0e
where I0= (Pmax/w2
pump)(2/π) is the peak irradiance in the center of the focus. Even with
a large pump focus of wpump= 113±5 µm, the maximum peak irradiance Imaxthat can
be obtained in our setup still exceeds 1 TWcm−2. This large excess irradiance indicates
that it is feasible to switch an even larger sample, or to use less powerful lasers on small
samples, which is important to facilitate possible future applications of ultrafast switching.
The probe beam was focused to a Gaussian spot of typical radius wprobe= 20±5µm,
depending on the diffraction limited size of the spot given by λprobe. Since the probe focus
is much smaller than the pump focus, we obtain excellent lateral homogeneity of the
nonlinear excitation throughout the probe focus. This turns out to be crucial to permit
successful physical interpretation of complex photonic structures. In all experiments, we
explicitly ensured that only the central flat part of the pump focus is probed by testing
with a Si wafer.
In Figure 1, the delay between pump- and probe pulse was set by a 40 cm long optical
delay line with a time resolution of ∆t= 10 fs. Since the delay time is also computer
controlled, we can scan the reflectivity spectrum as a function of frequency at a chosen
time delay after the pump pulse.
B.Data acquisition method
FIG. 2: (Color online) Schematic drawing illustrating the alignment of the pump- en probe
beams (red and green circles) onto the chopper blade. The rotation of the chopper wheel is
synchronized to the laser output. One full revolution of the chopper blade takes 8 ms, such
that that for each pulse event, pump and probe beams are blocked or unblocked in a different
permutation. In one sequence of four consecutive laser pulses, both (a) excited reflectivity, (d)
linear reflectivity,(b) pump background, and (c) detection background are collected.
In our setup, the OPAs show typical relative irradiance variation between 2% RMS
variation near λ= 1300 nm and of 7% in the worst case near the degeneracy point near
λ= 1600 nm. If the signals are not corrected for, such variations in pump irradiance
in a one-photon process would fundamentally limit the relative accuracy of the probe
signal. To improve the signal-to-noise to better than the laser stability, it is important
to probe individual pulse events so that pulse selection can be performed. Therefore, the
irradiance of each pump and probe pulse is monitored by two InGaAs photodiodes and
the reflectivity signal is measured by a third InGaAs photodiode, shown as black squares
in Fig. 1. Three boxcar averagers are used to hold the short output pulses of each detector
for 1 ms, allowing simultaneous acquisition of separate pulse events of all three detector
channels by a data acquisition card. Both pump and probe beam pass through a chopper
whose frequency is synchronized to the repetition rate of the laser ( Ωrep= 1 kHz). The
alignment of the two beams on the chopper blade is such that each millisecond, pump
and probe beam are blocked or unblocked in a different permutation, shown in Fig. 2.
In this flexible measurement scheme, detector signals for each pulse event are collected,
allowing various data processing routines such as automatic background subtraction and
the selection of pulses within a certain pump energy range after the experiment.
For a measurement on a reflecting sample, the linear (unpumped) reflectance is given
by Rup= Jup− Jup
(d), while Jup
bg, where Jupis the detector signal when the chopper is in position
bgis the probe background signal measured at chopper position (c). To
compensate for probe pulse fluctuations, Rupis then ratioed by the background-corrected
probe monitor signals Mup, measured when the chopper is at position (d) and (c). As the
background measurements are taken in between the reflectivity measurements, temporal
fluctuations in the background signal originating from pump and from the surroundings
are eliminated. In a similar manner, the non-linear (pumped) reflectance is equal to
Rp= Jp− Jp
(a) and (b), respectively. This signal is also ratioed to the corresponding probe monitor
bg, where Jpand Jp
bgare the signals measured on R at chopper positions
signals. This process obviously requires the three detectors to store all four signals during
a time (4/Ωrep). When this happens, the differential reflectivity ∆R/R corrected for
background and fluctuations is thus determined by
The signal J is offered to the DAC card by the boxcar measuring the sample reflectance.
Neglecting electronic amplification factors, J is equal to the magnitude of the time- and
space integrated Poynting vector S,
J = πr2
Here, the beam is collimated to a radius r and tintis the integration time of the boxcar.
ǫ0and µ0denote the permittivity and permeability of free space, respectively. The electric
field ̥(t) reflected by a sample onto the detector can be separated in a Gaussian envelope
˜ ̥(t) of temporal width τP (see Eq. 1) and amplitude ˜ ̥0, multiplied by a sinusoidal
component with a carrier frequency ω0in rad/s.29The squared oscillating term can then
be integrated separately and yields 1/2, and the time integration can be taken to infinity
because tint>> τP. Since the integration time of the boxcar (tint∼ 150 ns) is much longer
than any probe pulse duration, the dynamics of the sample is essentially integrated over.
Figure 3 shows a typical time trace for probe monitor, pump monitor and reflected
probe signal collected by the data acquisition card. Note that between 1 ms (pump off)
and 2 ms (pump on) the probe reflectance signal goes up, suggesting an increase in reflec-
tivity, while between 5 and 6 ms, the probe reflectance signal decreases. These artifacts
are caused by the pulse-to-pulse variations in the laser output, and are easily eliminated
in our method by referencing to the probe monitor signal. An additional advantage of
our scheme is that excited and linear reflectivity signals can be simultaneously monitored
on an oscilloscope, which greatly facilitates the alignment procedure.
III. EXPERIMENTAL RESULTS
In this section we will demonstrate how our technique yields precise nonlinear reflection
and transmission measurements, both on intricate photonic crystal samples as well as on
FIG. 3: (Color online) Time traces of the boxcar output signals for probe monitor, pump
monitor, and probe reflectance. The sample was a GaAs/AlAs distributed Bragg reflector, the
experimental conditions were the same as in Ref. 15. The pump irradiance was ≈100 GWcm−2
and the probe frequency was λ= 1490 nm. The switched reflectivity is roughly 10% lower than
the unswitched reflectivity. Each datapoint in the plot corresponds to a single pulse event. The
letters a, b, c, and d correspond to the chopper position during each event (see Fig. 2).
A.Statistical analysis of measured data
In this section we describe the statistical analysis of the data collected in our experi-
ments. At each time delay and for each wavelength setting for the probe OPA, all detector
signals from 4x250 pulse events were collected and stored. The probe reflectance signal
for 4x250 pulse events of a pump-probe experiment on a GaAs/AlAs multilayer structure
is plotted versus probe monitor signal in Figure 4. Experimental details for this structure
can be found in Ref. 15. Both signals show a variation as a result of the pulse-to-pulse
variations of the laser. The datapoints constitute two separate lines whose slopes corre-
spond to the unpumped and pumped reflectance of the sample. To exemplify the noise
reduction of our method, we have chosen a data set during which the alignment of the
pump laser was not optimized and pulse-to-pulse variations of the probe signal were larger
than normal, amounting to a large relative standard deviation σSD,probe= 13%.
The corresponding standard error in the mean detector signal is δR/R=σSD,probe/√N=
13%/√250= 0.8%, which is relatively large compared to the effects that we wish to study.
We therefore use an automated data processing routine to process the probe reflectance
and probe monitor data to increase the signal-to-noise ratio. From the entire data set,
the averages of the background levels (b) and (c) were determined, and subtracted from
the pumped (a) and unpumped (d) reflectance data respectively (see Fig. 2). The result-
ing background-subtracted reflectance signal was divided by the corresponding monitor
signal to compensate for intensity variations in the output of the laser. Through this
procedure, the RMS variation in the unpumped reflectivity that was found from the data
in Fig. 4 was strongly reduced to σSD,probe= 1.1%. We attribute the remaining noise to
uncorrelated electronic noise in the detection system. The resulting standard error in
the probe reflectivity is thus tenfold improved to δR/R= 0.07%, even if the laser is not
running optimally. Our scheme allows a sensitive measurement of the reflectivity and of
small reflectivity changes, while maintaining an acceptable measurement time of about 1
second per frequency-delay setting.
Pulse to pulse variations in the pump energy are a more subtle issue, since such fluc-
tuations will often propagate in a nonlinear, and sometimes unpredictable, way in the
reflectivity change ∆R/R of the sample. The open circles in Fig. 4 correspond to the
switched reflectance data. The slope of the line that is formed by these data points is
reduced by about 10% compared to the unswitched data (closed squares). The corre-
sponding reflectivity decrease is equal to ∆R/R= 10%. We also observe that the line is
about twice as broad as the line corresponding to the unpumped data. We attribute the
probe monitor (V)
probe reflectance (V)
FIG. 4: Reflectance signal versus probe monitor data for 1000 single pulse events of the data
set shown in Fig. 3, displayed as a scatter plot. The 250 unpumped reflectivity datapoints
(d) constitute a line, indicating that variations in monitor and reflectance signal are strongly
correlated. The slope of the line is proportional to the reflectivity of the sample. The pumped
datapoints (a) form a line with a reduced slope, due to the reflectivity decrease of about δR/R=
10% in the switched sample. Both background data sets (b) and (c) tend to the origin of the
plot as it should in absence of offsets. Note that the small offset in the signals is automatically
removed in the data processing routine.
broadening to pulse to pulse variations of the pump beam.
In the example in Fig. 4 the standard deviation of the pump pulse energy σSD,pump=
12%, from which we deduce a standard error in the pump irradiance δI0/I0=
0.8%. The error in the reflectivity change ∆R/R due to the pulse-to-pulse irradiance
fluctuations is equal to δ(∆R/R)= 2(δI0/I0)(∆R/R), where the factor 2 is due to the
quadratic dependence of ∆R/R on I0 for a two-photon process. Using the reflectivity
change in the data in Fig. 4 (∆R/R= 10%) we obtain the pump contribution to the
standard error in ∆R/R to be δ(∆R/R)= 0.16%. The error in reflectivity changes ∆R/R
also contains a contribution of the fluctuations in the probe pulse that were discussed
before. The error due to the probe variation is equal to√2(δR/R)= 0.1%, since the two
independent errors in the pumped- and unpumped datasets are added. We calculate the
total error by adding the contributions of both probe and pump variations. We obtain a
which is sufficiently sensitive for our switching experiments.
In some applications, an even higher sensitivity is required. Fortunately, pump-monitor
detector signals for each individual pulse event are stored. It is thus possible to reduce
the pump term in Eq. 6 by selecting pump pulses within a certain narrow energy range
after the experiment, at the expense of longer integration times. Alternatively, in ex-
periments where the relation between pump intensity and sample response is linear, the
pump-monitor signal can be used to correct the measured signal. In our switching ex-
periments on photonic nanostructures, however, such a correction cannot be made since
the sample response is typically nonlinear with pump intensity. Therefore a pulse se-
lection procedure was applied in z-scan measurements (see Section IIID), where pump
stability is essential for the correct interpretation of the experimental data. Our strongly
improved sensitivity has recently allowed us to identify two femtosecond contributions to
the spectral properties of a switched Si woodpile photonic bandgap crystal: the optical
Kerr effect, and nondegenerate two-photon absorption.16
B.Ultrafast switching of bulk Si
An example of free carrier-induced change of refractive index in bulk silicon is given
in Fig. 5 (upper panel).In this experiment, a powerful ultrashort pump pulse with
wavelength λpump= 800 nm was focused to a spot with radius wpump=70±10 µm, resulting
in a peak irradiance at the sample interface of I0= 115±40 GWcm−2. The reflectivity of a
weaker probe pulse (λprobe= 1300 nm) with a smaller spot radius of wprobe= 20±5 µm was
measured in the center of the pumped spot at different time delays with respect to the
pump pulse. The scan in Fig. 5 (upper panel) shows that the reflectivity of the sample
changes from 32% to 28%. The 10%−90% rise time is 230 fs, clearly an ultrafast change
in refractive index n′. From Fresnel’s formula we find the refractive index change to be
more than 10%. The lower panel shows the intensity autocorrelation function (ACF) of
the pump pulses. The full width half maximum (FWHM) is 200 fs, we therefore conclude
that the free carriers have been generated almost instantaneously.
Fig. 6 shows reflectivity from an extended probe delay range of -12 to +5 ps. Quite
remarkably, at a negative probe delay of 8.6 ps, we observe an additional large step in
the reflectivity from 38% to 32%. We can identify three distinct probe delay regimes A,
B, and C, which are separated by two large steps in the reflectivity. The time difference
between the first and second step is 8.6±0.5 ps, this value corresponds well to twice the
optical thickness of the wafer 2LnSi/c= 8.3±0.1 ps, where nSi= 3.5 is the refractive index
of Si at λ= 1300 nm,17and L= 356±5 µm is the measured thickness of the wafer.
To interpret the observed unusual time dependence, we show in Fig. 7 snapshots of the
reflected irradiance, taken at the moment that the pump pulse switches the front face of
the wafer. The reflectivity of the wafer consists of multiply reflected pulses from front and
back surface of the wafer, which are indicated by R0, R1, and R2. The magnitude of each
successive reflection is given by Rm= (1−R0)2R2m−1
R2in our analysis. It is important to note that each subsequent reflection Rmis delayed
. We neglect any reflections beyond
with respect to R0by an even multiple (2m) of the optical thickness ∆tm= 2mLnSi/c.
The pump conditions in the experiment in Fig. 6 result in an inhomogeneous, dense
carrier plasma near the front face of the wafer.14Free-carrier absorption and diffraction
from the dense plasma results in a strongly attenuated transmission. The plasma thus acts
as an ultrafast shutter that blocks internally reflected pulses Rmthat arrive at the front
face after the switching. At probe delay A, the pump arrives before reflection R0, and the
measured signal corresponds to the reflection of the switched wafer, indicated by R∗
FIG. 5: Time resolved reflectivity measurement on bulk Si, pumped at λpump= 800, pulse energy
Epump= 2.0±0.1 µJ, Gaussian pulse duration τpump= 120±10 fs, wpump= 70±10 µm and peak
irradiance 115±40 GWcm−2(upper panel). The reflectivity of a probe with λprobe= 1300 nm,
wprobe= 20±10 µm and Gaussian probe pulse duration τprobe= 120±10 fs decreases from 32%
to 28%, corresponding to a calculated carrier density Neh= 1.6×1020cm−3at the surface of
the sample, using a Drude response (see right-hand scale). The time difference between 10%
and 90% of the total change is 230±40 fs, as indicated by the vertical dashed lines. The lower
panel shows the irradiance autocorrelation function (ACF) of the pump pulses. The full width
half maximum (FWHM) of the ACF of 200 fs corresponds to a Gaussian pulse duration of τp=
delay setting B, the pump pulse arrives in between reflection R1and R0, thus blocking
R1and R2. This reflection corresponds to the front face refection of the unswitched wafer
R0. In Fig. 6 we observe that the reflection in this time range is indeed comparable to the
Fresnel reflection from a single air-Si interface (R= 31%). At probe delay C, the pump
pulse arrives in between reflection R2and R1, and only R2is blocked. The total reflection
is thus equal to R0+R1. We note that the reflectivity changes in a switched double side
FIG. 6: Time resolved reflectivity of a switched double side polished Si wafer. Unswitched
reflectivity (open squares) and switched reflectivity (closed squares) are plotted over an extended
range of probe delays compared to Fig. 5. Surprisingly, at a negative probe delay of 8.6 ps, a
large step in the reflectivity from 38% to 32% appears. At zero probe delay the reflectivity
decreases further from 32% to 28%. The time difference between the first and second step in
reflectivity (indicated by dotted lines) is 8.6±0.5 ps, which corresponds well to twice the optical
thickness of the wafer (8.3±0.1 ps). We identify three different probe delay regimes A, B, and
C, that are explained in the schematic plot in Fig. 7.
polished wafer are very large, particularly when the back face reflection R1is blocked.
Double side polished Si wafers are therefore ideal test samples to find- and optimize the
spatial- and temporal overlap of our pump and probe pulses.
C. Ultrafast switching of 3D Si inverse opal photonic bandgap crystals
As a second example we demonstrate ultrafast switching experiments that were carried
out on the Si inverse opal photonic crystal shown in Fig. 8(a) (inset). The broadband
FIG. 7: Snap shots of the reflected irradiance of a bulk Si wafer in the experiment in Fig. 6 at the
arrival time of the pump. We consider three different probe delay positions, corresponding to the
regions indicated by A, B, and C in Fig. 6. The intense pump pulse generates an inhomogeneous
carrier plasma near the front face of the wafer indicated by the dark gray layer. This absorbing
layer acts as an ultrafast shutter that blocks any internally reflected pulse Rmthat arrives at
the front face after the pump pulse. At probe delay A, the pump arrives before the probe, and
the switched reflectivity of the front face of the wafer R∗
0is probed. At probe delay B, the pump
pulse arrives in between reflection R1and R0, thus blocking pulses R1and R2. This reflection
corresponds to the front face refection of the unswitched wafer R0. At probe delay C, the pump
pulse arrives in between reflection R2 and R1, thus only blocking R2. The total reflection is
equal to R0+R1.
reflectivity data, shown in Fig. 8(a) covers the complete range of second order stop bands
in our crystal where a 3D photonic band gap has been predicted.18A two-photon process
was used to homogeneously excite carriers in the photonic crystal. The pump frequency
was chosen in relation to the probe frequency range, to allow polarization based separation
of pump and probe light. The time and frequency resolved differential reflectivity of
the crystal ∆R/R(τ,ωprobe) at ultrafast time scales is represented as a three-dimensional
surface plot in Fig. 8(b). The plot contains over 1500 datapoints, each obtained from 500
or 1000 single pulse measurements and represents nearly an octave on probe frequency.
Such a large scanning range is typically required for strongly photonic crystals, since
their photonic gaps have large bandwidths. The data collection was performed in as little
as 40 minutes, much shorter than in conventional setups without automated scanning,
-referencing and -background subtraction.7,8,9The data show clear dispersive shapes in
the differential reflectivity, caused by a shift of the peaks towards higher frequency. We
observe a large frequency shift of up to ∆ω/ω= 1.5% of all spectral features including
the peak that corresponds to the photonic band gap. We deduce a corresponding large
refractive index change of ∆nSi/nsi= 2.0%, where nSiis the refractive index of the silicon
backbone of the crystal. Our broad probe scanning range allowed us to observe that
both the low and high frequency edge of the stop bands have shifted. This indicates the
absence of separate dielectric and air bands in the range of second order Bragg diffraction
in inverse opals, which is consistent with predictions based on quasistatic band structure
calculations. A detailed description of the ultrafast switching of Si inverse opal photonic
bandgap crystals is presented in Ref. 10.
D.Z-scan measurements on GaP at IR wavelengths.
As a final demonstration of our technique, we have obtained open aperture z-scan data
for the semiconductors GaP, Si, and GaAs. A detailed description of these experiments
is given in Appendix IV. In this section we present measurements of the three-photon
absorption coefficient of GaP, a highly suitable material for photonic bandgap crystals
because of its high refractive index and low absorption in the visible wavelength range.
The pump wavelength was chosen in the range of three-photon absorption:
3Egap< ?ω <
2Egap. We therefore neglect both linear and two-photon absorption in our analysis (α=β=
0). The resulting equation for the nonlinear transmission of the sample, normalized to
the linear transmission (1 − R)2is:
?1 + 2I0(z)2γL,
where γ is the three-photon absorption coefficient.
Fig. 9(a) shows typical z-scan data taken at a wavelength λ= 1600 nm, close to the
three-photon absorption edge of GaP. We observe that the z-scan data in Fig. 9(a) is
asymmetric; the transmission of the sample is slightly elevated at positive z-values, where
the sample is located in between the beam waist and the detector. This asymmetry of
less than 5% indicates that nonlinear refraction also plays a role in this experiment, and
represents a slight deviation from a true open aperture z-scan. From the shape of the
curve we conclude that the sign of the nonlinear refraction in GaP is positive in the
wavelength range 1400-1600 nm. We therefore exclude that the asymmetry is caused by
free-carriers generated by three-photon absorption, since this would result in a negative
refractive index change.
To obtain the three-photon absorption coefficient γ for GaP, we disregard the rela-
tively small nonlinear refraction. We compare our results to a numerically calculated
transmission curve, shown in Fig. 9(a). We have varied γ until the depth of the minimum
of the calculated scan matches the data. The calculated curve agrees well with the data.
At λ= 1600 nm, we deduce γ= 1.0±0.3×10−3cm3GW−2. Four additional scans were
made at λ= 1400 nm, λ= 1450 nm, λ= 1500 nm, and at λ= 1550 nm. The resulting
deduced three-photon absorption coefficients are plotted versus frequency in Fig. 9(b).
We observe that γ tends to zero as the frequency approaches the1
3Egap, similar to what
was observed in Ref. 19 for Si. The frequency scaling confirms a three-photon absorp-
tion process. We propose that the observed opposite sign of the negative refractive index
change by free-carrier effects and the positive change due to nonlinear refraction in GaP
allows for intricate non-monotonic temporal switching of GaP photonic crystals.20This
effect would allow ultrafast back-and-forth switching of photonic gaps.16
The results of the z-scan measurements that were performed on Si and GaAs in the
frequency range close to half the electronic bandgap are summarized in Table I. The Si
data are in good agreement with Refs. 21,22. The GaAs data are in excellent agreement
with Ref. 23. The experiments are described in detail in Appendix IV.
TABLE I: Two-photon absorption coefficients for Si and GaAs
Materialλ [nm]β [cmGW−1]
Si 16300.6± 0.3
We have built a two-color pump-probe setup that provides high energy, ultrashort laser
pulses at optical frequencies in the range between 3850 and 21050 cm−1. Our versatile
measurement scheme automatically subtracts the pump background from the probe signal
and compensates for pulse-to-pulse variations in the output of our laser. We deduce a
tenfold improvement of the precision of the setup, allowing a measurement accuracy of
better than ∆R= 0.07% in a 1 s measurement time, even if the laser is not running
optimally. Demonstrations of the technique are presented for a bulk Si wafer, 3D Si inverse
opal photonic bandgap crystal, GaAs/AlAs photonic structures, and z-scan measurements
on bulk semiconductors.
We thank Cock Harteveld, Frans Segerink, and Rindert Nauta for technical support,
Soile Suomalainen and Mircea Guina for the Bragg stack sample, the group of David
Norris for the Si inverse opal, and Mischa Bonn for useful remarks. This work is part of the
research program of the ”Stichting voor Fundamenteel Onderzoek der Materie” (FOM),
which is supported by the ”Nederlandse Organisatie voor Wetenschappelijk Onderzoek”
(NWO). WLV thanks FOM for a ”Inrichting leerstoelpositie” grant, and support from
NWO/VICI and STW/NanoNed.
∗Electronic address: firstname.lastname@example.org; URL: www.photonicbandgaps.com
1”Laser Spectroscopy: Basic Concepts and Instrumentation”, Ed. W. Demtr¨ oder (Springer-
Verlag, Berlin, 3 edition, 2002).
2”Lasers”, A. E. Siegman (University Science Books, Mill Valley, USA, 1986).
3”Ultrashort laser pulse phenomena”, J- .C. Diels and W. Rudolph (Academic Press, USA,
4O. D. M¨ ucke, T. Tritschler, M. Wegener, U. Morgner, and F. X. K¨ artner, Phys. Rev. Lett.
87, 057401 (2001).
5B. D. Esry, A. M. Sayler, P. Q. Wang, K. D. Carnes, and I. Ben-Itzhak, Phys. Rev. Lett. 97,
6S. Roke, J. Schins, M. M¨ uller, and M. Bonn, Phys. Rev. Lett. 90, 128101 (2003).
7S. W. Leonard, H. M. van Driel, J. Schilling, and R. B. Wehrspohn, Phys. Rev. B 66,
8D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov,
A. B. Pevtsov, and A. V. Selkin, Phys. Rev. Lett. 91, 213903 (2003).
9C. Becker, S. Linden, G. von Freymann, M. Wegener, N. T´ etreault, E. Vekris, V. Kitaev,
and G. A. Ozin, Appl. Phys. Lett. 87, 091111 (2005).
10T. G. Euser, H. Wei, J. Kalkman, Y. Jun, A. Polman, D. J. Norris, and W. L. Vos, J. Appl.
Phys. 102, 053111 (2007).
11I. Fushman, E. Waks, D. Englund, N. Stoltz, P. Petroff, and J. Vuckovic, Appl. Phys. Lett.
90, 091118 (2007).
12S. F. Preble, Q. Xu, and M. Lipson, Nat. Photonics 1, 293 (2007).
13P. J. Harding, T. G. Euser, Y. Nowicki-Bringuier, J. M. G´ erard, and W. L. Vos, Appl. Phys.
Lett. 91, 111103 (2007).
14T. G. Euser and W. L. Vos, J. Appl. Phys. 97, 043102 (2005).
15T. G. Euser, H. Wei, J. Kalkman, Y. Jun, M. Guina, S. Suomalainen, A. Polman, D. J. Norris,
and W. L. Vos, In ”Active Photonic Crystals”, Ed. S. M. Weiss, G. S. Subramania, F. Garcia-
Santamaria, Proc. SPIE 6640, 66400G: 1-4 (2007)(Invited paper).
16P. J. Harding,T. G. Euser,and W. L. Vos, J. Opt. Soc. Am. B (Accepted)
17”Handbook of optical constants of solids”, E. D. Palik, (Academic press Inc., London 1985).
18Y. A. Vlasov, X- Z. Bo, J. C. Sturm, and D. J. Norris, Nature 414, 289 (2001).
19S. Pearl, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 93, 131102 (2008).
20R. W. Tjerkstra, F. B. Segerink, J. J. Kelly, and W. L. Vos, J. Vac. Sci. Technol. B. 26,
21M. Dinu, F. Quochi, and H. Garcia, Appl. Phys. Lett. 82, 2954 (2003).
22A. D. Bristow, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 90, 191104 (2007).
23W. C. Hurlbut, Yun-Shik Lee, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer, Opt. Lett.
32, 668 (2007).
24M. Sheik-Bahae, A. A. Said, and E. W. van Stryland, Opt. Lett. 14, 955 (1989).
25M. Sheik-Bahae, D. J. Hagan, and E. W. Van Stryland, Phys. Rev. Lett. 65, 96 (1990).
26M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. van Stryland, IEEE J.
Quantum Electron. 26, 760 (1990).
27M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. van Stryland, IEEE J.
Quantum Electron. 27, 1296 (1991).
28M. Balu, J. Hales, D. J. Hagan, and E. W. Van Stryland, Opt. Express 16, 3840 (2004).
29This Slowly Varying Envelope Approximation (SVEA, see, e.g. Ref. 3) can be applied to
pulses where τP>> 1/ω0, and where ω0does not change over τP, i.e., for bandwidth limited
A.Two-photon absorption in Si
An elegant method to measure the nonlinear refraction n2 of semiconductors is the
z-scan technique that was first demonstrated by Sheik-Bahae et al..24,25A z-scan is a
simple and robust measurement of the transmission of a single beam that is focused by a
lens. The focal length of the lens is chosen such that the focal depth is much larger than
the sample thickness. The transmitted power of a focused laser beam is measured while
the sample is scanned in the z-direction, along the optical axes of the beam, see Fig. 10.
The nonlinear refraction results in both Kerr-lensing due to the change in real part of
the refractive index, as well as attenuation of the transmitted power due to nonlinear
absorption. Both effects will attain a maximum if the sample is located in the beam waist
To separate the refractive and absorptive effects, two scans must be made. The first
experiment is a closed aperture z-scan, in which refraction and absorption are measured
simultaneously. A diaphragm that is placed in front of the detector blocks part of the
linearly transmitted light. For example, a positive n2will induce a positive Kerr lens in
the sample, which will guide more light into the detectors if the sample is placed at a
positive z-position in between the beam waist and detector (see Fig. 10). The transmitted
intensity will be reduced if the sample is placed in between the lens band beam waist. The
nonlinear refraction will cause an asymmetry in the z-scan data. The second experiment
is a an open aperture z-scan, in which the aperture is removed, and all transmitted light
is collected. The effect of nonlinear refraction is thus removed. The resulting curve only
depends on the induced absorption, and is therefore symmetric around the beam waist
(z=0). By subtracting the open aperture data from the closed aperture data, the refractive
and absorptive effects can be separated.21,26,27,28
In our switching experiments we are mostly interested in the nonlinear absorption co-
efficients near the two-photon absorption edge of Si and GaAs. Therefore this Appendix
describes open aperture z-scan experiments that were done on Si and GaAs single crys-
talline wafers. To the best of our knowledge the results presented here are the first mea-
surements of the two-photon absorption coefficient GaAs near the two photon absorption
edge (?ω ≈1
Fig. 10 shows a schematic drawing of our z-scan setup. The power of the incoming
beam is monitored by detector D1. The beam is focused by a lens with focal length f.
The sample, typically a double-side polished wafer, is placed on a translation stage that
scans the sample along the z-direction. The zero position is taken at the beam waist. The
transmitted power is collected by a second lens (not shown) and measured by a InGaAs
The shape of the transmission curve strongly depends on pump irradiance, and pump
power stability is therefore essential for the correct interpretation of the experimental data.
Each pulse was therefore measured individually using the detection scheme described in
Section IIA. Both pump-monitor detector signals (D1) and transmission signals (D2) for
each pulse event are stored. We minimize the effect of pulse-to-pulse variations in the
laser output (which can be as high as 10%) by selectively removing all pulses with energy
beyond a certain threshold. In all experiments, the number of pulses collected and the
threshold were chosen such that the standard deviation in pump energy remained below
3%. Typically between 2500 and 10000 pulses were collected for each datapoint. The
corresponding standard error in the transmission was typically better than δT/T<1%,
which is sufficiently sensitive for our z-scan measurements. The sensitivity can be further
increased by narrowing the pulse energy range, at the price of longer integration times.
To interpret the z-scan data, we have numerically calculated the nonlinear transmission
of a Gaussian beam through a thin slab. The beam radius of a diffraction limited Gaussian
w(z) = w0
where λ is the wavelength, z is the sample position relative to the focus.1The diffraction
limited radius of the beam waist is equal to:
where f is the focal length of the lens and wbis the Gaussian radius of the unfocused
beam at the position of the lens. At each wavelength, wbwas determined by a knife edge
In our calculation we have discretized the sample into 256×256 independent trans-
mission channels of 10×10 µm2. We have made sure that the lateral dimensions of each
channel are smaller than the focus radius w0, to avoid discretization artifacts at z=0. We
calculate the nonlinear transmission through each channel. Since our pump frequencies
are in the two-photon absorption range
2Egap< ?ω < Egapwhere α=0, therefore, the
transmitted power through a sample with thickness L, normalized to the linear transmis-
sion (1 − R)2is equal to:
1 + I0(z)βL,
where R is the Fresnel reflectance at the front- and back-face of the sample, β is the
two-photon absorption coefficient, and I0(z) the irradiance at the sample interface after
subtraction of the front-face reflection at position z. The added calculated transmission
of all channels is plotted versus sample position z. The adjustable parameter in this
calculation is β.
First we consider open aperture z-scan measurements on a double-side polished Si
wafer with thickness L= 360 µm. Normalized transmission is plotted in Fig. 11 as a
function of sample position z. Data were taken at two wavelengths: λ= 1630 nm (open
circles) and at λ= 1720 nm (closed squares). The measured data were normalized to the
linear transmission away from the focus. We observe that in both scans, the transmission
is strongly reduced as the sample scans through the focus. The curves are numerically
calculated transmission data, where β was used as fitting parameter. We find good agree-
ment for β= 0.6±0.3 cmGW−2(λ= 1630 nm), and for β= 0.2±0.1 cmGW−1at λ= 1720
nm. Fig. 12 shows a z-scan of the same Si wafer at a pump wavelength λ= 2000 nm, close
to the two-photon absorption edge of Si. The peak irradiance during this scan was I0=
800±200 GWcm−2. We find good agreement for β= 0.20±0.05 cmGW−1.
C. Two-photon absorption in GaAs
We have performed open aperture z-scan experiments on a double-side polished GaAs
wafer with a thickness of 189 µm. Figure 13 shows z-scan data taken at λ= 1720 nm,
just above the two-photon absorption edge of GaAs. The measured data were normalized
to the linear transmission away from the focus. The peak irradiance was I0= 366±60
GWcm−2in Fig. 13. The strongly attenuated transmission near the waist of the beam
indicates a strong nonlinear absorption. The curve is calculated using β as an adjustable
parameter. We find good agreement for β= 1.5±0.5 cmGW−1. Fig. 14 shows z-scan data
for GaAs at a shorter wavelength λ= 1630 nm. Here, we find good correspondance for β=
3.5±1.0 cmGW−1. Our data are in excellent agreement with Ref. 23. We conclude that in
GaAs, the two-photon absorption coefficient strongly decreases as the pump wavelength
approaches half the band gap energy, allowing spatially more homogeneous switching.14
We have measured the two-photon absorption coefficients of Si and GaAs near the
two-photon absorption edge by an open-aperture z-scan technique. The experimental
data was compared to a model that includes nonlinear absorption in the sample. For
both Si and GaAs we find that the two-photon absorption coefficient tends to zero near
half the gap energy1
FIG. 8: (Color online) (a) Broadband linear reflectivity spectrum in the (111) direction of a Si
inverse opal, measured by combining the signal and idler range of our optical amplifier. Inset:
High resolution SEM image of the Si inverse opal. The scale bar is 2 µm. Image courtesy of
Jeroen Kalkman. (b) Differential reflectivity as a function of both probe frequency ωprobeand
probe delay. The pump frequency and peak irradiance were λpump= 1550 nm and I0= 4±1
GWcm−2on the red part, and λpump= 2000 nm and I0= 25±3 GWcm−2on the blue part of
the spectrum. The probe delay was varied in small steps of ∆t= 50 fs on the blue edge and in
steps of ∆t= 500 fs at the red edge. The probe wavelength was tuned from 1600 to 2100 nm in
∆λ= 10 nm steps in the low frequency range, and from 1160 to 1600 nm in 5 nm steps in the
sample position Z (cm)
FIG. 9: (A). Open aperture z-scan measurement for a 300 µm thick double-side polished GaP
wafer. Pump parameters: λ= 1600 nm, f= 100 mm, τp= 130 fs, I0= 285±60 GWcm−2. The
curve represents the calculated transmission using a three-photon coefficient γ= 1.0±0.3×10−3.
(B). Three-photon coefficient γ for GaP were obtained at five wavelengths. The dashed vertical
line indicates the three-photon absorption edge for GaP1
3Egap, the solid line serves to guide the
eye. We observe that γ decreases as the pump frequency approaches1
FIG. 10: (Color online) Schematic drawing of the z-scan setup. Incoming laser beam from our
OPA is split by a beam splitter (BS). Two InGaAs photodiodes are used to monitor the output
variation of the OPA (D1) as well as the transmitted signal (D2). The detector signals are
measured as a function of sample position z.
sample position Z (cm)
FIG. 11: Open aperture z-scan measurement for a 360 µm thick double-side polished Si wafer.
Open circles: λ= 1630 nm, f= 100 mm, I0= 385±40 GWcm−2. Closed squares: circles, λ=
1720 nm, f= 100 mm, I0= 315±40 GWcm−2. The curves are calculated transmission using β=
0.6±0.3 cmGW−2(dashed curve, λ= 1630 nm) and β= 0.2±0.1 cmGW−2(solid curve, λ= 1720
sample position Z (cm)
FIG. 12: Open aperture z-scan measurement for a 360 µm thick double-side polished Si wafer.
Pump parameters: λ= 2000 nm, f= 150 mm, τp= 130 fs, I0= 800±200 GWcm−2. The dashed
curve represent the calculated transmission using β= 0.20±0.05 cmGW−1
sample position Z (cm)
FIG. 13: Open aperture z-scan measurement for a 189 µm thick double-side polished GaAs
wafer. Pump parameters: λ= 1720 nm, f= 100 mm, τp= 130 fs, I0= 366±60 GWcm−2. The
curve represents the calculated transmission using β= 1.5±0.5 cmGW−1
-15-10-505 1015 Download full-text
sample position Z (cm)
FIG. 14: z-scan measurement for a 189 µm thick double-side polished GaAs wafer. Pump
parameters: λ= 1630 nm, f= 100 mm, τp= 130 fs, I0= 244±40 GWcm−2. The curve represents
the calculated transmission using β= 3.5±1.0 cmGW−1