Consistent characterization of semiconductor saturable absorber mirrors with single-pulse and pump-probe spectroscopy

We study the comparability of the two most important measurement methods used for the characterization of semiconductor saturable absorber mirrors (SESAMs). For both methods, single-pulse spectroscopy (SPS) and pump-probe spectroscopy (PPS), we analyze in detail the time-dependent saturation dynamics inside a SESAM. Based on this analysis, we find that fluence-dependent PPS at complete spatial overlap and zero time delay is equivalent to SPS. We confirm our findings experimentally by comparing data from SPS and PPS of two samples. We show how to interpret this data consistently and we give explanations for possible deviations. © 2013 Optical Society of America OCIS codes: (140.4050) Mode-locked lasers; (230.4320) Nonlinear optical devices; (120.5700) Reflection. References and links 1. U. Keller, K. Weingarten, F. Kärtner, D. Kopf, B. Braun, I. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Quantum Electron. 2, 435–453 (1996). 2. F. Kärtner, I. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Quantum Electron. 2, 540–556 (1996). 3. F. Kärtner, J. Aus der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers What’s the difference?” IEEE J. Quantum Electron. 4, 159–168 (1998). 4. J. Aus der Au, S. Schaer, R. Paschotta, C. Hönninger, U. Keller, and M. Moser, “High-power diode-pumped passively mode-locked Yb: YAG lasers,” Opt. Lett. 24, 1281–1283 (1999). 5. J. Neuhaus, D. Bauer, J. Zhang, A. Killi, J. Kleinbauer, M. Kumkar, S. Weiler, M. Guina, D. H. Sutter, and T. Dekorsy, “Subpicosecond thin-disk laser oscillator with pulse energies of up to 25.9 microjoules by use of an active multipass geometry,” Opt. Express 16, 20530–20539 (2008). 6. C. Lecaplain, C. Chédot, A. Hideur, B. Ortaç, and J. Limpert, “High-power all-normal-dispersion femtosecond pulse generation from a Yb-doped large-mode-area microstructure fiber laser,” Opt. Lett. 32, 2738–2740 (2007). 7. O. Okhotnikov, A. Grudinin, and M. Pessa, “Ultra-fast fibre laser systems based on SESAM technology: new horizons and applications,” New J. Phys. (2011). 8. D. Bauer, I. Zawischa, D. H. Sutter, A. Killi, and T. Dekorsy, “Mode-locked Yb:YAG thin-disk oscillator with 41 μ J pulse energy at 145 W average infrared power and high power frequency conversion,” Opt. Express 20, 9698–9704 (2012). 9. C. Saraceno, F. Emaury, O. Heckl, C. Baer, M. Hoffmann, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, “275 W average output power from a femtosecond thin disk oscillator operated in a vacuum environment,” Opt. Express20, 23535–23541 (2012). 10. J. Li, D. Hudson, Y. Liu, and S. Jackson, “Efficient 2.87 μm fiber laser passively switched using a semiconductor saturable absorber mirror,” Opt. Lett. 37, 3747–3749 (2012). #180401 $15.00 USDReceived 21 Nov 2012; revised 10 Jan 2013; accepted 4 Feb 2013; published 11 Mar 2013 (C) 2013 OSA 25 March 2013 / Vol. 21, No. 6 / OPTICS EXPRESS 6764 11. M. Haiml, R. Grange, and U. Keller, “Optical characterizat ion of semiconductor saturable absorbers,” Appl. Phys. B: Lasers and Optics 79, 331–339 (2004). 12. D. J. Maas, B. Rudin, A.-R. Bellancourt, D. Iwaniuk, S. V. Marchese, T. Südmeyer, and U. Keller, “High precision optical characterization of semiconductor saturable absorber mirrors,” Opt. Express 16, 7571–7579 (2008). 13. F. Schättiger, D. Bauer, J. Demsar, T. Dekorsy, J. Kleinbauer, D. Sutter, J. Puustinen, and M. Guina, “Characterization of InGaAs and InGaAsN semiconductor saturable absorber mirrors for high-power mode-locked thin-disk lasers,” Appl. Phys. B: Lasers and Optics 106, 605–612 (2012). 14. C. J. Saraceno, C. Schriber, M. Mangold, M. Hoffmann, O. H. Heckl, C. R. E. Baer, M. Golling, T. Südmeyer, and U. Keller, “SESAMs for High-Power Oscillators: Design Guidelines and Damage Thresholds,” IEEE J. Quantum Electron.18, 29–41 (2012). 15. G. Spühler, K. Weingarten, R. Grange, L. Krainer, M. Haiml, V. Liverini, M. Golling, S. Schön, and U. Keller, “Semiconductor saturable absorber mirror structures with low saturation fluence,” Appl. Phys. B: Lasers and Optics81, 27–32 (2005). 16. G. Agrawal and N. Olsson, “Self-Phase Modulation and Spectral Broadening of Optical Pulses in Semiconductorlasers and Amplifiers,” IEEE J. Quantum Electron. 25, 2297–2306 (1989). 17. R. Gebs, G. Klatt, C. Janke, T. Dekorsy, and A. Bartels, “High-speed asynchronous optical sampling with sub50fs time resolution,” Opt. Express 18, 5974–5983 (2010).


Introduction
From their advent in the early nineties until today, semiconductor saturable absorber mirrors (SESAMs) have developed to be a key component in modern laser technology [1][2][3].Their success is based on providing a robust and self-starting mechanism for passive mode-locking which can be adapted for quite different laser concepts ranging from conventional solid state lasers to fiber lasers and semiconductor lasers.Driven by the ever growing need both in science and industry, SESAMs have enabled new power regimes and an unprecedented reliability of ultrashort pulsed laser sources [4][5][6][7][8][9][10].
However, to reach stable mode-locking operation at average output powers of currently more than 200 W and pulse energies exceeding 40 µJ is still a very demanding task.Pushing the limits here, requires a highly optimized SESAM with parameters custom-designed to a specific laser resonator.It is thus not surprising that SESAMs themselves have been a subject of active research.In this context, especially the accurate measurement of parameters characterizing a SESAM sample is an important task [11][12][13][14].Only with a precisely characterized SESAM sample one is able to correctly predict the dynamics of a laser cavity and to provide feedback for the SESAM design and the SESAM growth process.
In the past several measurement techniques have been established to characterize SESAMs.One relatively recent method uses what we term "single-pulse spectroscopy" (SPS), following a concept first presented by Maas et al. [12].The purpose of this method is to measure the dependence of the SESAM reflectivity on the fluence of the incident laser pulse.It uses a twoarm configuration with a highly reflective (HR-) mirror as a reference and a chopper closed to a central beam splitter (see left panel of Fig. 1).The axis of the chopper is positioned slightly above or below beam height.Then, a four-state signal is generated such that in succession only the SESAM, the dark signal, only the HR-mirror, or both reflections simultaneously are measured.The ratio of the SESAM signal to the HR-mirror, each with the dark signal subtracted and averaged over many chopper cycles gives the absolute reflectivity of the SESAM with high precision (see [12] for details).A second method is pump-probe spectroscopy (PPS) in its standard form, as it is widely used to study time-dependent phenomena (see right panel of Fig. 1).Hence, its purpose is to measure the time dependence of the SESAM reflectivity such that it can provide important information on the dynamics of the SESAM, e.g. the relaxation time.
There are several reasons why one could be interested to compare SPS and PPS.First of all, because the two methods partly complement each other, it makes sense to use both on the same sample.In this way one is not only able to get a more complete picture of a SESAM but A chopper is positioned such that no pulse, only one, or both reflected pulses are detected.
In PPS shown on the right side, a pump pulse (solid line) and a time-delayed probe pulse (dashed line) are incident on a SESAM.Only the probe pulse is detected.also to compensate for the disadvantages of one measurement setup by the other.For example, scattered light from the pump beam on the probe detector can be an issue in PPS which naturally does not occur in SPS.Instead, in SPS the relatively high dynamic range in detected powers makes it much more challenging to realize a completely linear signal processing.In this way, one can obtain a better confidence for the measurement results as far as PPS and SPS coincide.Another reason could be that one has only a setup for PPS available but wants to measure fluence-dependent SESAM reflectivity without building another setup.In this case care has to be taken to correctly extract the data from PPS and we will in detail analyze this issue.
Both SPS and PPS aim to determine the SESAM reflectivity but realize inherently different types of measurements.In SPS only a single laser pulse is incident on the SESAM.It records the reflectivity change which is induced by the pulse itself.Instead, in PPS two pulses are involved, a pump pulse which saturates the SESAM and a probe pulse which records the relative change in reflectivity over time.
Of course, using both methods one expects that the measurements should be consistent as far as the methods' results overlap.But as PPS measures a time-dependent reflectivity whereas SPS measures a time-integrated reflectivity it is not obvious how to interpret the measurement data such that the results of both setups can be compared.More precisely, one depends on understanding the time-dependent saturation dynamics in the SESAM to determine which quantities are actually measured.
In this paper we study the issue in two ways.First, we analyze the time-dependent saturation dynamics for both measurement methods in detail.The analysis provides the necessary insight in order to clarify how to correctly interpret the respective measurement data.Then, we present measurements of two different samples, each measured with both PPS and SPS.We compare the results and we demonstrate that they can be interpreted consistently based on the prior anal-ysis.At the same time we show and discuss the deviations that will occur if the measurement data is evaluated incorrectly and we also discuss experimental methods which help to minimize these deviations.
The paper is structured as follows.The next section (Sec.2) is dedicated to the theoretical analysis of the time-dependent saturation dynamics in a SESAM and the differences of the two measurement methods.Afterwards (Sec.3), we present the experimental data and compare the results obtained with the two measurement methods.In the last section (Sec.4), we summarize our results and shortly discuss possible applications for our analysis.

Theoretical analysis
The structure of a SESAM typically consists of a passive semiconductor Bragg mirror with an active, non-linearly absorbing layer on top.The active layer contains a saturable absorber usually in the form of one or several semiconductor quantum wells (QWs).When the QWs' band gap is smaller than the impinging laser photon energy, the resonant carrier generation and successive relaxation processes create a bleachable, time-dependent absorption.In this way a non-linear optical response in the form of an intensity-dependent reflectivity is generated [1].
In the following, we focus on the dynamics of a light pulse inside the absorptive material of the active layer.This is the part which is most relevant for our analysis of the two measurement methods.Any additional effects like residual absorption of the Bragg mirror, a resonant or antiresonant active layer design [15], or non-linear effects of spacer layers between QWs can then be accounted for by re-scaling the presented model or by supplementing an additional factor.

Slow-Absorber Model
The light propagation inside the absorber can be modeled in two-level approximation by a onedimensional equation for the intensity I(z,t) coupled to an equation for the time-dependent change of the absorption α(z,t) [11].The equations read where z is the space coordinate, t is the time, α 0 is the residual absorption coefficient in the fully saturated state, and F sat is the saturation fluence, i.e. the characteristic fluence necessary to saturate the absorber.These two equations constitute the so-called "slow-absorber model", since relaxation of the absorption back to the unsaturated state due to different carrier relaxation processes is not included.Furthermore, the model is based on a traveling-wave approach and the double pass through the absorptive material due to reflection at the Bragg mirror is calculated by a single pass with twice the absorber thickness.This neglects the effect of a standing-wave pattern formed inside the active layer.Because such a pattern only leads to a re-scaling of the SESAM modulation depth and the saturation fluence, it is not important for our analysis.Further details can be found in [11] and reference [19] therein.
Employing energy conservation which is fulfilled in the limit of α 0 z ≪ 1, an analytic solution for Eqs.(1) can be derived [16] with the instantaneous reflectivity where I(0,t) is the initial time-dependent intensity.R lin (z) = e −(α(z,0)+α 0 )z is the linear reflectivity in the unsaturated state, R ns (z) = e −α 0 z is the maximum reflectivity corresponding to the non-saturable absorption, and is the saturation parameter.The solution quantifies, how the instantaneous reflectivity at each position increases from its initial linear value R lin (z) up to a maximum R ns (z) depending on the accumulated fluence relative to the saturation fluence F sat .

Single-Pulse Spectroscopy (SPS)
We now consider the presented solution (Eq. ( 2)) for a single pulse incident on the SESAM as it is the case in SPS.An example for the incoming and outgoing pulse together with the instantaneous reflectivity is shown in Fig. 2. To provide clarity, we chose parameters corresponding to a large modulation depth SESAM, like it is used in mode-locked fiber lasers [7].The example shows a short, strongly saturating pulse (τ p = 1 ps, S = 7.5) which increases the instantaneous reflectivity from its linear value (R lin = 25 %) to about its maximum (R ns = 95 %).To make the solution more realistic, we include carrier relaxation by adding a phenomenological factor of the form e −S(t)t/τ to the saturation parameter (τ = 8 ps).We see that the outgoing pulse gets modulated according to the time-dependent instantaneous reflectivity.This results in a reduction of the front edge of the pulse where the absorber is not yet fully saturated.For example, at t = −0.5 ps the instantaneous reflectivity has reached a value of about 50 % such that the pulse is reduced from 0.5 to 0.25 of its normalized intensity.
In SPS the actual measurement is done by detecting the outgoing pulse intensity relative to the incident pulse intensity which comes as an unaffected copy from the HR mirror (see Fig. 1).Due to the detection process we have to integrate Eq. ( 2) over the pulse duration and we find for the fluence dependent reflectivity where the fluence is given by F = I(0,t)dt and we have assumed that the overall thickness of absorptive material for a double pass is z = L such that R lin = R lin (L) and R ns = R ns (L).In Eq. ( 5) we have supplemented an additional fluence-dependent factor of the form e −F/F 2 .It accounts for the fact that at very high fluences the SESAM saturation cannot be increased any further but typically suffers some reduction instead.This is due to non-linear effects like two-photon absorption or free-carrier absorption and is characterized by the roll-off fluence F 2 [11].Furthermore, for the interpretation of real measurement data we have to consider the transverse profile of the light pulse.When a Gaussian beam profile w 2 (6) with a mean pulse fluence F p = E p /(πw 2 ), a pulse energy E p , and a beam waist w is assumed, this can be done by a simple integration over the beam radius r which, however, cannot be carried out analytically.The result is the standard formula for the fluence-dependent SESAM Fig. 2. A pulsed light field intensity (left y-axis) is shown together with the corresponding SESAM reflectivity (right y-axis).A strongly saturating pulse I(0,t) (blue solid line) changes the instantaneous reflectivity R inst (t) (red solid line) and the outgoing pulse I(L,t) (dark-shaded area) is modulated accordingly.A much weaker probe pulse Ĩ(0,t) (blue dashed line and light-shaded area, drawn scaled and for two different time delays) can then experience a higher overall reflectivity at a later time.It traces the instantaneous reflectivity but convolves it with its pulse shape to R conv (t) (red dashed line).
reflectivity [11,12] as measured by SPS This formula gives the time-integrated reflectivity of a single pulse as a function of the mean pulse fluence.It is of fundamental importance in laser development because the measurement method it describes is equivalent to the situation when a single pulse is reflected by a SESAM inside a laser cavity.Thus, it characterizes the loss of the pulse at the SESAM and thereby the attainable efficiency of the laser.

Pump-Probe Spectroscopy (PPS)
The key difference between PPS and SPS is that in PPS two pulses are involved in the measurement process instead of one.A strong pump pulse saturates the SESAM exactly as we have described in the last section (Sec.2.2).But instead of detecting this pulse, a second much weaker pulse is used to probe the SESAM.By means of different time delays it traces the time evolution of the reflectivity.Since this probe pulse is also integrated over in the detection process, the time-dependent reflectivity measured in PPS is a convolution of the instantaneous reflectivity due to the pump pulse and the pulse shape of the probe pulse, where F is the probe pulse fluence, t is now the time delay, Ĩ(0,t ′ ) is the shape of the probe pulse, and the dependence on the pump fluence F is implicit in the saturation parameter S. In our example (see Fig. 2), we have drawn this convolution under the assumption that the probe pulse intensity is small enough to be neglected in the integral for S (Eq.( 4)).With a slight delay to the pump pulse, the probe pulse will profit from the optimum reflectivity at a time when the accumulated fluence and the carrier relaxation dynamics just counterbalance.This leads to the fact, that the maximum of the reflectivity time trace in PPS will always be higher than the timeintegrated reflectivity measured with the same pulse fluence in SPS.In Fig. 2 we have drawn the probe pulse for two different time delays and the second time delay corresponds exactly to this optimum reflectivity case.We can see that the area of the probe pulse is much less reduced as compared to the outgoing pump pulse.Just as in SPS, for the interpretation of real measurement data from PPS we have to consider the transverse beam profiles.An integration over different local fluences has to be done, where F(r) and F(r) are the respective beam profiles of pump and probe beam as defined in Eq. ( 6).Similar to the higher reflectivity by a slight time delay, a smaller probe beam diameter will also increase the reflectivity measured in PPS as compared to SPS.From Eq. ( 9) we see that the probe pulse will profit from the higher saturation close to the center of the pump beam.

SPS and PPS reconciled
At first sight, the two measurement methods SPS and PPS seem to be incomparable, because time-integrated reflectivity of a single pulse and time-dependent reflectivity convolved with the probe pulse shape are just two different types of measurements.However, the question of consistency arises when PPS is done at different pump-pulse fluences F p and one tries to extract the same kind of fluence-dependent reflectivity from PPS which is generically measured with SPS.
In particular, one would like to identify for each fluence F p a point in time where the reflectivity time trace from PPS corresponds to the single-pulse reflectivity from SPS.With no other prominent feature present, one might be tempted to pick the local maximum in the beginning of the time trace.But this will not yield correct results as our analysis in the last section (Sec.2.3) has shown.
The solution to make PPS and SPS consistent is to only use reflectivity values from PPS where the pump and probe pulse completely overlap in space and in time.This can be achieved by using col-linear pump and probe beams with the same spot size and by taking the reflectivity at zero time delay.
Assume, that the probe pulse is incident on the SESAM at exactly the same time as the pump pulse and that it exhibits the same pulse shape which is usually the case in PPS.As a result, it will undergo exactly the same kind of modulation and the outgoing probe pulse will be changed in area the same way as a single pulse in SPS would have been changed (see first probe pulse in Fig. 2).The convolution of probe pulse and instantaneous reflectivity will then be equal to the time-integrated reflectivity of the pump pulse, i.e. in Fig. 2 the value of R conv at zero time delay tells us that the pump pulse has been reduced to about 75 % of its incoming area.This guarantees that the same reflectivity value is measured as for a single pulse, R conv (F,t = 0) = R(F), (10) regardless of the possibly complicated time evolution of the instantaneous reflectivity depending on the exact carrier relaxation dynamics.
The overlap in space is equally important because of the integration over the transverse profile of the pulse.Only if pump and probe beam have the same beam characteristics and especially the same spot size, the same profile F(r) = F(r) can be assumed.Furthermore, if the included angle is small enough, the time delay is approximately constant over the illuminated spot.Together with the time overlap (Eq.( 10)) at zero time delay, Eq. ( 9) then reduces to such that the same reflectivity value is measured in SPS and PPS.

Experimental results
In this section, we present measurements of two different commercially available SESAM samples, each measured with both PPS and SPS.We used an Yb:YAG thin-disk laser at 1030 nm with a pulse length of about t p = 1 ps (FWHM) as a laser source [5].For PPS we rely on a standard, degenerate pump-probe setup including an automatic scan-delay which allowed for a time-delay window of about 50 ps.We use a constant probe fluence and only vary the pump fluence to obtain fluence-dependent data.The probe fluence is kept much smaller than the saturation fluence of the measured sample to avoid additional saturation.To convert the relative change of reflectivity to absolute values, we measure the absolute value of the linear reflectivity separately.The setup used for SPS has been build in line with the original concept by Maas et al. [12].The two samples mainly differ in that the first SESAM, sample A, has a larger modulation depth, i.e. larger change in reflectivity, and a smaller saturation fluence F sat , which is typical for SESAMs used in fiber lasers [6,7,10].The second SESAM, sample B, has a smaller modulation depth and a larger saturation fluence F sat as needed for example in thin-disk lasers [4,8,9,14].Measuring a small change in reflectivity requires a higher measurement accuracy, such that sample A and sample B cover different measurement-accuracy regimes.
We first look at the measurement data taken with PPS from sample A. The data is presented in Fig. 3 as a complete set of time traces measured for different pump fluences spanning more than four orders of magnitude.It nicely shows the different time-dependent saturation dynamics ranging from the linear reflectivity regime at very small fluences, through the gradual saturation at medium fluences, up to a roll-off and the final destruction of the absorber at high fluences.But without further information, it is not clear how to correctly extract a fluence-dependent reflectivity from this data.This becomes even more apparent when we have a closer look at the reflectivity time traces around their first maximum.In Fig. 4 we have drawn just this section of the time traces and we can observe how the increasing pump fluence changes their shape which in turn affects the position of the first maximum (see Fig. 4, blue dot markers).
From the theoretical analysis in the last section (Sec.2), we know that the correct fluence dependence corresponding to the data from SPS can be found by completely overlapping the pump and probe pulse in space and time.Experimentally, we therefore made sure that in our PPS setup at the sample position the pump and probe beam have the same beam parameter.We recombine pump and probe beam via a polarizing beam splitter and focus down both beams with the same lens.For the time overlay, one needs to find the zero time delay by an autocorrelation of the pump pulse.Here, we have used PPS of a pure GaAs sample with equally strong pump and probe pulse.The two-photon absorption signal provides an intensity autocorrelation and we verified that the peak position does not change when the pump beam is detected instead of the probe beam.The autocorrelation data together with a fit on the basis of a sech 2 (t) pulse shape is also shown in Fig. 4. As predicted by the theoretical analysis, we find the autocorrelation maximum corresponding to zero time delay at earlier times than the first local maximum of the time traces.Only for very high fluences the superposition of a second maximum due to non-linear carrier generation shifts the first maximum to earlier times.
In the following, we thus ignore the first maximum and extract the fluence-dependent reflectivity at zero time delay, i.e. at the autocorrelation maximum.The result is shown in Fig. 3 and Fig. 5 and compared to data taken with SPS.To demonstrate the influence of non-overlapping pump and probe pulse, we also plotted curves for a time delay of ±0.5 ps and ±1.0 ps corresponding to (a) to (e) in 4. We see that the best agreement of PPS and SPS data is clearly achieved for zero time delay (curve (c)).Using negative or positive time delays does not change the minimum and maximum value of the reflectivity so much.Instead, it strongly shifts the curve to higher or lower fluences.This behavior is understandable since the same saturation state of the absorber can still be reached by a higher or lower pump fluence.A mismatch of pump and probe pulse of only 0.5 ps can already shift the fluence axis by more than a factor of two.In the same way we also compare data from PPS and SPS of sample B. The results are shown in Fig. 6.Again, the zero time delay curve from PPS is in good agreement with the SPS data.But with the smaller modulation depth the deviations due to limits in measurement accuracy become more apparent.
In our setups there are two main sources of measurement uncertainty.One is that the fluence determination relies on measuring the beam diameter at the sample position.This is done with the help of a pin hole transmission measurement which is quite sensitive to mode quality loss due to various optical elements.We estimate the accuracy for fluence measurements to be about ±5 %.The other limiting factor is due to stray light.This is of particular concern for PPS where the sample can scatter parts of the pump light onto the probe detector.We have tried to minimize its influence by using crossed pump and probe polarization together with a polarization filter in front of the detector, separating pump and probe beam by a small angle, and subtracting a dark signal with blocked-out pump beam.But also in SPS stray light, especially from the chopper can be a problem.Here, the fact that more than four orders of magnitude in power are detected makes it quite demanding to realize a linear detection and signal processing for high powers and still avoid any disturbing noise or stray light at low powers.Nevertheless, the accuracy level reached with our SPS setup is on the 0.1 % level, which is verified by the HR-mirrorreference curves also shown in Fig. 5 and Fig. 6.To reach a high precision, we have found the interference signal created by the simultaneous measurement of the SESAM and HR-mirror reflection to be quite helpful.This signal is not necessary to obtain the SESAM's absolute reflectivity but due to the short coherence length of the laser pulse it can provide an accurate means to realize an equal arm length setup.As such, it can be used to ensures a completely  symmetric beam evolution with equal spot sizes for both beams on the detector.This in turn facilitates a good reproducibility of the optical adjustment and the HR-mirror reference curves such that it helps to pinpoint the influence of stray light and non-linearity in detection.An additional source of error only present in PPS is the automatic scan-delay device.If the retroreflector mounted on a mechanical shaker is not moving absolutely in parallel to the beam direction, this will superimpose an additional modulation onto the time traces.As a result, the measured reflectivity values can be corrupted in a way which is hard to correct for.Here, more sophisticated pump-probe techniques such as asynchronous optical sampling [17] can be an elegant solution.All fits to data from sample A and B have been done by using Eq. ( 7) as the fit model.The fit parameters are the linear reflectivity R lin , the reflectivity corresponding to the non-saturable absoption R ns , the saturation fluence F sat , and the roll-off fluence F 2 .The extracted values for sample A and B using PPS data with zero time delay and the SPS data are listed together with the residual fit error σ of a least squares fit in Tab. 1.When comparing the values from PPS and SPS, we see that the linear reflectivity R lin and the reflectivity corresponding to the nonsaturable absorption R ns are in good agreement and the deviations for sample A and B are of the same order of magnitude.The saturation fluence F sat for sample A is also consistent within the limits of measurement accuracy.For sample B the difference in F sat is a bit higher.On the one hand, this difference could be explained by a shift in time delay of only 0.1 ps in PPS, which shows the sensitivity to complete overlap of pump and probe pulse.On the other hand, the F sat parameter is also strongly influenced by the determination of the roll-off fluence F 2 .Here, for sample B the fit is less significant than for sample A, because the roll-off regime could not be characterized as extensively due to a limit in measurable fluence values.This is also the reason why the F 2 parameter itself is more consistent for sample A than for sample B.
In general, we believe that the single-pulse reflectivity measured with SPS is more reliable than PPS.Due to the requirement in PPS to ensure complete overlap of pump and probe pulse, there are more sources of error present than in SPS.This is also supported by the residual fit error, which is smaller for the results from SPS both for sample A and B. For information about the relaxation dynamics of the SESAM PPS is the method of choice.As we have shown correct fluence-dependent reflectivity curves can also be extracted from PPS data.

Summary and conclusions
In summary, we have compared the two different SESAM characterization methods PPS and SPS.Based on a detailed analysis of the time-dependent saturation dynamics inside a SESAM, we have pointed out the differences of the two methods and we have discussed the requirements to make measurement results from both methods comparable.As the main result, we have found that a complete overlap in space and time of pump and probe pulse in PPS makes it equivalent to SPS.We have also confirmed our findings experimentally and have presented data from SPS and PPS of two samples.We have shown how to interpret this data consistently and we have given possible explanations for any deviations.
Ideally, when characterizing a SESAM one would like to have both a setup for SPS and for PPS available.Only then one is able to use each method for the measurement it has been designed for and additionally take advantage of the possibility to compare fluence-dependent data for a better confidence in the measurement results.Otherwise, PPS can deliver both timeand fluence-dependent data.As such it is the method of choice if one needs to measure both data for a sample but wants to keep the experimental effort to a minimum.Here, our analysis will help to correctly extract the fluence-dependent data from the PPS setup.In contrast to PPS, SPS will give a better measurement precision if only fluence-dependent measurements are needed.
We conclude that due to the growing utilization of mode-locked lasers with femtosecond and picosecond pulse duration, i.e. for material processing, we believe our results are of relevance for the future design and characterization of saturable absorbers.

Fig. 1 .
Fig.1.Overview of the two discussed measurement schemes.In SPS shown on the left side, a single pulse is split and incident both on a SESAM and on a highly reflective (HR) mirror.A chopper is positioned such that no pulse, only one, or both reflected pulses are detected.In PPS shown on the right side, a pump pulse (solid line) and a time-delayed probe pulse (dashed line) are incident on a SESAM.Only the probe pulse is detected.

Fig. 3 .
Fig. 3. Complete experimental data taken with PPS from sample A. The individual time traces (thin black lines) show the reflectivity for different time delays each at a fixed pumppulse fluence.The set of time traces has been connected to a single surface in three dimensions where the reflectivity has been color coded.On the rear-left side the autocorrelation of the pump pulse is shown (thick blue line).It fixes the zero time delay at which the fluence-dependent reflectivity can be extracted from the PPS data (circular markers on surface).The extracted fluence-dependent reflectivity is also projected on the rear-right side (circular markers) and compared to a fit based on the corresponding SPS data (red line).A thick dashed black line marks the fluence limit where the sample became permanently damaged.

Fig. 4 .
Fig. 4. Zoom in of the PPS data from sample A around zero time delay.The reflectivity time traces (black solid lines, left y-axis) for increasing pump fluences (arrow) are shown together with the autocorrelation data (grey shaded area) and a corresponding fit (thick blue line, right y-axis).The first local maximum is marked by blue dots whereas the zero time delay (red dashed line) and two more earlier and later time delays (black dashed lines) are each marked by a vertical line annotated (a)-(e).

Fig. 5 .
Fig.5.Data from PPS and SPS of sample A. The PPS data which is the basis for fit curves (a)-(e) (dot markers for data, thin black lines for fit curves, thick black line for zero time delay fit) has been extracted at the corresponding time delays marked in Fig.4.Fit curves (d) and (e) are nearly indistinguishable since the corresponding data is very similar.The SPS measurement (circular markers for data, red line for fit) has been repeated with a high-reflectivity mirror (100 % line, circular markers) to show the accuracy.All fits have been done including only data points for fluence values smaller than the limit of permanent damage (dashed black line).

Fig. 6 .
Fig.6.Data from PPS and SPS of sample B. The PPS data which is the basis for fit curves (a)-(e) (dot markers for data, thin black lines for fit curves, thick black line for zero time delay fit) has been extracted from the time traces analogous to the procedure for sample A. The SPS measurement (circular markers for data, red line for fit) has again been repeated with a high-reflectivity mirror (100 % line, circular markers) to show the accuracy.

Table 1 .
Fit parameters resulting from the PPS and SPS data of sample A and B.