Compact optically pumped passively modelocked semiconductor disk lasers (SDLs) based on active quantum wells (QWs) such as vertical external-cavity surface-emitting lasers (VECSELs) or modelocked integrated external-cavity surface-emitting lasers (MIXSELs) are wavelength-versatile sources that offer a unique combination of gigahertz pulse repetition rates and short pulse durations. In this paper, we present record-short pulses of 184 fs from a gigahertz MIXSEL emitting at a center wavelength of 1048 nm. This result comes at the expense of low optical-to-optical pump efficiency (<1%) and average output power limited to 115 mW. We experimentally observe that shorter pulses significantly reduce the macroscopic gain saturation fluence and develop a QW model based on rate equations to reproduce the gain saturation behavior and quantitatively explain the VECSEL and MIXSEL modelocking performances. We identify spectral hole burning as the main cause of the reduced gain at shorter pulse durations, which in combination with the short lifetime of the excited carriers strongly reduces the optical pump efficiency. Our better understanding will help to address these limitations in future ultrafast SDL designs.
© 2017 Optical Society of America
We have obtained systematic improvements of ultrafast optically pumped semiconductor disk lasers (SDLs)  during the last decade [2, 3] since the first demonstration in 2000 . Semiconductor bandgap engineering of optically pumped vertical-external cavity surface-emitting lasers (VECSELs)  provides selected lasing wavelengths optimized for specific applications. To date, modelocked operation has been demonstrated from the UV up to 2 µm and in continuous wave (cw) operation even up to the mid-IR (i.e. up to 5 µm) [5–8]. The highest output power is achieved with InGaAs quantum well gain materials emitting at a center wavelength of around 1 µm. In continuous wave (cw) operation, InGaAs based VECSELs demonstrated up to 20 W of output power in a fundamental Gaussian mode  and 106 W in multimode . For modelocked SDLs, optically pumped VECSELs passively modelocked with semiconductor saturable absorber mirrors (SESAMs)  provide the shortest pulses of 96 fs with 100 mW of average output power in fundamental modelocking (i.e. one single pulse per roundtrip) . A more compact ultrafast SDL is obtained with the modelocked integrated external-cavity surface-emitting laser (MIXSEL) , where the SESAM’s saturable absorber is vertically integrated in the VECSEL gain structure. This results in a simple linear cavity with just 2 end mirrors represented by the semiconductor MIXSEL chip and the curved output coupler [Fig. 1(c)]. MIXSELs have demonstrated the highest output power of any modelocked SDLs, with 6.4 W in 28 ps pulses  and have reached pulse durations as short as 253 fs so far . Furthermore the simple linear cavity enabled record-high pulse repetition rates up to 100 GHz  and dual-comb modelocking with excellent stability [17, 18]. Following the design guidelines explained in , we present here further performance improvement with a MIXSEL generating pulses as short as 184 fs at a pulse repetition rate of 4.33 GHz. The average output power was limited to 115 mW, corresponding to a peak power of 127 W, and the optical-to-optical pump efficiency was 0.65%.
For cw InGaAs QW-VECSELs, optical-to-optical pump efficiencies as high as 45% in multimode output  and 43.2% in fundamental Gaussian mode output  are reported. For femtosecond pulse durations, however, the efficiency is typically reduced to below 1% [12, 15]. Furthermore, for shorter pulse durations we typically observe a decreased pulse energy and therefore a limited average output power. This trade-off in both the pump efficiency and average output power with shorter pulse durations sets serious restrictions for applications that require a combination of short femtosecond pulses and high peak power to drive nonlinear optical processes such as frequency doubling for material processing , multiphoton microscopy  and supercontinuum generation for metrology and frequency comb applications [22, 23]. For this reason we recently focused our efforts to relax the hard peak power requirements of sub-100-femtosecond pulses necessary to detect and stabilize the carrier-envelope-offset (CEO) frequency in a self-referenced f-to-2f interferometry scheme  for frequency comb stabilization thanks to promising results with Si3N4 waveguides for supercontinuum generation [25, 26].
In this paper, we want to develop a simple model that explains the observed trade-off between short pulse duration and pump efficiency. Recently, simulations relying on the development of fully microscopic many-body QW models based on Maxwell semiconductor Bloch equations [27–29] revealed that amplification of short pulses significantly decreases the carrier population in the inverted distribution creating kinetic holes. Under strong pumping conditions we have a reservoir of unused carriers outside of the spectral pulse domain that can seed additional pulses which destabilize fundamental modelocking. Such ab-initio models offer a deep understanding for modelocked QW-VECSELs, but rely on a considerable computational effort and were up to now calculated only for resonant periodic gain structures . Furthermore, several important quantities that cannot be theoretically predicted like inevitable growth inaccuracies, inhomogeneity of the layer thicknesses and influence of defect-recombination on the carrier lifetime limit the quantitative prediction capability of fully microscopic models for real structures, forcing a final adjustment of the theoretical results to macroscopic experimental data to obtain a proper quantitative description of the modelocking process.
Following the more phenomenological approach we introduced in  to simulate pulse formation processes in ultrafast SDLs, we expand here our efforts with a simplified QW gain model based on single carrier type rate equations (REs) [31, 32]. Our model provides a better understanding on various limitations of current SDLs and can reproduce the experimental values of output power and pump efficiency for different MIXSELs and VECSELs [12, 15]. As a key advantage of the introduced simplifications, most physical input parameters necessary for simulation can be directly measured.
We distinguish three time scales involved in SDL carrier dynamics : a nanosecond time scale for the diffusion process of the optically pumped electrons and holes into the QW gain region, a 100-ps time scale for interband spontaneous recombination and finally a time scale in the hundreds of femtoseconds for intraband scattering phenomena. Through pump-probe and gain/absorption saturation measurements of our VECSELs, MIXSELs and SESAMs, we directly obtain or fit the model input parameters and arrive at a quantitative explanation for the limited pulse fluence that is experimentally observed during modelocking.
Consistently with , we confirm in this paper that spectral hole burning is responsible for a lower gain saturation fluence with shorter pulse durations and is currently preventing power scaling in the sub-200-fs regime. In addition we can demonstrate that two-photon absorption (TPA) does not yet set a significant limitation for the output power even though TPA becomes stronger with shorter pulses [34, 35]. In contrast, we confirm that a short carrier lifetime in the conduction band in the order of 100 ps strongly reduces the optical-to-optical pump efficiency.
The paper is structured as follows. In section 2 we describe the recent modelocking improvements for our MIXSEL generating 184-fs pulses; section 3 focuses on the description of the RE QW model, while sections 4 and 5 show that the measured pulse-energy-dependent gain dynamics and gain saturation can be reproduced by this model. In section 6 and 7 we use this model to simulate and explain the modelocking performances and pump efficiencies of the SESAM modelocked VECSEL generating 100-fs pulses, as described in more details in , and of the 184-fs MIXSEL result.
2. Experimental MIXSEL modelocking results
2.1 MIXSEL design and fabrication
In Fig. 1(a) we show the semiconductor epitaxial layer stack of the MIXSEL chip which is the same as described in . The structure is designed for an operation wavelength around 1040-1050 nm. Going from the bottom to the top, the MIXSEL chip consists of a bottom 24-pair AlAs/GaAs distributed Bragg reflector (DBR) which forms a high reflective mirror for the lasing wavelength, followed by an absorber section with a single 11-nm thick In0.2Ga0.8As W and a 9.5 pair Al0.15Ga0.85As/AlAs DBR designed to reflect the pump wavelength and prevent bleaching of the absorber due to the residual pump light. This is followed by an active region with 10 In0.19Ga0.81As QWs of 9 nm thickness embedded in GaAs barriers. The compressive strain of the gain QWs is balanced by tensile strained layers of GaAs0.94P0.06.
Passive modelocking is achieved following the design guidelines in . The average electric field intensity enhancement factor at the QW positions was reduced to 0.65 (normalized to 4 out of a 100% reflective mirror) to increase the gain saturation fluence and flattened with variations below 10% over a range of ± 20 nm around the center wavelength to support broadband operation. A numerically optimized antireflection (AR) section with seven alternating layers of Al0.15Ga0.85As and AlAs followed by a single fused silica (FS) layer finalizes the structure. This last AR section minimizes the pump reflection and provides a close to constant group delay dispersion (GDD) in a range of ± 200 fs2 over a 40-nm bandwidth around the lasing wavelength.
As described in , the semiconductor layer structure was grown in the FIRST lab at ETH Zurich. The growth was in reverse order for subsequent flip-chip bonding on a diamond heat spreader. The etch-stop layer, the AR section and the active region were grown in a metalorganic vapor phase epitaxy (MOVPE) machine to benefit from the P-based strain compensation layers. The two DBRs and the saturable absorber were grown using a molecular beam epitaxy (MBE) system to take advantage of the currently lower saturation fluence achieved with saturable absorbers grown by MBE. The single fused silica layer was deposited by plasma enhanced chemical vapor deposition (PECVD).
Compared to the structure used in , we improved the precision of the PECVD deposition process and adapted the fused silica thickness to partially compensate small deviations from design observed in the epitaxial structure due to growth errors. This provided a better dispersion management and enabled generation of shorter pulses.
2.2 Modelocking performance
The MIXSEL chip was mounted on a copper heatsink and temperature stabilized at 9°C. A linear laser cavity is obtained with the MIXSEL chip as one end mirror and a curved output coupler (OC) as the other [Fig. 1(c)]. The OC has a 350-mm radius of curvature (ROC) and a transmission TOC of 0.44%. The cavity length was set to 34.6 mm, corresponding to a pulse repetition rate of 4.33 GHz in fundamental modelocking operation. The MIXSEL chip was pumped under an angle of 45° with a commercial multimode 808 nm fiber coupled diode array. To ensure single transverse mode operation, the laser spot size on the MIXSEL was set to a 184-µm radius, slightly larger than the circular pump spot size of a 180-µm radius on the MIXSEL chip. A 1-mm thick wedged fused silica plate was inserted into the cavity at Brewster angle to obtain a single linear polarization output. With the incident pump power increased to 17.6 W, self-starting stable modelocking operation was achieved at an average output power of 115 mW, corresponding to a pulse peak power of 127 W. A detailed pulse characterization carried out with second harmonic generation frequency resolved optical gating (SHG FROG) revealed a duration of 184 fs, which represents the shortest pulse duration ever achieved with the MIXSEL technology. Good agreement between the measured and the retrieved trace is visible in Figs. 2(a) and 2(b), with a reconstruction error of 0.0011 . The pulse spectrum, measured with both FROG and optical spectrum analyzer, shows a center wavelength of 1048 nm and a full width at half maximum (FWHM) bandwidth of 7.4 nm, corresponding to 1.15 times the time-bandwidth product for an ideal transform-limited sech2–shaped pulse.
The detected microwave spectrum was measured with a 22-GHz photodetector without additional amplification. The fundamental pulse repetition rate of 4.33 GHz measured in in a 15-MHz span with a narrow resolution bandwidth (RBW) of 100 Hz shows a high signal-to-noise ratio of more than 80 dB indicating fundamental modelocking operation [Fig. 2(e)]. In addition, we show several harmonics of the fundamental pulse repetition rate in a large-span measurement taken with a RBW of 30 kHz [Fig. 2(f)]. The reduced power in the higher harmonics results from the limited detection bandwidth.
2.3 Current limitations
With this new modelocking result we demonstrate for the first time pulse durations below 250 fs with a MIXSEL. This improvement validates our design guidelines as presented in . However, it unfortunately confirms again the significant trade-off in output power and pump efficiency with shorter pulse durations. In particular, for our 184-fs result the optical-to optical pump efficiency does not exceed the low value of 0.65%. Moreover, the intracavity pulse fluence on the MIXSEL device during modelocked operation was limited to 5.8 µJ/cm2 and the OC transmission to 0.44%.
To better understand the physical origin for this trade-off, we develop a QW rate equation model that can benefit from our measured input parameters.
3. QW rate equation model
We have employed a rate equation model for the strain compensated In0.19Ga0.81As gain QWs embedded in GaAs barriers used in both a MIXSEL (Fig. 1) and a SESAM modelocked VECSEL presented in . Our goal is to obtain a precise quantitative description of the laser performance and a better understanding of their limitations. It is therefore important to minimize the number of input parameters for our model which cannot be measured directly. This leads to the introduction of several assumptions and simplifications that are explained as follows.
- • Flat-band approximation. No external electric field is applied and no net current is flowing in the undoped laser structure. Carriers diffuse in the optically pumped GaAs barriers and are captured in the QW. An internal electric field is always formed due to a Coulomb interaction between electrons and holes that diffuse with different diffusion coefficients. The electric field causes a nonuniform carrier distribution with a larger carrier density close to the P side of the junction . However, in the present structure the effect is minor and the carrier transport can be modeled as an ambipolar process .
- • Band structure of the QW. The band-offset between GaAs barriers and strain compensated In0.19Ga0.81As QW is 255 meV at 300 K. Since the temperature dependence of the energy bandgap is similar for the two materials, we consider the band-offset constant and keep the same value for the laser operation temperature in the active region, which is assumed to be 370-400 K. We define the zero energy in correspondence of the bottom of the bulk In0.19Ga0.81As conduction band and estimate a band-offset ratio of 0.67 , meaning that the GaAs barriers are 170 meV high. The confinement effects shift the first energy sub-band at ≈30 meV and the second at ≈110 meV respectively (Fig. 3).
- • Capture and escape rates. The different QWs in the laser structure are separated by several tens of nanometers, making electron coupling (by tunneling) between them negligible. We define a constant net carrier capture rate into the QW () which is determined by carrier diffusion through the pumped barriers and the relaxation rate into the QW itself. This net rate considers also the escape rate, which is related, at equilibrium to the capture rate by the principle of detailed balance. The ratio of escape-to-capture rate is assumed to remain constant under steady-state modelocking conditions. This is verified by the fact that under normal operation, the QW is not completely filled and 2 – 3 separate the last occupied QW state and the barriers which ensures that the escape probability is unperturbed.
- • Two-level approximation. We divide the continuum of the energy states in the QW into two spectral regions. We define an interaction region which corresponds to the lowest 18-20 meV of the conduction band (sufficient to support the full spectral content of a ≈100 fs pulse at 1 µm), and call the corresponding carrier density (Fig. 3). We make the assumption that spontaneous and stimulated emission events take place in this region independently of the spectral bandwidth of the incoming pulse, which is reasonable for pulses longer than the typical Rabi oscillation time scale (≈50 fs [39–41]). The population at higher energies, referred to as acts as a carrier reservoir.
- • Carrier dynamics. We assume that carriers diffuse from the barriers into N2 with a capture time constant in the nanosecond regime . The relaxation to (i.e. the bottom of the band) takes place with a relative slow intraband time constant in the hundreds of femtoseconds . Carriers in decay through spontaneous recombination with a time constant in the hundreds of picoseconds. The local internal carrier re-distributions inside the single regions and are dominated by highly efficient intraband scattering processes involving small energy transfers with characteristic times in the tens of femtosecond range [40, 44], significantly shorter than the considered pulse durations. They are therefore assumed to be instantaneous.
- • Fermi-Dirac distribution. The maximum occupancy in at equilibrium is governed by a Fermi-Dirac probability distribution and is therefore related to the total carrier density of the QW. While lasers are naturally not in real equilibrium, this approximation is commonly used in ambipolar models and works well.
These assumptions and approximations lead us to the following rate equations:Fig. 3), leads to until the second sub-band is reached. Defining as the energy difference between the two confined sub-bands, we obtain after the second sub-band: .
In order to reproduce all the elements of a SDL cavity, we need to introduce an additional rate equation for the saturable absorber. We describe the population dynamics in the SESAM QW as follows:
Assuming the gain proportional to , we define the reflectivity experienced by a modelocked pulse after a full roundtrip time T in a straight MIXSEL cavity:34] and is:
With being the measurable small signal gain and the asymptotic value of obtained through (1) and (2) with no incoming pulse. If we take into account the double pass in the gain chip and the different laser spot sizes on VECSEL and SESAM, the roundtrip reflectivity is calculated for a VECSEL V-shaped cavity:
4. Measurement and fit for the model input parameters
We fitted the RE model to experimental data in order to quantitatively reconstruct the gain dynamics and obtain values for the three time constants , , as well as for the stimulated emission coefficient . To directly obtain a value range for and , we performed pump-probe measurements on a structure consisting of a DBR on top of which we placed a single In0.19Ga0.81As QW, grown by MOVPE with the same growth parameters used for the active QWs of [12, 15] and for the 184-fs MIXSEL.
We used a standard degenerate pump-probe setup with a tunable Ti:sapphire laser generating 100-fs pulses (stretched to 130 fs at the sample position) at 80 MHz with an average power of 900 mW. The center wavelength was adjusted to the photoluminescence peak of the QW at room temperature (1020 nm). During the pump-probe measurement the structure was not cw pumped with 808-nm diode. The measurement revealed a saturation recovery with a fast temporal component of ≈300-400 fs followed by a slow component of 130-140 ps [Fig. 4(a)]. These correspond to the value ranges used in the following for and respectively.
Recently, in situ measurements of gain dynamics during modelocking operation have been shown in  for two VECSELs generating 300 fs and 800 fs pulses (these samples will be called hereon 300-fs VECSEL and 800-fs VECSEL). The fit of these experimental curves allowed us to extract values for and for (listed in Table 1). With all the parameters implemented in the RE model, the curves presented in  are well reproduced for both the 300-fs VECSEL and 800-fs VECSEL result [Figs. 4(b) and 4(c)].
5. Gain saturation
To verify the effect of pulse duration on gain saturation, we measured the pulse-fluence-dependent reflectivity of a diode pumped VECSEL probing the sample with different pulse durations but keeping the probe spectrum unchanged. To achieve a better signal-to-noise ratio in gain measurements, we designed for this experiment a high-gain, 10-QW, strain compensated VECSEL with relatively high average field intensity enhancement factor of 0.7 at the QW positions (at 1020 nm). This VECSEL chip (that we will call the 672-fs VECSEL) delivered up to 10 W of output power in cw operation and 700 mW of modelocked average output power with 672-fs pulses at 1022 nm.
We probed 672-fs VECSEL chip with the same Ti:sapphire laser previously described for the pump-probe measurements; the center wavelength was adjusted to 1020 nm and with a measured FWHM bandwidth of 12.3 nm [Fig. 5(a)].
To accurately measure the VECSEL reflectivity, we used a setup similar to . The setup adds about 5000 fs2 of group delay dispersion (GDD), therefore stretching the initial 100-fs pulse to 170 fs [Fig. 5(b)]. We test different pulse durations by stretching the pulses with 1, 3, 5, and 7 passages through a 9-cm block of SF-10 glass, adding roughly 9000 fs2 of GDD per passage. As shown in Fig. 5(c), we obtained a maximum pulse duration of 1.72 ps before the setup, corresponding to 1.89 ps on the sample. The VECSEL was mounted on a temperature stabilized heat sink and pumped with a cw multimode 808-nm diode laser array. During the measurement, we set the heat sink temperature to 5°C and the pump intensity to 57 kW/cm2.
The measured reflectivity curves are shown in Fig. 6(a). We observe that the small signal gain is not significantly affected by the pulse duration. However, longer pulse durations decrease the induced TPA losses [Fig. 6(a)] and also increase the gain saturation fluence [Fig. 6(b)]. When we use the input parameters summarized in Table 1 for the 672-fs VECSEL into the RE model, we obtain simulated reflectivity curves which are in good agreement with the measured data points [Fig. 6(a)]. The extracted numerical values for the gain saturation fluence (defined as in ) could also be reproduced by the simulation [Fig. 6(b)].
The measured behavior is explained as a consequence of spectral hole burning as follows. The incoming pulse stimulates recombination in the QW energetic region covered by the pulse spectrum (in our model) and burns a spectral hole in the QW population. For low pulse fluence, the spectral hole is shallow and no effect of pulse duration on the small signal gain is observed. On the other hand, as the pulse fluence increases, the spectral hole deepens and is consequently filled via the decay of carriers from the reservoir (). However, if the pulse duration is shorter or comparable to the typical intraband carrier relaxation time, the hole is not completely refilled during the time the pulse is interacting with the QW. This decreases the carrier density available for the pulse amplification and results in a gain saturation which limits the laser average output power and pulse energy in ultrafast operation.
6. Analysis of the 100-fs VECSEL
In this section, we apply the RE model to fully describe the cavity elements used in the 100-fs VECSEL result reported in . In particular, we obtain quantitative information on the maximum pulse fluence reachable in modelocked operation and on the maximum achievable output coupling (OC) rates. Moreover, we explore the possible advantages of chirped ps-pulses (with subsequent external pulse compression) in terms of output power and efficiency.
Finally, since two different mechanisms (i.e. TPA and gain saturation) are decreasing the effective gain for short pulses, we want to better understand their significance in limiting high-power and efficient ultrafast operation.
6.1 Simulation of the 100-fs VECSEL result
We measured gain saturation for the 100-fs VECSEL under the same experimental conditions that allowed short pulse generation, as reported in . We matched the probing center wavelength to the lasing center wavelength (1034 nm) and applied the same heat-sink temperature (1°C) and pump intensity (21 kW/cm2). We then fitted the measurement to obtain the correct parameters for the RE model [Fig. 7(a)]. The same was done to reproduce the saturation characteristic of the SESAM used in  [Fig. 7(b)]. The SESAM recovery time of 1.5 ps was directly measured in the pump-probe setup. The parameters used in simulations for the 100-fs VECSEL are summarized in Table 1. It is important to emphasize that the model parameters summarized in Table 1 are in the same range for the different SDLs, which is not surprising since all the SDL materials are very similar.
Using Eq. (7), we reproduced the reflectivity of the 100-fs VECSEL cavity (obtained as the sum of the VECSEL’s and SESAM’s saturation curves) with a pulse repetition rate of 1.6 GHz and a 100-fs pulse duration as described in . In Fig. 7(c) we observe a cavity reflectivity maximum at a fluence of F0 = 6 µJ/cm2, which is in good agreement with the actual modelocking fluence of 6.5 µJ/cm2. As expected from the model, the laser operates close to the maximum of cavity amplification, where an optimal balance between the effects of unsaturated SESAM, saturated gain and TPA losses occurs.
The quantity F0 indicates the intracavity pulse fluence that the laser reaches in modelocked operation while the OC rate (defined as R(F0) - 100% - cavity losses) sets the power fraction that can be extracted at every roundtrip. Therefore, the combination of the two quantities represents a figure of merit for output power and efficiency of SDLs.
From Fig. 7(c), we extracted R(F0) = 101.2% for for the 100-fs VECSEL generating 100-fs pulses at 1.6 GHz. In addition, we need to consider ≈0.3% of additional fluence-independent cavity losses mainly introduced by the intracavity Brewster plate, which leads to a total OC rate of 0.9%, in agreement with our previous results .
6.2 Simulation of long pulse operation
We simulated the same cavity for 100-fs VECSEL with different pulse durations. We clearly observe that longer pulses shift F0 to higher fluences [Fig. 7(c)]: for a 4-ps pulse, F0 = 12 µJ/cm2 which is two times the intracavity pulse energy compared to a 100-fs pulse under the same conditions. This comes at the expense of a reduced OC rate for two reasons:
- 1. The fast SESAM recovery introduces significant losses for long pulses, increasing the effective absorber saturation fluence. This can be avoided by using a slower saturable absorber.
- 2. A long pulse extracts carriers more efficiently from the gain QWs. Due to the high repetition rate of the pulse interacting with the gain on the VECSEL (for a V-shaped cavity ≈2 frep), the QW cannot be completely refilled in the short interval between two pulses. The stationary population level reached by the QWs after several roundtrips is then reduced together with the gain.
In conclusion, the advantages of a chirped pulse formation in SDL cavities, which would in principle allow for a higher F0 are strongly reduced when a fast saturable absorber is used. In addition, repetition rates below the GHz range cannot be reached without encountering multi pulse instabilities due to the short carrier lifetime in the QW conduction band and also intracavity multi-pass geometries [47, 48] do not reduce the effective repetition rate experienced by the gain chip.
6.3 Effects of gain saturation and TPA
Without modifying the SESAM parameters, we simulated the 100-fs VECSEL cavity for 100‑fs pulses removing separately the effects of gain saturation and TPA in the VECSEL chip. As seen in Fig. 7(d), TPA is not playing a dominant role at the low F0 values we are considering. In contrast, gain saturation is seriously limiting the VECSEL performance: an unsaturable VECSEL could reach an F0 value twice as high with roughly 1.5 times the OC rate compared to the actual results, meaning 3 times the average output power and pulse energy. The best performances would be clearly achieved in case of absent saturation and TPA, approaching the behavior of solid state lasers, which don’t suffer from these limitations .
7. Analysis of the 184-fs MIXSEL and optical-to-optical efficiency
7.1 MIXSEL saturation
We measured the fluence-dependent reflectivity for the 184-fs MIXSEL and for the 253-fs MIXSEL described in . Thanks to its monolithic structure including both gain and absorber in the same chip, the MIXSEL offers a direct access to F0. We probed the MIXSEL reflectivity at the same lasing conditions (same center wavelength, pump intensity, heat-sink temperature and comparable pulse durations).
As shown in Fig. 8(a) the measured F0 values are in good agreement with the experimental modelocking fluences observed for the two lasers, confirming the correlation between F0 and laser’s operation point. We fitted the reflectivity measurements of 184-fs MIXSEL chip [Fig. 8(b)] according to Eq. (6) and extracted the parameters reported in Table 1, which we then use in the following for optical-to-optical efficiency calculations. The maximum OC rate for 184-fs MIXSEL is measured to be 0.68% and F0 around 7 µJ/cm2, both slightly higher compared to the experimental modelocking values. The low probing repetition rate of 80 MHz allows for maximum refilling of the QWs and therefore a higher F0 compared to the 4.33-GHz pulse repetition rate, while the cavity losses, principally introduced by the intracavity Brewster plate, reduced TOC to 0.44%. When these effects are taken into account, the model reproduces correctly the actual performance.
7.2 Calculation of optical-to-optical efficiency
We define the optical-to-optical pump efficiency η of the MIXSEL as the ratio between the emitted modelocked power and the incident optical pump power. We used the RE model to numerically reproduce the experimental efficiency value observed for the 184-fs MIXSEL result. Efficiency is a fluence-dependent quantity and hereinafter we will calculate its value at the laser working fluence F0, which in turn varies with the pulse duration and the pulse repetition rate. We determine from:
We obtain = 0.97% for the 184-fs MIXSEL at a pulse repetition rate of 4.33 GHz, in good agreement with the experimental value = 0.65%. Since we do not take into account any recombination process during carrier diffusion in the pumped GaAs and GaAs0.94P0.06 barriers, we expected the calculated efficiency to be slightly higher than the real efficiency.
7.3 Possible solutions to reach higher pump efficiency
Higher pump efficiencies of several percent are reported in [14, 50] for ultrafast SDLs generating picosecond pulses. However, we would like to emphasize that stays below 1.3% for the 184-fs MIXSEL chip when modelocking is simulated for pulse durations up to 10 ps. As discussed for the 100-fs VECSEL, in ps-operation the incomplete QW refilling and the increased absorber losses prevent significant increases in F0 and OC. This cancels the beneficial effects on the efficiency of the higher gain saturation experimented by long ps-pulses (Fig. 9).
A different behavior is observed when the recovery time of the embedded absorber is increased by a factor of 10, from 2.5 ps to 25 ps. According to , sub-300-fs operation cannot be obtained with such a slow saturable absorber but from Fig. 9 we can conclude that would actually be increased to about 3% for 10-ps pulses, which is in agreement with the previously demonstrated better pump efficiency for picosecond MIXSELs.
According to Eq. (9), a short carrier lifetime in the conduction band of the QW gain is the most detrimental parameter for the optical-to-optical pump efficiency. The pulse can interact with the gain medium only for a small fraction of a roundtrip time, while for the remaining time carriers diffuse through the barriers into the QWs and spontaneously recombine before contributing to pulse amplification. We simulated the 184-fs MIXSEL with a τlife five times higher compared to the experimental value, obtaining a significant efficiency increase for all pulse durations, with exceeding 8% for a 3-ps pulse duration.
As indicated in Eq. (9), a shorter roundtrip time reduces the relative efficiency drop caused by spontaneous emission. We simulated modelocked operation for the 184-fs MIXSEL at higher pulse repetition rates of 10 and 30 GHz keeping the pulse duration fixed at 184 fs. In Fig. 10(a) we cannot observe an improvement of F0 and available OC rate with higher pulse repetition rates. This is consistent with what was measured in : higher repetition rates come at the expense of reduced intracavity pulse fluence and OC rate.
Compared to the 4.33-GHz result we observe a higher efficiency at 10 GHz (= 1.66%), but then a lower efficiency for 30 GHz ( = 0.85%). This means that reduced gain for higher pulse repetition rates cancels the potential benefit of the reduced losses of the excited carriers with shorter cavity roundtrip times. One can compare the QW population dynamics in Figs. 10(b)-10(d), simulated at different repetition rates at the respective F0. The overall carrier population, and therefore the gain is decreased by the more frequent incoming pulses on the MIXSEL chip.
In conclusion, a longer carrier lifetime in the conduction band is the most promising solution to increase the optical-to-optical pump efficiency for femtosecond SDLs.
8. Conclusion and outlook
In this paper, we have demonstrated a new world-record MIXSEL performance with pulses as short as 184 fs, with an average output power of 115 mW, a pulse repetition rate of 4.33 GHz and a center wavelength of 1048 nm. This corresponds to a peak power of 127 W. The MIXSEL chip has 10 InGaAs QWs for the gain and one single InGaAs QW for the saturable absorber. We used a simple linear cavity with an output coupler transmission of 0.44% and an intracavity Bewster plate to obtain linear polarization. This new result was obtained with a pump efficiency of only 0.65% and unfortunately confirms the trade-off in output power and optical-to-optical pump efficiency with shorter pulses.
To explain in more details the physical reasons for this trade-off, we employed and justified a rate equation (RE) model describing the InGaAs QWs normally used as active medium. By making careful approximations it was possible to make the model parameters accessible through direct measurements or fits of available experimental data. Despite its simplicity compared to other QW laser dynamical models, our model succeeds to accurately reproduce the experimental gain saturation curves obtained by probing the reflectivity of a pumped VECSEL at different pulse durations and correctly describes the output power and the pump efficiency for several different ultrafast SDL results based on SESAM modelocked VECSELs and MIXSELs. For shorter pulses, spectral hole burning decreases the carrier density available for the pulse amplification and therefore increases gain saturation effects and lowers the output power.
With the intent of analyzing the behavior of a full SDL cavity, we measured and fitted the VECSEL and the SESAM used for the 100-fs pulse generation presented in . We concluded that the operation point of a modelocked SDL is set by the macroscopic fluence parameter F0, where the cavity round-trip pulse amplification is maximized. We can conclude that gain saturation in general and not TPA in the VECSEL chip is the dominant process that limits F0, the output coupling rate and therefore the output power.
The saturation characteristic was also measured and fitted for the 184-fs MIXSEL and confirmed our understanding from the ultrafast VECSEL analysis. Furthermore, a more detailed study on optical-to-optical pump efficiency was carried out searching for possible improvements. Long picosecond pulses are less affected by spectral hole burning but can achieve higher efficiencies only if the absorber recovery is kept slow (in the tens of picosecond). Higher repetition rates can in principle benefit from higher frequent and efficient amplification in the gain chip, but they do not offer improved efficiency performances because of the incomplete carrier refilling of the QWs between two consecutive pulses. We found that the main efficiency limitation is given by the short carrier lifetime in the conduction band of our QWs (measured to be approximately 140 ps). This low carrier lifetime is typical for high-power ultrafast SDLs with a typical output coupler of less than 1%.
From this analysis we can conclude that the main parameter that needs to be optimized for more efficient femtosecond SDLs is the carrier lifetime. We believe that significant improvements can be achieved with quantum dot (QD) instead of QW gain materials.
Swiss Confederation Program Nano-Tera.ch, which was scientifically evaluated by the Swiss National Science Foundation (SNSF).
The authors acknowledge support of the technology and cleanroom facility FIRST for advanced micro-and nanotechnology.
References and links
1. U. Keller and A. C. Tropper, “Passively modelocked surface-emitting semiconductor lasers,” Phys. Rep. 429(2), 67–120 (2006). [CrossRef]
2. B. W. Tilma, M. Mangold, C. A. Zaugg, S. M. Link, D. Waldburger, A. Klenner, A. S. Mayer, E. Gini, M. Golling, and U. Keller, “Recent advances in ultrafast semiconductor disk lasers,” Light Sci. Appl. 4(7), e310 (2015). [CrossRef]
3. M. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked semiconductor disk lasers,” Adv. Opt. Photonics 8(3), 370–400 (2016). [CrossRef]
4. S. Hoogland, S. Dhanjal, A. C. Tropper, J. S. Roberts, R. Haring, R. Paschotta, F. Morier-Genoud, and U. Keller, “Passively mode-locked diode-pumped surface-emitting semiconductor laser,” IEEE Photonics Technol. Lett. 12(9), 1135–1137 (2000). [CrossRef]
5. M. Kuznetsov, F. Hakimi, R. Sprague, and A. Mooradian, “High-power (>0.5-W CW) diode-pumped vertical-external-cavity surface-emitting semiconductor lasers with circular TEM00 beams,” IEEE Photonics Technol. Lett. 9(8), 1063–1065 (1997). [CrossRef]
6. S. H. Park, J. Kim, H. Jeon, T. Sakong, S. N. Lee, S. Chae, Y. Park, C. H. Jeong, G. Y. Yeom, and Y. H. Cho, “Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,” Appl. Phys. Lett. 83(11), 2121–2123 (2003). [CrossRef]
7. M. Guina, A. Härkönen, V.-M. Korpijärvi, T. Leinonen, and S. Suomalainen, “Semiconductor Disk Lasers: Recent Advances in Generation of Yellow-Orange and Mid-IR Radiation,” Adv. Opt. Technol. 2012(19), 265010 (2012).
8. R.-I. Arash, “Recent advances in VECSELs,” J. Optics-UK 18(9), 093003 (2016). [CrossRef]
9. B. Rudin, A. Rutz, M. Hoffmann, D. J. H. C. Maas, A.-R. Bellancourt, E. Gini, T. Südmeyer, and U. Keller, “Highly efficient optically pumped vertical-emitting semiconductor laser with more than 20 W average output power in a fundamental transverse mode,” Opt. Lett. 33(22), 2719–2721 (2008). [CrossRef] [PubMed]
10. B. Heinen, T. L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48(9), 516–517 (2012). [CrossRef]
11. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996). [CrossRef]
12. D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3(8), 844–852 (2016). [CrossRef]
13. D. J. H. C. Maas, A.-R. Bellancourt, B. Rudin, M. Golling, H. J. Unold, T. Südmeyer, and U. Keller, “Vertical integration of ultrafast semiconductor lasers,” Appl. Phys. B 88(4), 493–497 (2007). [CrossRef]
14. B. Rudin, V. J. Wittwer, D. J. H. C. Maas, M. Hoffmann, O. D. Sieber, Y. Barbarin, M. Golling, T. Südmeyer, and U. Keller, “High-power MIXSEL: an integrated ultrafast semiconductor laser with 6.4 W average power,” Opt. Express 18(26), 27582–27588 (2010). [CrossRef] [PubMed]
16. M. Mangold, C. A. Zaugg, S. M. Link, M. Golling, B. W. Tilma, and U. Keller, “Pulse repetition rate scaling from 5 to 100 GHz with a high-power semiconductor disk laser,” Opt. Express 22(5), 6099–6107 (2014). [CrossRef] [PubMed]
18. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, Submitted to Science (January 2017).
19. O. D. Sieber, M. Hoffmann, V. J. Wittwer, M. Mangold, M. Golling, B. W. Tilma, T. Südmeyer, and U. Keller, “Experimentally verified pulse formation model for high-power femtosecond VECSELs,” Appl. Phys. B 113(1), 133–145 (2013). [CrossRef]
20. K. Sugioka and Y. Cheng, “Ultrafast lasers—reliable tools for advanced materials processing,” Light Sci. Appl. 3(4), e149 (2014). [CrossRef]
21. R. Aviles-Espinosa, G. Filippidis, C. Hamilton, G. Malcolm, K. J. Weingarten, T. Südmeyer, Y. Barbarin, U. Keller, S. I. C. O. Santos, D. Artigas, and P. Loza-Alvarez, “Compact ultrafast semiconductor disk laser: targeting GFP based nonlinear applications in living organisms,” Biomed. Opt. Express 2(4), 739–747 (2011). [CrossRef] [PubMed]
22. C. A. Zaugg, A. Klenner, M. Mangold, A. S. Mayer, S. M. Link, F. Emaury, M. Golling, E. Gini, C. J. Saraceno, B. W. Tilma, and U. Keller, “Gigahertz self-referenceable frequency comb from a semiconductor disk laser,” Opt. Express 22(13), 16445–16455 (2014). [CrossRef] [PubMed]
23. A. H. Quarterman, L. E. Hooper, P. J. Mosley, and K. G. Wilcox, “Gigahertz pulse source by compression of mode-locked VECSEL pulses coherently broadened in the normal dispersion regime,” Opt. Express 22(10), 12096–12101 (2014). [CrossRef] [PubMed]
24. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, “Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation,” Appl. Phys. B 69(4), 327–332 (1999). [CrossRef]
25. A. Klenner, A. S. Mayer, A. R. Johnson, K. Luke, M. R. E. Lamont, Y. Okawachi, M. Lipson, A. L. Gaeta, and U. Keller, “Gigahertz frequency comb offset stabilization based on supercontinuum generation in silicon nitride waveguides,” Opt. Express 24(10), 11043–11053 (2016). [CrossRef] [PubMed]
26. A. S. Mayer, A. Klenner, A. R. Johnson, K. Luke, M. R. E. Lamont, Y. Okawachi, M. Lipson, A. L. Gaeta, and U. Keller, “Frequency comb offset detection using supercontinuum generation in silicon nitride waveguides,” Opt. Express 23(12), 15440–15451 (2015). [CrossRef] [PubMed]
28. I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1(4), 192–197 (2014). [CrossRef]
29. J. Hader, M. Scheller, A. Laurain, I. Kilen, C. Baker, J. V. Moloney, and S. W. Koch, “Ultrafast non-equilibrium carrier dynamics in semiconductor laser mode-locking,” Semicond. Sci. Technol. 32(1), 013002 (2017). [CrossRef]
30. I. Kilen, S. W. Koch, J. Hader, and J. V. Moloney, “Fully microscopic modeling of mode locking in microcavity lasers,” J. Opt. Soc. Am. B 33(1), 75–80 (2016). [CrossRef]
31. N. Tessler and G. Eisenstein, “Modelling carrier dynamics and small-signal modulation response in quantum-well lasers,” Opt. Quantum Electron. 26(7), S767–S787 (1994). [CrossRef]
32. N. Tessler and G. Eistenstein, “On carrier injection and gain dynamics in quantum well lasers,” IEEE J. Quantum Electron. 29(6), 1586–1595 (1993). [CrossRef]
33. H. Dery, B. Tromborg, and G. Eisenstein, “Carrier-carrier relaxation kinetics in quantum well semiconductor structures with nonparabolic energy bands,” Phys. Rev. B 68(16), 165323 (2003). [CrossRef]
34. C. G. E. Alfieri, A. Diebold, F. Emaury, E. Gini, C. J. Saraceno, and U. Keller, “Improved SESAMs for femtosecond pulse generation approaching the kW average power regime,” Opt. Express 24(24), 27587–27599 (2016). [CrossRef] [PubMed]
35. T. R. Schibli, E. R. Thoen, F. X. Kärtner, and E. P. Ippen, “Suppression of Q-switched mode locking and break-up into multiple pulses by inverse saturable absorption,” Appl. Phys. B 70(S1Suppl.), S41–S49 (2000). [CrossRef]
36. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997). [CrossRef]
37. N. Tessler, R. Nagar, and G. Eisenstein, “Structure dependent modulation responses in quantum-well lasers,” IEEE J. Quantum Electron. 28(10), 2242–2250 (1992). [CrossRef]
38. H. Toktamiş, B. Gönül, and M. Oduncuoğlu, “Comparative study of the band-offset ratio of conventionally strained and strain-compensated InGaAs/GaAs QW lasers,” Physica E 24(3–4), 183–186 (2004). [CrossRef]
40. J. Hader, J. V. Moloney, and S. W. Koch, “Microscopic analysis of non-equilibrium dynamics in the semiconductor-laser gain medium,” Appl. Phys. Lett. 104(15), 151111 (2014). [CrossRef]
41. O. Karni, A. K. Mishra, G. Eisenstein, V. Ivanov, and J. P. Reithmaier, “Coherent control in room-temperature quantum dot semiconductor optical amplifiers using shaped pulses,” Optica 3(6), 570–576 (2016). [CrossRef]
42. A. P. Ongstad, D. J. Gallant, and G. C. Dente, “Carrier lifetime saturation in InGaAs single quantum wells,” Appl. Phys. Lett. 66(20), 2730–2732 (1995). [CrossRef]
43. C. K. Sun, B. Golubovic, H. K. Choi, C. A. Wang, and J. G. Fujimoto, “Femtosecond investigations of spectral hole burning in semiconductor lasers,” Appl. Phys. Lett. 66(13), 1650–1652 (1995). [CrossRef]
44. M. Asada, “Intraband relaxation time in quantum-well lasers,” IEEE J. Quantum Electron. 25(9), 2019–2026 (1989). [CrossRef]
45. C. Baker, M. Scheller, S. W. Koch, A. R. Perez, W. Stolz, R. Jason Jones, and J. V. Moloney, “In situ probing of mode-locked vertical-external-cavity-surface-emitting lasers,” Opt. Lett. 40(23), 5459–5462 (2015). [CrossRef] [PubMed]
46. M. Mangold, V. J. Wittwer, O. D. Sieber, M. Hoffmann, I. L. Krestnikov, D. A. Livshits, M. Golling, T. Südmeyer, and U. Keller, “VECSEL gain characterization,” Opt. Express 20(4), 4136–4148 (2012). [CrossRef] [PubMed]
47. M. Butkus, E. A. Viktorov, T. Erneux, C. J. Hamilton, G. Maker, G. P. A. Malcolm, and E. U. Rafailov, “85.7 MHz repetition rate mode-locked semiconductor disk laser: fundamental and soliton bound states,” Opt. Express 21(21), 25526–25531 (2013). [CrossRef] [PubMed]
48. C. A. Zaugg, A. Klenner, O. D. Sieber, M. Golling, B. W. Tilma, and U. Keller, “Sub-100 MHz Passively Modelocked VECSEL,” in CLEO:2013, OSA Technical Digest (online) (Optical Society of America, 2013), CW1G.6.
50. C. G. E. Alfieri, D. Waldburger, S. M. Link, E. Gini, M. Golling, B. W. Tilma, M. Mangold, and U. Keller, “Recent progress in high power ultrafast MIXSELs,” in Proc. SPIE (2016), p. 973407.