Optically pumped passively modelocked vertical external-cavity surface-emitting lasers (VECSELs) can generate pulses as short as 100 fs with an intracavity semiconductor saturable absorber mirror (SESAM). Very stable soliton modelocking can be obtained, however, the high-Q-cavity, the short gain lifetime, and the kinetic-hole burning can also support rather complex multipulse instabilities which we analyze in more details here. This onset of multipulse operation limits the maximum average output power with fundamental modelocking and occurs at the roll-over of the cavity round trip reflectivity. Unfortunately, such multipulse operation sometimes can mimic stable modelocking when only limited diagnostics are available.
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Optically pumped semiconductor disk lasers (SDLs) are high-power laser sources which convert low-coherence light from pump diode arrays into high brightness beams with excellent quality. Semiconductor bandgap engineering can set the center wavelength of this source from the visible to the mid-infrared . In particular, optically pumped vertical external-cavity surface-emitting lasers (VECSELs)  have demonstrated continuous wave (cw) operation with an average output power as high as 20 W in fundamental transverse mode and 106 W in multimode [3,4]. The first ultrafast VECSEL was modelocked with a semiconductor saturable absorber mirror (SESAM)  in 2000 . Since then, the performance of ultrafast SDLs has been improved, as summarized in recent reviews [1,7–9]. In SESAM-modelocked operation, pulse repetition rates range from 85 MHz up to 100 GHz [10,11] and emission wavelengths from 489 nm up to 1960 nm have been demonstrated [12,13]. The best performance in terms of power and pulse duration has been achieved inthe 1-µm wavelength range (Fig. 1), with pulse durations as short as 100 fs combined with pulse peak powers in the kW-range at gigahertz repetition rates. The performance of modelocked SDLs has become comparable with fiber, Ti:sapphire, and diode-pumped solid state lasers. Many applications have been demonstrated such as multi-photon imaging [15,16] and frequency comb metrology [17–20].
Here, we investigate the complex multipulse instabilities of a high-power 100-fs SESAM-modelocked VECSEL (red circles in Fig. 1) . We carefully analyze different modelocking states and their hysteresis depending on the pump power. We find that the maximum power in fundamental modelocking operation is not limited by thermal effects, but by the onset of multipulse instabilities, where more than one pulse oscillates in the laser cavity. While some applications may tolerate multipulse operation or some minor intensity fluctuations, other applications such as frequency metrology become only possible with low intensity noise, low timing jitter, or even a stabilized carrier envelope offset frequency . Stable modelocking with excellent low noise operation has been demonstrated for such lasers [22,23]. The onset of multipulse operation currently limits the output power and a better understanding is required to further scale the power in fundamental modelocking. Additionally, the multipulse analysis provides new insights in the physics of highly inverted semiconductor structures at the timescale of 100 fs, where interesting effects start to play a role, such as kinetic hole burning, theoretically predicted by fully microscopic many-body models [24,25]. Comprehensive modelocking characterization allows us to compare the different modelocking states. The similarity of single measurement parameters for different modelocking states shows the importance of a clean and complete characterization to proof fundamental modelocking, as described in [26,27]. Finally, with an extensive characterization of the nonlinear reflectivity of the VECSEL and SESAM, we can show that the onset of multipulse operation occurs at the roll-over of the total cavity round trip reflectivity.
The VECSEL used for the more detailed investigation of multipulse dynamics can generate stable 100-fs pulses in fundamental modelocking and has been described in . We operate the laser in the same configuration that allowed the shortest pulses reported in  (i.e. same SESAM and VECSEL chips, same cavity design and heat-sink temperatures), however, we then continued to increase the pump power.
We observe that, once the laser has reached a certain maximum average output power in fundamental modelocking operation, more pump power does not simply increase of average output power with the same slope efficiency. Before thermal roll-over starts to occur, we observe several steps in increased output power with different modelocking states for which multiple pulses simultaneously oscillate in the cavity. We also observe a hysteresis effect for which these modelocking states depend on the pump history with continuously increased or decreased pump power (Fig. 2). To carefully analyze every modelocking state, we therefore characterized the laser performance at different pump powers. Clear discontinuities in average output power appear when ramping up the pump power [Fig. 2(a)], which also indicate a new modelocking regime [Fig. 2(b)].
Increasing the pump intensity starting from a low level, we observe a first threshold at a pump power of 20 W, where lasing action in fundamental modelocking begins. Then at 22.6 W, we observe an abrupt increase of the average output power by a factor of 1.6 and, similarly, new discontinuities are observed at 24.8 W and 27 W. A clear hysteresis effect is observed when starting from a high pump level and continuously decreasing the pump power during which we do not reproduce the same average output power and also not in all cases the same multipulse state. Compared to the “increasing pump path”, the laser delivers a higher average output power when the pump is between 27.7 and 22.9 W. Fundamental modelocking operation, with only one pulse per cavity round trip, extends to a lower pump power of17.2 W. Hysteresis behaviors for SDLs in modelocking operation were already reported for picosecond pulses . However, the femtosecond modelocking states we want to analyzed here [Fig. 2(b)] differ from what was previously characterized and are referred to as:
- • Fundamental modelocking: One single pulse oscillates in the laser cavity.
- • Side pulse: An additional side pulse close to the main pulse with a temporal spacing much shorter than the cavity round trip time.
- • Double pulse: Two pulses oscillate in the laser cavity, spaced by approximately a quarter of the cavity round trip time.
- • Double & side pulse: A combination of side pulse and double pulse operation, where we have two pulse groups or a pulse and a pulse group separated by approximately a quarter of the cavity round trip time similar to the double pulse operation. The pulse groups features a main pulse accompanied by a side pulse similar to the side pulse operation. The total number of pulses adds up to three or four pulses.
2.1 Pulse duration
The pulse duration is measured with a non-collinear second-harmonic generation (SHG) autocorrelation (FR-103MN from Femtochrome Resarch, Inc). The autocorrelation traces of the fundamental and the double pulse states [Fig. 3(a)] are fitted with the autocorrelation of a sech2-pulse with a pulse duration τpulse. They feature one single pulse, whereas the autocorrelation of the side pulse and double & side pulse states indicates the presence of two pulses next to each other [Fig. 3(a)]. These traces can be fitted with two subsequent sech2-pulses separated by τsep with an asymmetric intensity ratio of the two pulses [Fig. 3(b)].
The pulse duration of the fundamental state reaches the minimum value just before the transition to side pulse operation [Fig. 4(a)], as the laser cavity is optimized for the shortest pulse duration in fundamental modelocking at the highest possible average power. The pulse durations of the side pulse and double & side pulse states are slightly longer with a side pulseasymmetry of roughly 61% and 27%, respectively. We also remark that the separation of the side pulse increases with increasing pump power from 270 to 340 fs. For the double pulse state, the pulse duration is shorter again, similar to the values observed for the fundamental state [Fig. 4(a)]. Interestingly, sweeping the hysteresis path going down from high pump intensity, we obtain even shorter pulse durations (94 fs instead of 96 fs) for the fundamental state when we reach it from a multipulse state [Fig. 4(a)].
2.2 Optical spectrum
The optical spectrum is measured with a fiber coupled optical spectrum analyzer HP 70952B with a resolution of 0.1 nm [Fig. 5(a)]. All optical spectra show no indication of any instability or continuous wave breakthroughs. While the optical spectra are almost sech2-shaped for the fundamental and double pulse states, the optical spectra of the side pulse and double & side pulse states feature shoulders on both the short and long wavelength side. The center wavelength shifts almost linearly (0.65 nm/W) to higher wavelengths with increasingpump power. The fundamental state features the broadest spectral full width at half maximum (FWHM), while the multipulse states at higher pump powers have a narrower spectrum [Fig. 4(b)]. Interestingly, the optical bandwidths of the fundamental states are reduced (from 15.9 nm to 13.5 nm) after the back transition from multipulse states. Combined with the shorter pulse duration, this corresponds to a decrease of the time-bandwidth product from 0.43 to 0.34 at the center wavelength of 1035 nm. Which means that the chirp of the pulse substantially changed while the average output power of 96 mW stayed the same.
2.3 Noise characterization
The first harmonic of the pulse repetition rate is analyzed with the signal source analyzer E5052B from Agilent with a resolution bandwidth of 97.7 Hz resulting in a high signal-to-noise ratio of approximately 80 dB. For this, the laser intensity is measured with a highly linear photodiode (HLPD from Discovery Semiconductor). The microwave spectra are centered around the pulse repetition rate of 1.641 GHz with a span of 10 MHz [Fig. 5(b)]. For the fundamental and the double pulse states, the microwave spectra feature a delta like peak, without any visible broadening or pedestal, as it is theoretically expected for stable fundamental modelocking. The side pulse and double & side pulse states can be clearly identified by the 3 pairs of side peaks below −25 dBc next to the main peak of the pulse repetition rate. The side peak separation is 0.95 and 0.81 MHz for the double pulse and double & side pulse state, respectively. These side peaks indicate a modulation of the pulse train intensity. We assume an intensity variation of the main and the side pulse similar to theirregular pulse train with varying intensities predicted by the simulation result descried in section 3.1 and illustrated in Fig. 8(b). The intensity modulation of the pulse train is further revealed by the additional noise peaks in the amplitude and phase noise at the given frequencies (Fig. 6). The amplitude and phase noise of the first harmonic of the repetition rate is measured using the same signal source analyzer.
2.4 Temporal dynamics
So far, the presented measurements do not differentiate between the fundamental and the double pulse state or between the side pulse and the double & side pulse state. But, a difference becomes evident when looking at the laser intensity over several cavity round trip times [Fig. 7(a)]. The time traces are measured with a sequential equivalent-time sampling scope (CSA 803 from Tektronix with a 50-GHz sampling unit SD-32) and a high-speed photodetector (Model 1454 from Newport with an 18.5-ps rise time) amplified by an 18-GHz bandwidth preamplifier (87405C from Agilent).
While for fundamental and the side pulse state one pulse per round trip is measured, an additional pulse is observed for the double pulse and the double & side pulse state. In contrast to second harmonic modelocking where the separation of the additional pulse is given by one half of the round trip time , the additional pulse is separated by one quarter of the round trip time. For the side pulse and double & side pulse states, the pulse separation τsep is too small and cannot be resolved with the sampling scope. Only when we characterize the modelocking with both the autocorrelation and the sampling scope we can directly observe the full number of pulses simultaneously oscillating in the cavity (i.e. one pulse for the fundamental, two for the side pulse, two for the double pulse, and four for the double & side pulse state).
The dynamics of the VECSEL is further characterized by a microwave spectrum analyzer (8565EC from Agilent) using the same high-speed photodetector and preamplifier. A stable fundamentally modelocked laser creates equally powerful harmonic peaks positioned at the repetition rate and at multiples of the repetition rate as measured for the fundamental and side pulse states [Fig. 7(b)], only limited by the bandwidth of the preamplifier for frequencies >18 GHz. Again, the two pulses separated by τsep of the side pulse and double & side pulse state are below the resolution of the photodetector and therefore are not resolved in the microwave spectrum measurement. For the double pulse and double & side pulse states, where the pulses are spaced by a quarter of the round trip time, the higher harmonics are periodically modulated [Fig. 7(b)]. This stands in contrast to second harmonic modelocking,where only even harmonics would be visible and the fundamental frequency, corresponding to the inverse of the cavity round trip time, would not be visible at all.
The modelocking analysis reveals different hysteresis effects. Similar to what was reported for the antiresonant gain medium design in , we see a large hysteresis loop of the fundamental state, such that the stable fundamental modelocking continues far below the original threshold [Fig. 2(a)]. Smaller hysteresis loops are observed for the other modelocking states. The double pulse state is special. It is more stable than the side pulse state and sometimes it switches directly back to fundamental modelocking, if the pump power is reduced. The double pulse states also have an increased average power with slightly longer pulses during the “decreasing pump path” when compared to the “increasing pump path”.
Interesting is also the hysteresis of the fundamental states which have shorter pulse durations with narrower spectral bandwidths on the “decreasing pump path”. This shows that different stable modelocking states can exist for one given pump power. These features are going beyond the theoretical predictions of a fully microscopic many-body simulation .
To gain insights into the dynamical formation and stability of different modelocked pulse trains, we are using a simulation based on coupled multi-delay differential equations. In contrast to the delay model widely used for a ring cavity modelocked laser [29–31], our modeling approach considers the geometry of the V-shape without the need to change to the numerically demanding traveling wave approach. Previous works on VECSEL simulations either do not consider the effects induced by the cavity geometry [32,33] or do not allow for an efficient simulation of large external cavities [25,34]. To obtain our numerically efficient description of the VECSEL dynamics, we integrate the traveling-wave equation for the electric field amplitude E ± (z, t) and the excess charge-carrier density N(z, t) 36] for small sections ∆z. We then consider the limit of infinitely thin gain and SESAM sections with integrated carrier densities G(t) and Q(t). The free space between the optical elements is treated as large passive sections. Expressing the electric fields in all sections in terms of the electric field A(t) at the out-coupling mirror (OC) leads to a system of three coupled multi-delay differential equations Eq. (2)-(4).29], contain both propagation directions and the spatial configuration of the VECSEL cavity, which is encoded in the time delays τ1 and τ2. Charge-carrier induced amplitude-phase coupling is omitted in this model, but could easily be included for future studies by introducing an alpha-factor in Eq. (1). The gain bandwidth is denoted by γ, the intensity losses per round trip by κ, the cold-cavity round trip time by T, the pump current by JG, the unsaturated absorption by JQ, the gain and absorber recovery times by γG and γQ, and the ratio between the gain and absorberdifferential by rs. The delay times are determined by the resonator configuration τ1 = LOC-VECSEL/vg and τ2 = LVECSEL-SESAM/vg, where LOC-VECSEL is the distance between OC and VECSEL chip, LVECSEL-SESAM is the distance between VECSEL chip and SESAM, and vg is the group velocity. In this model, we use an “ideal” pump current directly setting the electron density for the VECSEL gain, which is simpler than using an optical pump power.
For the parameter values given in Table 1, the laser described with Eq. (2)-(4) exhibits a range of pump currents JG with stable modelocked pulses whose width directly depend on the gain bandwidth γ and therefore on the number of longitudinal modes that participate in the modelocking process. We choose γ = 2000, which yields pulses that have a width of about 1-2 ps. This is longer than observed in the experiments, but in order to reach the experimental value much larger γ would be necessary leading to much longer computation times. We use the above value in the following numeric characterization to be able to effectively scan a wide parameter region. Investigations of the effects of larger γ are still ongoing.
This simulation reveals multistability and their hysteresis in a parameter scan of the pump current JG [Fig. 8(a)]. The dynamics for increasing and decreasing pump current are simulated. For illustration, the pulse peak intensities of a simulated pulse train are shown. We can clearly distinguish three regimes: fundamental modelocking, irregular pulse trains, and double pulse emission.
The region of irregular pulse trains is characterized by a periodic emission of irregular pulse “cluster” with varying pulse intensities [Fig. 8(b)]. Interestingly, the autocorrelation function determined from these irregular pulsating time series shows similarities with theexperimentally found side pulse state, because also in the simulations side pulses show up next to the main peak of the autocorrelation. Due to the chosen gain bandwidth γ, the pulse width is on the picosecond scale and thus also the distance between side and main peak is larger than experimentally observed. However, the similarities to both the experimentally observed parameter region and the measured autocorrelation suggest that these kind of dynamic instabilities can be one reason for the emergence of side pulses in the autocorrelation. An additional explanation of the dynamics behind the observed side pulse regime will be discussed in section. 3.4.
After the region of irregular pulse trains, the laser switches to the double pulse state. Compared to the fundamental state, the intensity of the double pulse states are drastically decreased because for this regime two pulses need to be amplified per round trip. And additionally, the absorber can completely recover between two pulses thus cause increased absorption which leads to a reduced output power. Such that for a given pump current, two double pulses, bistable to a single pulse, carry less combined power than the single pulse. For reducing pump current, the double pulse emission extends in the region of irregular pulse trains, similar to our experiments [Fig. 2(a)].
3.2 Double pulse operation
The two pulses of the double pulse state are spaced by roughly one quarter of the cavity round trip time, which differs from second harmonic modelocking where the pulse separation would be half of the cavity round trip time. This double pulse operation is similar to the multipulse operation reported in . In both cases a similar modulation of the higher harmonics of the repetition rate is measured with a microwave spectrum analyzer [Fig. 7(b)].
Simulations using the above mentioned coupled multi-delay differential equations indicate that the type of multipulse state strongly depend on the arrangement of the V-shaped laser cavity. Changing the delay times τ1 and τ2 corresponds to changing the resonator configuration, i.e. the two arms LOC-VECSEL and LVECSEL-SESAM of the V-shaped geometry. By keeping the total cavity length LCAVITY constant, we can scan the gain chip position within the cavity. Varying both the gain chip position and the pump current reveals different stability regions: no lasing, fundamental operation, double pulse state, second harmonic modelocking, irregular pulse trains, and higher order states. Parameter ranges clearly favoring second harmonic modelocking or the double pulse state are found [Fig. 9(a)]. At sufficient pump currents, the laser is expected to operate in the double pulse state when the gain chip is placed in the center of the cavity. Whereas, second harmonic modelocking is favored when the gain chip is placed closer to the OC or closer to the SESAM.
This can be explained by looking at the time evolution of the electric field intensity and the evolution of the gain for two cavity geometries [Fig. 9(b)]. The preferred pulse configuration is obtained for the case where the two pulses hit the gain chip are equally spaced in time. This allows for a balanced recovery of the gain between the pulses. Since the recovery of the SESAM absorption is much faster, it is not limiting here. When the gain chip is in the center of the cavity (LOC-VECSEL/LCAVITY = 0.5) the double pulse state is preferred and when the gain chip is closer to the OC or to the SESAM (LOC-VECSEL/LCAVITY = 0.25 or 0.75) second harmonic modelocking is preferred. For the distance ratio of 0.53 used in the experimental cavity, the favored configuration is the observed double pulse state.
Moreover, a central positioning of the gain chip also increases the region of stable fundamental modelocking towards higher pump currents and thereby allows for higher output powers. Similar to the multi-pulse operation, the central configuration ensures equal times between pulse incidents in the gain chip and thus ensures a balanced recovery.
3.3 Cavity round trip reflectivity
To gain a deeper insight of the modelocking mechanisms and the multipulse operation, we investigated in more details the saturation characterization of the VECSEL cavity. Similarly,as described by Alfieri et al. , we calculate the saturation of the cavity round trip reflectivity by combining the saturation of the VECSEL and the SESAM. For different average output power, we calculate the corresponding intracavity pulse energy given the pulse repetition rate and the output coupler reflectivity. With the know cavity spot size on the VECSEL and the SESAM, we than calculate the corresponding fluences which relate to different reflectivities of the elements. For the cavity round trip reflectivity of the V-shaped cavity, we multiply the output coupler reflectivity with the SESAM reflectivity and with twice the VECSEL reflectivity. The reflectivity saturation of the VECSEL and the SESAM are measured beforehand with 170-fs probe pulses as described in . The VECSEL and the SESAM are characterized for different probing wavelengths, heat-sink temperatures, and optical pump powers. This allows us to estimate the laser saturation for different fundamental modelocking states by interpolation.
We estimated the saturation round trip reflectivity of the fundamental state at 20.0 W pump power [Fig. 2(a)] given the measured center wavelength [Fig. 4(b)] and the used heat-sink temperatures of the SESAM and the VECSEL. Compared to the 170-fs probe pulse of the reflectivity measurements, the pulse duration of the fundamental state is slightly shorter around 100 fs. It is assumed that the reflectivity is not significantly changed. The measuredaverage output power of 84 mW is in good agreement with the laser saturation estimation. This output power corresponds to an estimated reflectivity of 100% with relates to the stable lasing condition: gain equal loss. The measured output power and the estimated laser operation points are in good agreement for all the fundamental states in Fig. 2(a). The estimated laser operation points lie slightly in the roll-over of the round trip reflectivity. This behavior is common for SESAM-modelocked lasers and has been reported for SDLs based on active QWs , QDs  and for thin disk lasers . It can be seen, that the SESAM is not fully saturated and thus is not operated at the point of minimal loss. Hence, higher output power could be achieved with a fully saturated SESAM. Further investigations are ongoing which address the question: Does a fully saturated SESAM maintain the short pulse duration? However this is beyond the scope of this paper.
To investigate the transition to the side pulse state, we calculate the round trip reflectivity at 22.6 W pump power as if the laser would remain in the fundamental state [Fig. 10(a)], even though in the experiment the laser would have switched to the side pulse state. Despite the increased pump power, the reflectivity, and therefore the gain, of the VECSEL gain chip seems nearly unchanged. The reason is that the additional gain due to higher pumping is balanced by a reduction of gain caused by a red-shift of the laser spectrum with consequently lower gain at longer wavelengths. The red-shift of the laser is also the cause for the reflectivity increase of the SESAM. With this, the theoretical operation point is even further in the roll-over. On the other hand, the reflectivity for low power pulses is increased to nearly 100%. Thus, low power optical noise is not efficiently suppressed anymore. This can destabilize the laser operation, which explains a transition in lasing operation, such as the experimentally observed switch to side pulse operation.
This model cannot be extended to the side pulse and double pulse states as the successive pulses would see a partially saturated VECSEL gain and SESAM absorption and therefore substantially changing the reflectivity.
3.4 Side pulse operation
On the 100-fs timescale new effects of the semiconductor material start to play a role, such as kinetic hole burning, theoretically predicted by fully microscopic many-body models [24,25]. The related kinetic hole filling can explain the two time scales in the recovery of the VECSEL reflectivity measured in situ during modelocking operation . This in situ measurements revealed an initial fast gain recovery of up to 80% taking place in few hundreds of femtoseconds, followed by a slow recovery in the hundreds of picoseconds determined by the slow refilling of the quantum well by diffusion of the optically pumped carriers.
These 100-fs timescale effects are not included in the coupled multi-delay differential equations introduced in section 3.4. Thus, we implemented another simpler rate equation model to study the fast quantum well dynamics, as described in . This model cannot describe modelocking formation, but it describes the instantaneous response to an incoming pulse for both the gain of the VECSEL chip and the absorption of the SESAM. This allows for an estimation of the instantaneous round trip amplification, by considering two passes on the VECSEL chip, one pass on the SESAM, and taking into account all the cavity losses, such as the output coupler loss.
This simulation shows that for a 100-fs pulse at 20.0 W pump power the round trip amplification is limited to the temporal pulse width [Fig. 10(b)]. But for 22.6 W pump power, the instantaneous round trip amplification stays positive for an interval after the trailing edge of the pulse. Thus, the combination of the initial fast recovery of the gain and the partially saturated SESAM from the first pulse supports a weaker side pulse to reach lasing threshold. The corresponding simulation for a 100-fs probe pulse with an additional delayed side pulse separated by 300 fs reveals the increased positive instantaneous amplification for the side pulse, which enables the experimentally observed side pulse operation.
Side pulse operations have also been reported for example in a colliding pulse cavity or with a graphene saturable absorber [41,42]. The optical spectra of these previously reported results look like the combination of two spectra with different center wavelength. However in our case, the optical spectra of the side pulse states are still close to sech2-shaped with only two small shoulders on the side [Fig. 5(a)].
In conclusion, we present an analysis of the pump power dependent modelocking performance of a SESAM-modelocked VECSEL. We identify four different modelocking states correlated with a step-like increase of the average output power. Besides an initial fundamental modelocking state, we find stable multipulse operations, such as side pulse, double pulse, and double & side pulse states. A single characterization technique is not sufficient to distinguish between all these different modelocking states. Therefore, we can confirm again that modelocking results obtained with SDLs must be accompanied by a comprehensive characterization, similar to the findings in [26,27]. Side pulse operation can be distinguished from fundamental modelocking by side peaks in the autocorrelation, by shoulders in the optical spectrum, by side peaks next to the repetition rate in the microwave measurement, and by additional peaks in the amplitude and phase noise. On the other hand, the double pulse state can only be distinguished from fundamental modelocking by a time trace measured with a fast photodiode and by an oscillating signal strength of the harmonics of the repetition rate. The change in signal strength of the harmonics is less pronounced as for second harmonic modelocking where all odd harmonics are missing.
The modelocking analysis reveals interesting hysteresis effects, such as a hysteresis loops of the different modelocking states and also a shortening of the pulse duration combined with a narrower optical spectrum of the fundamental state when operating in the “decreasing pump path” of the hysteresis curve [Fig. 2(a)].
At higher pump power beyond stable fundamental modelocking, simulations show that the type of multipulse state strongly depends on the cavity arrangement. Different multipulse operation can be obtained with different gain chip positions within the cavity round trip. Operation is optimized when the two pulses hit the gain chip equally spaced in time. The highest power in fundamental modelocking is therefore achieved when the VECSEL gain chip is centered in the cavity (Fig. 9).
To improve the average output power of fundamental modelocking, which in our case is not limited by thermal effects but by multipulse instabilities, we have investigated the onset of multipulse instabilities in great detail. We find that the transition to multipulse states takes place in the roll-over of the cavity round trip reflectivity resulting from the interplay between the saturation of the VECSEL gain and the saturation of the SESAM absorption. The combination of the rapid filling of the kinetic hole in the electron-hole distribution, burned by the short femtosecond pulses, and the partially saturated SESAM by the first pulse favors the onset of a weaker side pulse. To prevent these side pulse operations, one could use a SESAM with a faster recovery time. Another possibility could be to operate the laser in a chirped pulse configuration with a slow SESAM, which would reduce the effect of kinetic hole burning and simultaneously increase the efficiency of the laser. Further increase in power could also be achieved by increasing the round trip reflectivity which would sustain a higher output coupler transmission. The cavity round trip reflectivity is mainly limited by the saturation of the VECSEL gain.
Swiss Confederation Program (Nano-Tera.ch); German Research Foundation (DFG) (Collaborative Research Centre 787).
We thank the technology and cleanroom facility FIRST of ETH Zürich for advanced micro- and nanotechnology. This work was financed by the Swiss Confederation Program Nano-Tera.ch, which was scientifically evaluated by the Swiss National Science Foundation (SNSF) and by the German Research Foundation (DFG) within the framework of Collaborative Research Centre 787.
1. M. Guina, A. Rantamäki, and A. Härkönen, “Optically pumped VECSELs: review of technology and progress,” J. Phys. D Appl. Phys. 50(38), 383001 (2017). [CrossRef]
2. 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]
3. 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]
4. 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 (2012). [CrossRef]
5. 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]
6. S. Hoogland, S. Dhanjal, A. C. Tropper, J. S. Roberts, R. Häring, 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]
7. 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]
8. M. A. 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]
9. A. Rahimi-Iman, “Recent advances in VECSELs,” J. Opt. 18(9), 093003 (2016). [CrossRef]
10. 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]
11. 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]
12. O. Casel, D. Woll, M. A. Tremont, H. Fuchs, R. Wallenstein, E. Gerster, P. Unger, M. Zorn, and M. Weyers, “Blue 489-nm picosecond pulses generated by intracavity frequency doubling in a passively mode-locked optically pumped semiconductor disk laser,” Appl. Phys. B 81(4), 443–446 (2005). [CrossRef]
13. A. Härkönen, C. Grebing, J. Paajaste, R. Koskinen, J. P. Alanko, S. Suomalainen, G. Steinmeyer, and M. Guina, “Modelocked GaSb disk laser producing 384 fs pulses at 2 µm wavelength,” Electron. Lett. 47(7), 454–455 (2011). [CrossRef]
14. 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]
15. 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]
16. F. F. Voigt, F. Emaury, P. Bethge, D. Waldburger, S. M. Link, S. Carta, A. van der Bourg, F. Helmchen, and U. Keller, “Multiphoton in vivo imaging with a femtosecond semiconductor disk laser,” Biomed. Opt. Express 8(7), 3213–3231 (2017). [CrossRef] [PubMed]
17. 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]
18. P. Brochard, N. Jornod, S. Schilt, V. J. Wittwer, S. Hakobyan, D. Waldburger, S. M. Link, C. G. E. Alfieri, M. Golling, L. Devenoges, J. Morel, U. Keller, and T. Südmeyer, “First investigation of the noise and modulation properties of the carrier-envelope offset in a modelocked semiconductor laser,” Opt. Lett. 41(14), 3165–3168 (2016). [CrossRef] [PubMed]
19. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356(6343), 1164–1168 (2017). [CrossRef] [PubMed]
20. N. Jornod, K. Gürel, V. J. Wittwer, P. Brochard, S. Hakobyan, S. Schilt, D. Waldburger, U. Keller, and T. Südmeyer, “Carrier-envelope offset frequency stabilization of a gigahertz semiconductor disk laser,” Optica 4(12), 1482–1487 (2017). [CrossRef]
21. 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]
22. V. J. Wittwer, R. van der Linden, B. W. Tilma, B. Resan, K. J. Weingarten, T. Sudmeyer, and U. Keller, “Sub-60-fs Timing Jitter of a SESAM Modelocked VECSEL,” IEEE Photonics J. 5, 1400107 (2013).
23. M. Mangold, S. M. Link, A. Klenner, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, “Amplitude Noise and Timing Jitter Characterization of a High-Power Mode-Locked Integrated External-Cavity Surface Emitting Laser,” IEEE Photonics J. 6, 1–9 (2014).
24. 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]
25. I. Kilen, S. W. Koch, J. Hader, and J. V. Moloney, “Non-equilibrium ultrashort pulse generation strategies in VECSELs,” Optica 4(4), 412–417 (2017). [CrossRef]
27. K. G. Wilcox and A. C. Tropper, “Comment on SESAM-free mode-locked semiconductor disk laser,” Laser Photonics Rev. 7(3), 422–423 (2013). [CrossRef]
28. E. J. Saarinen, J. Lyytikäinen, and O. G. Okhotnikov, “Hysteresis and multiple pulsing in a semiconductor disk laser with a saturable absorber,” Phys. Rev. E 78(1), 016207 (2008). [CrossRef] [PubMed]
29. A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72(3), 033808 (2005). [CrossRef]
30. C. Otto, L. C. Jaurigue, E. Schöll, and K. Lüdge, “Optimization of Timing Jitter Reduction by Optical Feedback for a Passively Mode-Locked Laser,” IEEE Photonics J. 6(5), 1–14 (2014). [CrossRef]
32. M. Marconi, J. Javaloyes, S. Balle, and M. Giudici, “Passive Mode-Locking and Tilted Waves in Broad-Area Vertical-Cavity Surface-Emitting Lasers,” IEEE J. Sel. Top. Quantum Electron. 21(1), 85–93 (2015). [CrossRef]
33. S. V. Gurevich and J. Javaloyes, “Spatial instabilities of light bullets in passively-mode-locked lasers,” Phys. Rev. A 96(2), 023821 (2017). [CrossRef]
34. J. Mulet and S. Balle, “Mode-Locking Dynamics in Electrically Driven Vertical-External-Cavity Surface-Emitting Lasers,” IEEE J. Quantum Electron. 41(9), 1148–1156 (2005). [CrossRef]
35. B. Tromborg, H. E. Lassen, and H. Olesen, “Traveling wave analysis of semiconductor lasers: modulation responses, mode stability and quantum mechanical treatment of noise spectra,” IEEE J. Quantum Electron. 30(4), 939–956 (1994). [CrossRef]
36. A. G. Vladimirov, A. S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser,” IEEE J. Quantum Electron. 45(5), 462–468 (2009). [CrossRef]
37. C. G. E. Alfieri, D. Waldburger, S. M. Link, E. Gini, M. Golling, G. Eisenstein, and U. Keller, “Optical efficiency and gain dynamics of modelocked semiconductor disk lasers,” Opt. Express 25(6), 6402–6420 (2017). [CrossRef] [PubMed]
38. C. G. E. Alfieri, D. Waldburger, M. Golling, and U. Keller, “High-power Sub-300-Femtosecond Quantum Dot Semiconductor Disk Lasers,” IEEE Photonics Technol. Lett. 30(6), 525–528 (2018). [CrossRef]
39. I. J. Graumann, A. Diebold, C. G. E. Alfieri, F. Emaury, B. Deppe, M. Golling, D. Bauer, D. Sutter, C. Kränkel, C. J. Saraceno, C. R. Phillips, and U. Keller, “Peak-power scaling of femtosecond Yb:Lu2O3 thin-disk lasers,” Opt. Express 25(19), 22519–22536 (2017). [CrossRef] [PubMed]
40. C. Baker, M. Scheller, S. W. Koch, A. R. Perez, W. Stolz, R. J. 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]
41. A. Laurain, R. Rockmore, H.-T. Chan, J. Hader, S. W. Koch, A. R. Perez, W. Stolz, and J. V. Moloney, “Pulse interactions in a colliding pulse mode-locked vertical external cavity surface emitting laser,” J. Opt. Soc. Am. B 34(2), 329–337 (2017). [CrossRef]
42. S. Husaini and R. G. Bedford, “Graphene saturable absorber for high power semiconductor disk laser mode-locking,” Appl. Phys. Lett. 104(16), 161107 (2014). [CrossRef]