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Almost chirp-free pulses with a duration of 190 fs were achieved from a mode-locked semiconductor disk laser (SDL) emitting at ≈1045 nm. Pulse shaping was different from the soliton-like mode-locking process known from lasers using dielectric gain media; passive amplitude modulation provided by a fast saturable absorber was essential. The spectrum of the absorber had to be matched to the gain spectrum within a few nm. A tapered diode amplifier was demonstrated to be a device for both picking and amplifying SDL pulses. The pulse repetition rate of the SDL output was reduced from 3 GHz to 47 MHz.
©2009 Optical Society of America
1. Introduction
Semiconductor heterostructures enable compact and cheap lasers operating in continuous wave (cw) or pulsed regimes. The appropriate choice of material composition gives great freedom concerning the emission wavelength, which can be chosen almost anywhere from ≈340 nm to ≈30 μm [1,2]. Using an optically pumped external-cavity surface-emitting laser design, in the following called “semiconductor disk laser” (SDL), high cw output powers have been demonstrated with an excellent beam profile [3–5]. SDLs can be passively mode-locked by a semiconductor saturable absorber mirror (SESAM) included in the resonator [6,7]. Pulse repetition rates up to 50 GHz have been reported [7]; such high rates are attractive for communications. In this paper we address the generation of shortest pulses from mode-locked SDLs and investigate the optimum operation parameters. Short-pulse SDLs are interesting as oscillators in laser amplifier systems that can serve a variety of applications in material processing and spectroscopy [8]. In these systems, a tapered diode amplifier (TDA) can preamplify the generally low-energy SDL output pulses and act as a pulse picker giving free choice of the repetition rate. Experiments are presented using such a device with ultrafast electrical pumping.
For a long time it was believed that the pulse durations now achieved by SDLs could be obtained only from lasers using dielectric or dye media and not from semiconductor lasers, since the strong carrier-density dependence of the complex refractive index and the carrier dynamics in semiconductors introduce a strong chirp. Experiments with SESAM-mode-locked SDLs have shown that in some operation regimes the chirp contributions approximately compensate each other. In this case, one may obtain something like a “soliton-like” pulse [9]. Nevertheless, the minimum achievable pulse duration in this case had not been much shorter than about half a picosecond [10,11], until we demonstrated a 290-fs InGaAs/AlGaAs SDL [12]. Recently, Wilcox et. al showed 260-fs pulses from a similar laser [13]. The authors of Refs. 7, 10, 11, and 13 consider the so-called “optical Stark effect” as an important pulse shaping effect in sub-ps SDLs; we will discuss this issue in section 3.5. In this paper, we present almost chirp-free pulses with durations down to 190 fs around 1 μm emission wavelength. This means, with respect to mode-locked pulse durations, in this emission region InGaAs/(Al)GaAs SDL gain media now surpass typical Nd3+-doped crystals and challenge Yb3+-doped ones. In principle, following the same strategies with other semiconductor material systems, similar results should be obtainable in other spectral regions. In general, the short upper-state lifetime in semiconductor gain media limits the amount of energy that can be stored in the medium to be extracted by a pulse. Therefore, mode-locked semiconductor lasers are not capable of producing pulse energies as high or pulse repetition frequencies as low as those obtainable from mode-locked dielectric-media laser oscillators. At this point, pulse picking and amplification come into play.
2. Semiconductor elements and laser setup
Detailed descriptions of the laser resonator and of the semiconductor elements used are given in [12,14]. The gain chip is a 4-quantum-well (QW) graded-index barrier (GRIN barrier) InGaAs/AlxGa1-xAs structure (0 ≤ x ≤ 0.2) with a 25-layer-pair GaAs/AlAs Bragg mirror and strain compensation by AlGaAsP layers. The 840-nm pump light was mainly absorbed in the barriers; absorption amounted to roughly 20%. The influence of the SESAM temperature was investigated with the gain chip used in [12]. Unless otherwise mentioned, all other investigations were performed with a chip based on the same design, but grown on a GaAs (100) substrate off-oriented 2° towards (111)-A instead of 2°towards (1-10). No influence of the slightly different substrate orientation has been recognized so far. The chip made from this wafer had dimensions of 4 x 6 mm2 instead of 2 x 2 mm2 previously. After soldering the elements to CuW submounts, the substrates were etched off, leaving only 5-μm-thin media. An antireflective dielectric coating was applied to largely eliminate group delay dispersion (GDD <200 fs2, see Ref. 14).
In such elements a very fast interband relaxation time is achieved by locating the QW near to the surface of the structure, i.e., the QW is capped only by a very thin GaAs layer [10,14]. The absorber, too, was antireflective coated. For a cap thickness of 2 nm, we measure 1/e-relaxation times of typically ≈1 ps. This is shown in Fig. 1 , displaying the change of reflection for such an absorber mirror (SESAM of experiment no. 7 in Table 1 ). The pump-probe measurement was performed with a mode-locked Nd:glass laser emitting around 1058 nm. The pump and probe pulses had a duration of ≈150 fs. The SESAM was heated to a temperature of 95 °C, which corresponds to a similar operating point as in the laser experiment. There was only a slight change of the absorber response, when the pulse fluence was increased from 2.7 to 9.9 μJ/cm2, i.e., for higher fluences the absorption recovered somewhat slower in the region after 2 ps. The curves in Fig. 1 were normalized.
Table 1. Optimum SESAM temperatures for shortest-pulse generation from our SDLs. Three near-surface SESAMs (photoluminescence at 1028 nm, 1031 nm, 1050 nm) and four gain chips (A - D) were used. The output coupler transmission was TOC = 0.5%, except for experiment no. 6, where TOC = 0.75%. Bold numbers: The wavelength of the SESAM exciton transition (error ± 5 nm) is compared to the respective laser emission wavelength.
Figure 2 shows a scheme of the 50-mm-long V-folded, nearly hemispherical SDL oscillator. The distance between the gain element, i.e., the folding point, and the SESAM was approximately 5 mm. The resonator was operated close to its limit of stability, such that there was a tight focus with a waist size of ≈20 μm to create a high pulse fluence (several times the saturation fluence) on the SESAM. Estimation of the focus size is very rough, since the solder-related deformation of the gain chip (see [15]) and the deviation of the output coupler curvature from its nominal value prevent an exact calculation. Mode-locked operation was investigated using output couplers with transmissions from 0.2 to 1.5% at 1040 nm.
Fig. 2 Semiconductor disk laser (SDL). The V-shaped cavity is 50 mm long. It contains a saturable absorber mirror (SESAM) as the mode-locker, an InGaAs/AlGaAs disk gain element at the folding point, and a curved output coupler with a transmission between 0.2% and 1.5% around 1040 nm. The diode pump light at 840 nm is focused by an f = 63 mm lens.
3. SDL femtosecond oscillator – Experimental Results
3.1 Influence of saturable-absorber temperature
The temperatures of the gain element and the SESAM were controlled using Peltier elements. The heat sink temperature of the gain chip was kept at 19°C. The optical pump power at ≈840 nm amounted to 0.92 W, and an 0.5% output coupler was used. The SESAM temperature was increased from room temperature to 93 °C. At room temperature, the laser photon energy was far below the energies of the band gap and the heavy-hole excitonic resonance of the absorber. By heating of the SESAM, these spectroscopic features were red-shifted towards the laser photon energy by 0.25 meV/°C (0.3 nm/°C). Band gap and exciton resonance are no sharp features, but smeared towards lower and higher energies by temperature-related and structurally induced broadening. Therefore, the increase of temperature corresponded to a continuous tuning of the saturable absorption experienced by the laser photons. Absorption increased from practically zero for the SESAM at room temperature, which resulted in an output power of 21 mW, to values comparable to the output coupling loss, indicated by the considerable decrease of the output power to 10 mW around 85 °C. At the same time the laser emission wavelength was shifted towards the red, from 1034.5 nm to 1039 nm, since the laser minimized absorption loss as far as this was advantageous considering the filtering loss from the limited gain bandwidth.
Figure 3 shows the pulse duration versus the saturable absorber temperature. For SESAM temperatures below 50 °C, the amplitude modulation provided by the absorber was too weak to support mode-locking. In the range from 50 to 72°C we observed multiple mode-locked pulses simultaneously circulating in the cavity. Their number was reduced with increasing SESAM temperature; the pulse duration was decreased. The multiple pulsing behavior can be explained by still insufficient pulse shaping and by oversaturation of the absorber in case of too high intracavity power. Decreasing the pump power could be used as a countermeasure, but the resulting pulses were much longer than those obtained for higher SESAM temperatures with a pump power of 0.92 W. From 73 to 78° C, one pulse was observed, but with an unstable, strong tail.
We observed stable single-pulse sub-ps mode-locking only around 85 °C in a range of about 10 °C. Here, the pulse had a duration around 300 fs and only very little chirp. If the SESAM temperature was driven too high, i.e., above 90 °C, the laser switched to a much longer pulse with a center wavelength of ≈1032 nm. This operation regime experienced lower loss from gain filtering, but obviously the contributions to chirp were not balanced. These contributions include self-phase modulation and spectral filtering that are provided by gain chip and absorber and depend on pulse duration and laser wavelength. Although the exact evolution of laser performance with changing SESAM temperature differed somewhat depending on the individual laser configuration and adjustment, so far for all our femtosecond SDLs we observed a similar behavior as in Fig. 3.
Varying the gain element temperature while keeping the SESAM at 85 °C we found a range of 10 °C, too, where the semiconductor elements were appropriately matched. A too cold gain chip led to a long, chirped pulse as observed also for a too warm SESAM. A too warm gain element led to a growing pulse tail and red shoulder in the autocorrelation and optical spectrum, respectively.
The optimum SESAM temperatures for shortest-pulse generation obtained from seven experiments are listed in Table 1, together with relevant parameters and characteristics of the respective laser configurations. The three saturable absorbers have the same design, but are made for different laser wavelengths. They are distinguished by the center wavelengths of their room temperature photoluminescence (PL) amounting to 1028 nm, 1031 nm and 1050 nm. Four gain chips were investigated; chip A was a 6-QW structure with ungraded barriers, chips B to D were based on the 4-QW graded-barrier design as described above. B and C were 2 x 2 mm2 samples from the same wafer; D is the 4 x 6 mm2 sample from the new wafer. From the comparison of PL spectra with photocurrent spectra recorded using a Fourier-transform spectrometer, we assume that for our type of SESAM at room temperature the heavy-hole excitonic resonance is about 10 nm below the PL maximum [16,17]. We found a variation of this shift in the range of ± 5 nm which we attribute basically to the difficulties in determining the exciton position in the photocurrent spectrum. Table 1 gives “estimated excitonic transition wavelengths” at the operating temperature, which we compare to the respective laser emission wavelengths. The estimation is based on the room temperature PL, the shift of 10 nm as mentioned above, and a red-shift by ≈0.3 nm/°C when increasing the SESAM temperature. The parameter is to be understood as a landmark in order to characterize the operating point on the slope of the SESAM absorption spectrum. The excitonic resonance is strongly broadened by interaction with phonons and by structural inhomogeneities.
In general, the laser emission wavelength is close to the excitonic resonance. The estimation of the exciton transition energy is only rough; we see a trend, however: While in our first experiments, the laser photon energy was rather below the exciton energy, the laser operated energetically at or even slightly above the exciton resonance in the experiments where pulse durations around 200 fs were obtained. In any case, we observed that heating a SESAM above its optimum operation temperature led to a further decreased output power of the respective SDL and in the shortest-pulse experiments no. 5-7 lasing even ceased above some temperature, which means that effective SESAM absorption was still increasing in this direction.
The harmonic mode-locking achievable at temperatures below what we here consider the optimum SESAM temperature range might be interesting if the focus is not on generating the shortest pulses, but on high laser repetition frequencies [19]. We observed up to 7 pulses circulating in the cavity resulting in a pulse repetition frequency of 21 GHz.
3.2 Dependence of laser performance on pump-power
The pump power incident on the gain medium was varied from 0.77 W to 1.32 W, while using an 0.5% output coupler and keeping the heatsink of the gain chip at 16 °C and that of the SESAM at 106 °C. A pump power of 0.77 W was very close to the laser threshold in case of mode-locking and the lower limit to permit measurements, since here the laser would cease emission within less than a minute due to temperature fluctuations of the semiconductor elements. If starting the laser, the laser threshold was around 1.0 W. This value must be considered the cw laser threshold. Continuous wave emission was not observed, however; obviously the laser built up a mode-locked regime practically instantaneously after cw lasing had started. This surprising behavior can be explained by a high amount of total absorption of the SESAM, which does not permit lasing for pump powers below 1 W, unless absorption is partially bleached due to a mode-locked regime. The output power showed a linear dependence on the incident pump power, amounting to 4 mW to 13 mW around 1045 nm for 0.77 W to 1.24 W of 840-nm pump light. At about 1.32 W of pump radiation, the output power jumped up to 17 mW, indicating that here the onset of ps radiation significantly reduced the total loss of the laser. This reduction resulted from the narrower spectrum of the ps pulses, which experienced less spectral filtering by both the gain chip and the absorber.
Figure 4 displays a set of nine autocorrelation traces from our SDL, recorded with an APE Pulse Check autocorrelator. The first trace at the bottom was recorded at 0.77 W of pump power and shows the autocorrelation of a practically perfect sech2 pulse. A sech2 temporal shape is characteristic for optical solitons. The pulse duration did not change much, when the pump power was increased, as can be seen also from Fig. 5(a) gathering the FWHM values obtained from the respective fits. This behavior is not soliton-like. The quality of the fits worsened while increasing the pump power up to 1.00 W. The pulse developed a tail, which was observed as a weak pedestal in the autocorrelation signal. At 1.00 W, single-pulse lasing became unstable. The double pulses at 1.00 W were again almost pedestal-free, just like the pulse at 0.77 W. In both cases the output pulse energy was approximately 1.5 pJ, as shown in Fig. 5(b). If the pump power was increased above 1.00 W, again a pulse tail developed. The related pedestal was most pronounced just before double pulsing became unstable and the laser started producing ps pulses. The ps-pulse shape deviated substantially from a sech2 profile and did not resemble a soliton-like pulse any more.
Fig. 4 Autocorrelation traces of SDL for different pump powers. Respective powers from 0.77 W to 1.32 W are indicated by arrows. All traces were background-free; offsets were used to arrange all traces in one graph. Traces to the left were observed while the laser was operating in a single-pulse regime, to the right while in double-pulsing regime. Solid curves are fits assuming a sech2 pulse shape.
Fig. 5 (a) Pulse durations from the SDL at different pump powers. At 1.00 W there was a transition from single-pulse operation (full squares) to double pulsing (half-filled squares). Slightly above 1.24 W, the laser switched back to single-pulse operation, with a much longer pulse duration, however; please note the axis break. (b) Pulse energies.
Comparing Fig. 5(a) with (b) illustrates that the pulse durations did not obey the soliton area theorem, which would predict an inverse proportionality of pulse duration and pulse energy. Durations are not even generally shorter for higher energies. Below 1.32 W of pump power, pulses were always around 220 fs. Minimum durations were 215 fs for the single pulse and 210 fs for double pulses.
The optical spectra are shown in Fig. 6 . Only at the respective lowest energies we find single and double pulses to be almost chirp-free, i.e., soliton-like.
Fig. 6 Optical spectra of the SDL emission at different pump powers, recorded simultaneously with the autocorrelation traces shown in Fig. 4. Offsets were used to present all spectra in one graph.
For 0.77 W of pump power, we observed emission centered near 1043 nm and a spectral bandwidth (FWHM) of 5.6 nm, corresponding to a time-bandwidth product of 0.35, close to the Fourier limit for a secant hyperbolic pulse with the observed duration of 226 fs. The development of a pulse tail was associated with the coming up of a red shoulder in the spectrum, which extended over almost 10 nm. So, the pulses acquired additional bandwidth, which would be expected for a soliton due to stronger SPM for higher pulse intensity. However, no new frequency components were generated on the blue side with respect to the spectrum at 0.77 W, and the pulse was becoming increasingly chirped.
As the laser switched to double pulses around 1.00 W of pump power, SPM and the saturation of the SESAM were reduced due to lower pulse energy and therefore the largest part of the red shoulder disappeared, growing again with increasing pump power. The evolution of spectral shape and width was very similar for single and double pulses. The shoulder growth was a little faster for the double pulses, if the pulse energies shown in Fig. 5(b) are considered. Picosecond pulses at 1.32 W of pump light corresponded to a spectrum with a FWHM of 1.1 nm.
With increasing pump power, the spectral maximum of the single pulse in Fig. 6 was red-shifted from 1043 to 1046 nm; the double-pulse spectral maximum went from 1045 to 1047 nm; the picosecond pulse is centered at 1048 nm. This shift documents the increase of the temperature in the gain region due to the growing heat load. Since the SESAM was operated in the region of the exciton transition wavelength, its absorption decreased towards the red; hence, the shift weakened the pulse shaping by the absorber. This resulted in insufficient suppression of the red shoulder and temporal tail; finally, the bandwidth that is required for sub-ps generation could not be mode-locked any more.
The emission spectra of sub-ps SDLs are never perfectly symmetric and there is at least a hint of a shoulder. This is valid for all SDLs so far, including those in Refs. 7, 9, 10, and 13. The strength and position of the shoulder varied for the different lasers, which we attribute basically to the individual filtering slopes of the respective absorber and gain media. In most cases, the shoulder was on the red side. With our SDLs, a red shoulder was tendentially more pronounced for higher gain-chip heat-sink temperature and higher pump power. Depending on the temperatures of SESAM and gain chip, a blue shoulder was observed with the lasers of experiments 3, 4, and 7 in Table 1.
3.3 Influence of output coupler transmission
We investigated the influence of the output coupler transmission TOC, using mirrors with TOC = 0.2% to 1.5%. With TOC = 3% we could not achieve lasing. Figure 7 shows the minimum pulse durations versus TOC.
Pulse durations did not differ much for all mirrors, with values between 190 fs and 230 fs. These values were obtained with pump powers that had been optimized individually for the respective mirrors. However, just like displayed in Fig. 5(a) and (b) for the TOC = 0.5% mirror, the pulse duration showed only slight dependencies of pulse duration on pump power and pulse energy for all mirrors, if the laser was operated below the threshold for the onset of ps pulses. The only exception was the output coupler with TOC = 0.2% at low pump powers. For this mirror, the pulse duration close to 190 fs was observed in a double-pulse regime. Decreasing the pump power transferred the laser into a single pulse regime, but this led to roughly-600-fs pulses. Intra-cavity pulse energies corresponding to the values in Fig. 7 were between ≈200 and 500 pJ. Multiplying the extra-cavity values for the sub-ps pulses in Fig. 5(b) with 1/TOC = 200, we are in the same range. Hence, comparable fluences on the SESAM and therefore comparable amounts of passive amplitude modulation provided by the absorber permitted similar pulse durations. The highest single-pulse output power in this comparison amounted to 11 mW with a duration of 210 fs and was obtained with the 1% output coupler for a pump power of 1.33 W. The shortest pulses, with a duration of 190 fs if assuming sech2 pulses, were achieved with TOC = 0.75%.
3.4 Generation of 190-fs pulses
This result is displayed in the autocorrelation trace in Fig. 8 . We found a practically bandwidth-limited sech2 pulse with a slight pedestal, which can be assumed to represent a weak tail, just like with the sub-ps traces in Fig. 4. The inset of Fig. 8 shows the optical spectrum centered around 1044 nm with a bandwidth (FWHM) of 6.0 nm, as expected for a Fourier-limited sech2 pulse. Between 1050 nm and 1055 nm there was a slight red shoulder. The output power of the laser amounted to 5 mW for an incident pump power of 0.99 W.
Fig. 8 Autocorrelation trace and optical spectrum (inset) of the InGaAs/AlGaAs SDL recorded for the shortest pulse, with a duration τp = 190 fs. The output coupler transmission was 0.75%. τac, autocorrelation width; Δλ, spectral width (FWHM).
A closer inspection of the optical spectrum from the inset of Fig. 8 revealed the presence of a “continuum”, a cw or at least long component of the signal. Figure 9 documents s polarized, p polarized, and unpolarized measurements. We find a small amount of p polarized radiation at 1044 nm, which did not leave a trace in the autocorrelation. The s polarized main component consists of a “soliton-like” part, indicated by the dashed curve showing the simulated spectrum of a Fourier-limited 190-fs sech2 pulse and an additional small peak at 1045 nm, which too was part of the “continuum”.
Fig. 9 Unpolarized (“s+p”) and polarized (“s”, “p”) spectra of the 190-fs SDL. The dashed curve is the simulated spectrum of a Fourier-limited 190-fs pulse and indicates the soliton-like part of the signal.
In case of soliton-like mode-locked lasers the “continuum” is a dispersive wave shed by the soliton-like pulse to maintain the soliton temporal shape and the energy corresponding to the duration while traversing alternating media in the laser cavity. Comparing cw lasers without frequency selection, the emission spectrum of a semiconductor laser will be much broader than that of a laser based on a dielectric medium. As we see, this is also true in case of continuum radiation in the respective mode-locked lasers. We observed the “continuum” component also for the 1.5% output coupler (in this case clearly distinguishable from the pulse-related peak, as the long component was shifted 3 nm to the red), but not for output coupler transmissions below 0.75% within the investigated range of pump power (≤1.32W). Too, Garnache et al. reported the observation of a “cw component” from their SDL; the shape of the optical spectrum belonging to the 477-fs pulses indicates a “continuum” [10].
The radio frequency spectrum for the 190-fs pulse output is displayed in Fig. 10(a) and (b) . It was recorded using a Rhode & Schwarz 7-GHz spectrum analyzer and an Alphalas photodiode with a rise time <70 ps. The wide-span scan in Fig. 10(a) indicated that the laser was operating in a single-pulse regime with a pulse repetition rate of 2.998 GHz, corresponding to the round-trip frequency of the resonator. A scan in the region of the first beat node with a radio bandwidth of 1 kHz (Fig. 10(b)) showed no spurious modulations and a noise floor that was approximately 70 dB below the signal, confirming stable mode-locking.
Fig. 10 Radio frequency spectrum of the 190-fs SDL. a) Wide-range scan (0-7 GHz), b) scan around the first beat node at the round-trip frequency froundtrip = 2.998GHz.
3.5 Discussion – Soliton mode-locking in SDLs?
“Soliton-like” pulse shaping is a good description for most sub-ps solid-state lasers; usually, it will be required for sub-ps pulse generation. Our sub-ps pulses show some characteristics similar to optical solitons (close-to-sech2 intensity shape, practically no chirp for appropriate operation parameters, spectral bandwidth increasing with pulse energy, multiple pulsing at high intracavity powers, occasional occurrence of “continuum”); other important ones are not fulfilled (inverse proportionality of pulse duration and energy, duration being largely independent of absorber properties).
Optical solitons as known from fiber transmission are solutions of a nonlinear Schrödinger equation (NSE) containing anomalous linear group delay dispersion (GDD) and Kerr self-phase modulation (Kerr SPM) [20]. Sub-ps lasers usually generate “soliton-like” pulses. These are solutions of master equations based on the NSE with gain and loss (and respective dynamics and dispersion) added and boundary conditions and - if necessary - the lumped structure of the laser resonator taken into account. GDD, Kerr SPM, and often the filtering by the limited gain bandwidth are the dominating pulse-shaping mechanisms and determine the pulse duration. Passive amplitude modulation generated by the absorber is important to initiate and stabilize mode-locking, but has a minor influence on the pulse duration [21]. A condition for very short pulses and a feature of both true optical solitons and soliton-like pulses is that contributions of the pulse shaping effects to chirp fully or largely compensate each other.
Pulse-shaping in our sub-ps SDLs cannot be described with the picture applicable to lasers with dielectric gain media. Important differences exist: SPM is not of the usual “Kerr type”; it is due to the changes of the carrier densities in the semiconductor media and the resulting evolution of the gain and absorption spectra. Therefore, SPM is not purely instantaneous, but depends on the distribution of carriers already created and their relaxation. In our lasers, GDD was minimized, such that its effect should be small. Passive amplitude modulation has a large effect on pulse duration and includes a significant contribution by the gain medium. Since the spectra are dynamic, filtering effects, which are static in the case of dielectric-media lasers, are dynamic in case of SDLs. The absorber is operated in the vicinity of the band gap, therefore filtering does not only mean gain dispersion, but is contributed to also by the SESAM.
There is no analytical treatment or simulational approach applicable to sub-ps SDLs so far. A theoretical investigation of a “soliton-like pulseshaping mechanism in passively mode-locked surface-emitting semiconductor lasers” was performed by Paschotta et al. in Ref. 9. Explicitly, the article does not deal with sub-ps pulses. The absorber relaxation time is long compared to the pulse duration; spectral hole burning and effects leading to fast recovery of absorption and gain are neglected, i.e., thermalization within the band and with the lattice as well as exciton ionization, which act on the same time scale as our pulses. Based on these assumptions, the pulse duration was found to depend proportionally on the square root of GDD, but a too low value of GDD caused instability. However, our elements are assumed to contribute only small amounts of GDD (<200 fs2) caused by imperfections of the antireflective coatings, by the substructures of the elements and by the Bragg mirrors [14]. Paschotta et al. noted that stable pulses with durations below 1 ps would be possible even without GDD if the SESAM was fast enough. We assume that this means a case like that of our lasers. The great importance of passive amplitude modulation is clearly demonstrated by the deterioration of our pulses when saturable absorption is reduced by temperature-shifting the absorption away from the gain spectrum.
We propose the following strategy for minimum pulse durations: Minimize GDD; this means use thin, AR-coated media. Minimize filtering effects. Minimize the absorber relaxation time. Maximize passive amplitude modulation in the absorber, i.e. the effective modulation depth, as far as this is possible with respect to increased losses and increased laser threshold and also with respect to oversaturation of the SESAM, which must be avoided to prevent a temporal tail and double or multiple pulsing. With a waist size on the order of 20 μm on the SESAM and with the pulse energies of Fig. 5(b), we estimate fluences in the order of 40 μJ/cm2 for practically chirp-free pulses and 100 μJ/cm2 for the highest-energy pulses before double pulsing started. This has to be compared to a saturation fluence of 10 μJ/cm2 we typically determine for our near-surface SESAMs using pulses with similar duration.
In principle, if exploitable in a SESAM, the so-called “optical Stark effect” (OSE), as suggested in Refs. 7, 10, 11, and 13, would be an excellent mechanism to realize a very fast absorber. OSE means that the high electrical field strength provided by a high-intensity light pulse shifts the heavy-hole exciton resonance and the band gap towards higher energies if the photon energy is chosen below the exciton and gap energies. This shift is purely a polarization effect and no real free carriers are generated. The absorption in the region of the former exciton and band edge position is bleached and will recover practically instantaneously when there is no light field. In experiments using a pump laser providing the shift and a weak laser probing exciton and band edge region, the OSE was confirmed in semiconductor quantum wells, e.g., by Chemla et al. [22].
In case of a SESAM in a mode-locked laser, however, there are no separate pump and probe lasers, the pulse circulating in the cavity must play both roles. The photon energy is located in the spectral tails of exciton and band gap - both features are smeared considerably at room temperature. Therefore, the “pump” is located where non-zero absorption exists and the “probe” is not weak. At least at the operating points of the SESAM where we have observed the shortest pulse durations, one runs into the problem that during the pulse transit the absorption will generate enough free carriers to largely bleach the SESAM before OSE will be effective. Chemla et al. had to use a very low probe intensity of <10 kW/cm2 to avoid perturbation by real free carriers, i.e., in case of 100-fs pulses as used by these authors the fluence on the semiconductor element had to be <10−3 μJ/cm2. From the decrease of laser output power when we heat the SESAM to its optimum temperature, we see that the element exhibits a considerable amount of effective (i.e., unsaturated saturable) absorption at this point of operation, and this agrees well with the above estimation finding the absorber only a few times saturated. Hence, it is obvious that at least in our lasers OSE is suppressed by real-carrier generation. One may consider the case of an extremely intense pulse bleaching the SESAM by OSE such that there is negligible effective absorption. However, this would be a drastically oversaturated absorber, which does not agree with single-pulse mode-locking. If we were able to push the onset of double pulsing to much higher pulse energies, real-carrier generation would arise from two-photon absorption (TPA). For pulse durations similar to ours, this effect is pronounced already at fluences of a few hundred μJ/cm2 [22]. In fact, significant TPA would eventually lead to double and multiple pulsing, since by this change of operation regime the laser would reduce the pulse intensity and the TPA loss. Even without OSE the near-surface SESAMs used in this paper are fast enough to support sub-ps pulses, as documented by the pump-probe experiment (Fig. 1). Furthermore, for pulse fluences ranging from 2.7 to 9.9 μJ/cm2 this measurement did not show any hint of OSE; there was no shortening of the absorber response towards higher fluences.
4. Pulse picking and pulse amplification by a tapered diode amplifier
In terms of pulse duration, the sub-200-fs pulses we have demonstrated by an SDL in the 1µm emission region can compete with the output of mode-locked Nd3+- or Yb3+-based lasers. However, for applications in material processing or time-resolved spectroscopy not only short pulse durations are desired, but also – with respect to output from mode-locked SDLs demonstrated so far – higher pulse energies, higher average power, and longer periods in between the pulses. Therefore, it is clear that an SDL should be used as an oscillator seeding an amplifier chain [8], which boosts and picks the pulsed SDL output accordingly. A tapered diode amplifier (TDA) is a possible solution for pulse-picking and preamplification in one device. In fact, for picking of pulses with repetition rates in the GHz range, there is no other solution we know of, aside from similar ones like in [23].
A scheme of the TDA used in our experiment is shown in Fig. 11(a) , the mounted device in Fig. 11(b). Our tapered diode amplifier consisted of two sections, a 0.5-mm-long ridge waveguide section (RW) and a 3.5-mm-long tapered section, which were driven by separate transistor electronics. The transistors were integrated on the same mount, to keep electrical paths short for high-speed operation. In the present version the current for the RW is pulsed (≈400 ps FWHM), that for the tapered part is constant (2.33 A). We coupled 2-ps-long SDL pulses with a center wavelength of 1040 nm, a pulse energy of ≈4 pJ and a repetition rate of 3.016 GHz into an X-fiber. One branch of the fiber was connected to a photodiode providing a trigger signal for an HP 8131A pulse generator, whose pulses switched the transistor for the RW at 1, 1/2, …, or 1/64 times the trigger pulse rate. Picosecond laser operation had been chosen due to higher pulse energy, as the trigger signal was too weak in the femtosecond regime. The other branch launched its output into a fiber with a tapered end located close to the TDA input facet. The fiber optics attenuated the original pulse by roughly 20 dB; therefore, after subtraction of amplified stimulated emission (ASE), we had a TDA output energy per pulse of 12 pJ. In case of effective coupling, energies in the order of 1 nJ are expected.
Fig. 11 Tapered diode amplifier (TDA). (a) Scheme. Pulse picker section: ridge waveguide operated with a pulsed electric current; amplifier section: tapered part operated with cw current. frep, optical-pulse rate of SDL; f´rep, electrical pulse rate = new optical-pulse rate; 1/2n, pulse picking ratio. (b) TDA (indicated by red circle) on mount.
The photodiode signal of an output pulse from the TDA is displayed in Fig. 12 . It was recorded with a 25-GHz-bandwidth photodiode. The input pulse rate was divided by 64, i.e., with a period of 21 ns instead of 330 ps between two pulses (see Fig. 12 inset, showing a 50 ns window). In principle, the pulse picking could be realized with arbitrary picking ratios, if a pulse divider other than the internal one of our HP generator was used. Our transistor design is capable of producing electrical 200-ps-pulses for the RW section, which will reduce the optical gain for neighboring pulses. Pulsing of the tapered-section current will suppress the observed ASE. At present, although the RW section was not yet operated with an inverse bias voltage, optical pulses outside of the gate defined by the electrical pulse were largely blocked. However, for smaller picking ratios – 2:1 to 32:1 were tested – we found a worse picking contrast, since the interval between two electrical pulses becomes short compared to the carrier recombination time in the RW and therefore carriers accumulate. A reverse bias voltage will remove carriers after the pulse.
Fig. 12 Optical pulse from the SDL after pulse picking and amplification by the TDA. Inset: two pulses on a 50-ns-timescale. The pulse repetition rate was reduced from 3 GHz to 47 MHz.
5. Summary
We investigated the optimum parameters for generation of low-chirp sech2 pulses with FWHM durations around 200 fs by an optically pumped semiconductor disk laser (SDL) emitting in the 1-μm region. The InGaAs/AlGaAs gain structure was mode-locked by a fast semiconductor saturable absorber mirror employing a surface-near quantum well. The absorption spectrum had to be matched to the gain spectrum within a range of a few nm, corresponding to temperatures of the semiconductor elements in a range of +/-5 Kelvin. Changing the pump power, almost Fourier-limited sech2 pulses were found only for low pulse energies; for increasing pulse energies, the pulse developed a tail and became increasingly chirped. Above a certain pump power, the SDL generated double pulses; at even higher pump power, the laser switched to a long, strongly chirped pulse. We explain tail, chirp, and double pulsing by insufficient passive amplitude modulation provided by the SESAM, when this device was not operated in the optimum region of its absorption spectrum, and/or oversaturation of the SESAM when pulse energies became too high.
Variation of the output coupler transmission yielded minimum pulse durations between 190 fs and 230 fs. The best value, 190 fs, was achieved with an 0.75%-transmission output coupler. This is what we believe to be the shortest pulse obtained directly from a semiconductor oscillator. The output power amounted to 5 mW for a pump power of 0.99 W. Although the laser showed some characteristics of soliton-like mode-locking, on the whole, the pulse shaping process is different from the familiar mechanism known from dielectric solid-state lasers.
Semiconductor disk lasers promise to be cheap, compact and versatile oscillators, that can be used in oscillator-amplifier systems generating ps- and sub-ps pulses for material processing and spectroscopy. A tapered diode amplifier (TDA) with pulsed electrical pumping can be an important component in such a system, since it is capable of acting both as a preamplifier and as a fast pulse picker, giving free choice of pulse repetition frequency. We examined a TDA in combination with our SDL and reduced the pulse repetition frequency from 3 GHz to 47 MHz, demonstrating that TDAs are especially useful where optical pulse rates are too high to be handled by any other methods of pulse picking.
Acknowledgments
The authors like to thank for financial support by the federal state Berlin and the European Union in the frame of the ProFIT program.
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