1 Introduction

Saturable absorbers based on semiconductor quantum dots (QDSAs) have been shown to successfully mode-lock a wide range of laser systems [1–5]. Large cross sections of the absorption transitions in QDs ensure low absorption saturation fluence and therefore give more freedom in designing QDSA parameters as compared to quantum well designs. This opportunity enables using anti-resonant structure designs for mode-locking of low-energy solid-state laser systems where a low saturation fluence as well as low modulation depth is necessary. For example, the integration of a quantum dot absorber into a semiconductor structure also containing the gain medium has shown to lead to very compact semiconductor lasers [4]. The low saturation fluence is also of interest for high repetition rate, diode-pumped solid state lasers (DPSSL) [5]. Upon approaching the 1 GHz region, reliable mode-locking becomes increasingly challenging, because the lower intra-cavity pulse energy calls for lower saturation fluence of the absorber to avoid Q-switching [6]. Another important feature of QDSA is their fast relaxation time [1]. This feature is crucial for pulse shaping in picosecond DPSSLs, where the Kerr effect and thus soliton shaping is weak due to the low intra-cavity peak intensity. In such sources, the absorber relaxation time essentially determines the generated pulse width.

The combination of high repetition rate and picosecond pulse duration is of interest, e.g. for biomedical imaging [7–9] in the near-infra-red region. Higher repetition rates enable shorter acquisition times in nonlinear laser scanning microscopy [9]. For two-photon fluorescence excitation microscopy, the repetition rate of the laser source has a limit determined by the lifetime of the exited state of fluorescent dye tags [10] and thus cannot extend much beyond 1 GHz. Coherent anti-stokes Raman scattering microscopy, on the other hand would definitely benefit from a laser source operating at GHz repetition rates and delivering picoseconds pulses at 1 μm [11]. Furthermore, picosecond pulses compared to femtosecond pulses simplify the synchronization of the pulse train, e.g. in optical parametric oscillators (OPO), and the lower peak power permits direct amplification in efficient fibre amplifiers.

So far, fundamental mode-locking of solid-state lasers has been very successful using absorbers based on quantum wells, for a wide range of repetition rates and gain media. These include not only the already mentioned all-semiconductor devices, but also DPSSLs based on Ytterbium-doped double tungstates (up to 5 GHz) [12, 13], Nd:YVO4 (up to 160 GHz) [14] and Erbium-based materials for lasing in the 1.55 μm region (up to 100 GHz) [15]. Quantum dots, on the other hand, have only been used to achieve high repetition rates with all semiconductor lasers (VECSEL, MIXSEL [4, 16]), whereas systems based on crystals have only been mode-locked up to 200 MHz [1, 2], not fully investigating the quantum dot absorbers’ potential to extend the range to the 1 GHz region. However, a 10 GHz Er:Yb:laser with an output power of 8 mW has recently been demonstrated using a QDSA to achieve mode-locking at 1.55 μm [17]. In this paper, we demonstrate a compact passively mode-locked Yb:KYW DPSSL operating around 1 GHz repetition rate and taking advantage of the aforementioned beneficial properties of saturable absorber structures containing layers of self-assembled InGaAs quantum dots.

2 Experiment and discussion

2.1 Quantum dot saturable absorber

In detail (see Fig. 1a), the structure hosts three sub-structures of which each contains five layers of self-assembled InGaAs quantum dots and 20 nm thick GaAs spacing layers. The three groups are separated by additional 44.8 nm of GaAs. Towards the cavity, the structure is capped by an additional 108.6 nm GaAs layer. The DBR structure consists of 33 pairs of GaAs/AlGaAs layers leading to a 100-nm wide high-reflectivity spectrum centred at 1,064 nm. An anti-resonant design was chosen to minimise the effect of growth errors during production and also to minimise the influence of thermal expansion during operation. Although the laser’s wavelength around 1,035 nm seems quite off from the structure’s design wavelength, the anti-resonant design still ensures high reflectivity.

Fig. 1
figure 1

a Simulation of the QDSA’s structure. The normalised electric field (red, dashed) and the refractive index (black, solid) are given as a function of position relative to the structure’s surface. The scaling of the y axis is valid for both curves. Only the first few of the Bragg stack’s 33 layer pairs are shown. A wavelength of 1,032 nm was used for calculation of the electric field. b Maximum of the enhancement factor inside the structure as a function of wavelength. Vertical dashed lines indicate the mode-locked laser’s and characterisation laser’s centre wavelengths at 1,032 and 1,040 nm, respectively

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Figure 2 shows our own measurement of the non-linear reflectivity. The data were obtained by a dual-beam lock-in method, where signals from a sample and a reference arm were detected with the same photodiode at two different reference frequencies. A two-frequency chopper wheel (SRS540) is used in a Michelson-type configuration to modulate sample and reference beam with two different frequencies. The sample beam is directed through the inner section of the chopper and the probe beam through the outer section. The ratio of the two lock-in signals directly yields the non-linear reflectivity. Fluctuations from the laser source and the photodiode’s response are thus efficiently removed. Since the dynamic range of the fluence used in the experiment is rather large, an additional attenuator is used in front of the photodiode to keep the signal inside the diode’s linear working range. Furthermore, the setup is calibrated with an HR mirror in place for the sample to remove systematic errors, e.g. arising from beam displacement on the photodiode when changing the attenuation. With this scheme, it is possible to detect modulations on the order of 0.1 % at a wide range of excitation fluences. The laser source used for the measurement had a centre wavelength of 1,040 nm and a pulse duration of 200 fs. A fit to the data gives a saturation fluence of about 4 μJ/cm2, a modulation depth of 0.26 % and non-saturable loss of 2 %. The modulation depth at the mode-locked laser wavelength is expected to be somewhat larger, about 0.4 % owing to increasing field enhancement factor or, in other words, the amplitude of the electric field standing wave at shorter wavelengths (see Fig. 1b). It should be noted that the value for the saturation fluence is subject to uncertainties related to the measurement of the beam size. It is important to note that the QDSA’s actual behaviour during laser operation might differ since the absorber is excited by picosecond pulses in the cavity as opposed to the femtosecond pulses in the characterisation experiments. The pulse duration has been proven to have an influence on the non-linear behaviour of semiconductor saturable absorbers [18]. Most notably, the onset of considerable TPA is shifted towards higher fluences in the picosecond case, simply because of the lower peak intensity. Nevertheless, the measurement confirms that low saturation fluence as well as low modulation depth is achievable in QDSAs.

Fig. 2
figure 2

Non-linear reflectivity measurement of the QDSA (black, dots). The blue, solid line shows a fit with the following parameters: saturation fluence of 4 μJ/cm², modulation depth of 0.26 %, non-saturable loss of 2 %, inverse saturable absorption parameter of 45 mJ/cm². The green, dashed line uses the same parameters except for the inverse saturable absorption

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The group delay dispersion was measured with a white-light interferometer (see Fig. 3 for results). The structure shows negative dispersion in the laser’s operating wavelength range, which is indicated by two vertical lines. In the operating range of the mode-locked laser, the group delay is negative with the value around −1,000 fs², which well compensates for the estimated normal dispersion in the crystal dispersion of ~800 fs² experienced by the pulse in a double-pass.

Fig. 3
figure 3

Measured group delay dispersion (GDD) of the QDSA. The vertical lines (red, dashed) mark the wavelength interval the laser is operating in

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To confirm the ultra-fast relaxation dynamics of the QDSA, its relaxation time was measured in a non-collinear pump-probe experiment using a 200 fs, 40 MHz laser centred at 1,040 nm. Figure 4 shows the measured differential reflectivity for two different pulse fluences, namely 140 μJ/cm², which is comparable to the intra-cavity pulse fluence at the onset of CW-mode-locking, and 400 μJ/cm². The measured data were fitted to the sum of an exponential and a linear function, which led to better agreement with the data than a double exponential fit. However, the exponential decay time and the fast component of the double exponential were very similar. Initial recovery of the saturable absorption is as short as 0.55 ps at 140 μJ/cm2 and increases to about 1 ps at the highest intensities. The slow-induced absorption tail following initial recovery is attributed to the absorption of radiation by free-carriers in GaAs barriers, which are created from excited quantum dots with a delay of a few picoseconds with respect to the pump pulse, as was determined by time-resolve THz reflectivity measurements in the same structures [19]. The delay-induced absorption facilitates an efficient removal of energy that shed from the pulse because of dispersive effects as well as the removal of noise following the pulse. In addition, the graphs in Fig. 4 can be assumed to include a certain amount of TPA due to the short-pulse duration used for characterisation (as discussed above), which is of less importance for picosecond laser operation. The induced free-carrier absorption typically relaxes on few hundred picoseconds to nanosecond time-scale. Therefore, for femtosecond pulse laser operation, it can be expected that this absorption would contribute to the increased cavity losses at high repetition rates, pushing Yb:KYW lasing into longer wavelengths. The fact, that in our picosecond laser setup, the trend is opposite, suggests that the induced absorption does not contribute significantly to the intra-cavity roundtrip losses even at 1 GHz repetition rate.

Fig. 4
figure 4

Relaxation behaviour of the QDSA. The differential reflectivity is given as the signal from the photo diode connected to a lock-in amplifier. Data are shown for pulse fluences of 140 μJ/cm² (circles) and 400 μJ/cm² (squares). Also shown are fits to these data (red, solid and green, dashed, respectively) and the obtained time constants for the exponential (t exp) and linear (t lin) contribution

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2.2 Laser experiment and discussion

The cavity layout is given in Fig. 5. The gain medium is 3 mm long, 5-at.%-doped, Ng-cut Yb:KYW crystal with an aperture of 3 × 3 mm² and AR-coatings for pump and laser wavelength on both sides. A collimated stack-diode (LIMO HLU35C) operated at 980 nm serves as pump source. The diode’s beam propagation factor was measured to be 64.3 in horizontal and 28 in vertical direction. An AR-coated, aspheric lens with a focal length of 30 mm are used to focus the pump beam to a spot size of 95 μm in horizontal direction and 70 μm in vertical direction. The pump beam also passes the curved mirror M1, which increases the spot size and shifts the focus further into the cavity. The laser-mode size in the crystal was calculated to be 50 μm. The QDSA is placed at the cavity’s end, where the laser mode size is ~35 μm. The crystal and the QDSA are each mounted to water-cooled copper blocks via indium foil and heat-conducting paste, respectively. The overall cavity length is 145 mm, which corresponds to a repetition rate of 1.036 GHz.

Fig. 5
figure 5

Cavity layout: L1: aspheric pump lens, focal length 30 mm. OC: outcoupling mirror, 1 % transmission. Mirrors M1–M4 are HR-coated (R > 99.9 %) for the laser wavelength; M1 and M2 are also AR-coated (R < 2 %) for the pump wavelength (980 nm). Radii of curvature are 25 mm for M1 and M4 and 50 mm for M2; M3 is flat. A scale is given in the lower right corner

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Continuous wave operation starts at a threshold incident pump power of 130 mW and continues with a slope efficiency of 6 % up to output powers of 42 mW, when Q-switched mode-locking (QSML) starts (see Fig. 6). Stable CW-mode-locking starts at an output power of 66 mW and continues with a slope efficiency of 10.8 % (the change in the slope efficiency at incident pump powers exceeding 1.1 W is related to the spectral shift of the laser diode output). At mode-locking threshold, the pulse fluence on the absorber is ~165 μJ/cm2. Mode-locked output powers up to 339 mW could be obtained, limited by the damage of the QDSA. From these data, we estimate the QDSA’s damage threshold corresponding to the energy fluence of 860 μJ/cm². The beam propagation factor (M 2) was measured using the knife edge method and found to be 1.3. By replacing the QDSA with a flat, high-reflectivity mirror (R > 99.9), we determined that in CW operation, the laser performance was very similar to the laser cavity containing the QDSA. Namely, the laser cavity with high reflector had a threshold of 120 mW and an average slope efficiency of 10.5 % for incident pump powers above 1.1 W. This measurement indicates that the slope efficiency for this particular cavity design is limited by pump and laser mode overlap in the laser crystal.

Fig. 6
figure 6

The measured output-power dependence on the incident pump power (squares) and linear fit to the data from the regime of CW-mode-locking (green, solid line). The vertical lines (red, dashed) indicate the transitions from CW to Q-switched mode-locked and finally to CW-mode-locked operation. The input power has been corrected for loss at the pump optics

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An estimate for the pump efficiency \( \eta_{p} \) can be found from the known cavity configuration and the measured slope efficiency \( \eta_{s} \):

$$ \eta_{s} = \eta_{p} \frac{{\gamma_{2} }}{2\gamma }\frac{{\lambda_{p} }}{{\lambda_{l} }}\frac{{A_{l} }}{{A_{p} }} $$
(1)

Considering the CW cavity, the total loss \( \gamma \) can be assumed to mainly consist of the outcoupling loss \( (\gamma_{2} /2) \)and the absorber’s non-saturable loss. The ratio of laser and pump mode area is calculated from the respective spot sizes to be ~38 %. With the measured slope efficiency of 10.5 % and the known ratio of pump and laser wavelength, the pump efficiency is estimated with a value of about 90 %. It is clear that the slope efficiency in such compact cavities can be increased by employing higher brightness pump diodes, or semiconductor master-oscillator-power amplifier assemblies.

The optical spectra show the centre wavelength to be located at 1,035.7 nm before CW-mode-locking starts and mode-locked spectra shifted towards shorter wavelengths (see Fig. 7), which we tentatively attribute to lower roundtrip losses due to saturation of QDSA in the pulsed regime. At the same time, the mode-locked spectrum is centred at the point with the lowest group delay dispersion of the QDSA (all other mirrors in the cavity are broad-band, high-reflective mirrors without additional GDD). The mode-locked spectrum in Fig. 7 suggests FWHM-bandwidths larger than 2 nm, corresponding to a Fourier-limit of 560 fs (assuming sech2-shaped pulse).

Fig. 7
figure 7

Normalized, linear optical power spectra at 24 mW in the CW regime before mode-locking starts (blue, solid), and at 216 mW in CW mode-locked operation (red, dash-dotted). The resolution bandwidth (RBW) is 0.07 nm

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The actual pulse width was measured with an intensity autocorrelator. The FWHM pulse width directly above CW-mode-locking threshold is 1.7 ps (see Fig. 8), which is three times longer than the absorber’s fast relaxation component for the given fluence. Also included in Fig. 7 is a fit assuming sech2-shaped intensity profile, revealing more power in the flanks and less in the centre. The flanks grow into a larger pedestal when power increases (see also Fig. 8). This can be explained by noting that the absorber’s relaxation time becomes longer with increasing fluence, whereas the absorption modulation amplitude does not change significantly. The absorber’s response thus becomes more like that of a slow absorber, with absorption modulation strongly affecting pulse’s front and leading to a pulse asymmetry if the soliton pulse shaping is not strong enough. This is reflected in the changes in the pulse autocorrelation trace at the highest intra-cavity intensities.

Fig. 8
figure 8

Measured intensity autocorrelation traces for output powers of 77 mW (solid, blue) and 210 mW (dash-dotted, red) as well as a fit to the lower power trace, assuming sech2-intensity profile (green, dashed). The centre of the pulse is only little affected by increase of power, whereas a considerable pedestal appears

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RF-spectra were recorded using an amplified and biased InGaAs-photodiode with a bandwidth of 10.7 GHz. A wide-range RF-scan is given in Fig. 9a to record up to the fifth harmonic of the fundamental frequency. Figure 9b shows a high resolution scan at the repetition rate frequency for output powers of 66 mW. The noise floor of the detection system is at −60 dB relative to the signal’s maximum. Furthermore, the signal at the repetition rate of 1.036 GHz is surrounded by a pedestal at a level of −35 dB. Its width broadens with increasing output power, whereas the given signal-to-noise ratios are maintained. The formation of the pedestal is attributed to amplitude fluctuations as a result of the slow component of the QDSA’s relaxation time, which disturbs the pulse forming process due to the short cavity round-trip time. The effect becomes more pronounced for higher fluences incident on the QDSA because of the stronger free-carrier absorption and increased two-photon absorption as mentioned above.

Fig. 9
figure 9

a Frequency comb of the mode-locked pulse train, averaged over 100 measurements, RBW is 1 MHz. b High resolution scan of the RF spectrum around the fundamental repetition rate for an output power of 66 mW. The shape does not change significantly for higher powers. The repetition rate f rep is 1.036 GHz, RBW is 9.1 kHz. The power spectral density is normalised to the carrier maximum

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3 Conclusion

We have demonstrated the use of a QDSA mirror for mode-locking of a 1.036 GHz diode-pumped Yb:KYW laser. The device directly emits picosecond pulses at centre wavelengths around 1,035 nm. Reliable CW-mode-locking sets in at laser output powers of 66 mW, i.e. for a pulse fluence of 165 μJ/cm² on the absorber. No Q-switched mode-locking was observed up to the damage threshold of the absorber.

The output power in this cavity was limited by the QDSA’s damage which occurs at pulse energy fluence of 860 μJ/cm². With no indication of other immediate issues preventing further power scaling, we conclude that reaching the 1 W level with high repetition rate Yb:KYW lasers should be achievable with QDSAs with similar characteristics by increasing beam size and improved non-saturable loss in the absorber. Nevertheless, it is important to note that the absorber’s dynamic behaviour in the high-fluence regime may present a future issue and thus has to be examined in order to ensure stable mode-locking at higher powers, especially for femtosecond pulses at GHz repetition rate regime. In the present QDSA structure, however, high-fluence absorber dynamics do not seem to prohibit CW-mode-locking. This is probably facilitated by the picosecond pulse length, which gives less rise to two-photon absorption than it would be the case in a femtosecond system. In any case, the results show that QDSAs are promising devices for mode-locking of low intra-cavity pulse energy, low peak power DPSSLs.