1. Introduction

The field of mode-locked SDLs was under intense research for over a decade and reached many significant technical milestones including sub-100 fs pulse duration, average output power above 5 W and high repetition rates up to 200 GHz [1–3]. However, to date their minimum repetition rate has not reached values below 100 MHz and has been limited to 200 MHz, which constrains peak power scaling [4, 5]. Meanwhile, conventional mode-locked SDLs are operated at multi-GHz repetition rates [6]. This constraint appeared to originate from short, few-ns level carrier lifetimes in semiconductor gain material [7, 8]. Although this feature is beneficial for high-repetition rate applications and noise suppression, it does limit the achievable parameters at lower repetition frequencies. It is in sharp contrast with solid state laser gain materials which feature upper-state lifetimes in microsecond and millisecond range. This allows mode-locked solid state lasers to be operated at tens of MHz or even lower repetition rates achieving large pulse energies [9]. In the case of SDLs, the reduction of repetition rate down to a record low 85.7 MHz reported in this paper and subsequent peak power scaling will enable an entirely new set of applications, especially where high peak power is an advantage [10, 11]. Also, ultra-low repetition rate will enable the use of SDLs as a seed source for regenerative amplifiers where single pulses need to be selected by using electro-optic switches for further energy amplification. We also present the results of modeling which propose the effect of phase-amplitude coupling playing a significant role in the long cavity fundamental mode-locking in addition to the interplay between gain and saturable absorber as in classical image of mode-locked SDLs. The phase amplitude coupling facilitates the overcoming of short carrier lifetime limitations in the mode locked long cavity semiconductor lasers.

2. Samples

The SDL gain structure used in our experiment was designed for an emission wavelength of 980 nm and was grown by Metal Organic Vapour Phase Epitaxy (MOPVE). The gain section contained 16 InGaAs quantum wells sandwiched between GaAs barriers and strain compensating GaAsP layers. The gain structure was resonant and was grown on top of a Distributed Bragg Reflector (DBR) which had 30 pairs of ¼ lambda thick GaAs/AlGaAs layers. For the experiment, an approximately 3x3mm2 size semiconductor chip was cleaved from the wafer and bonded to an intracavity diamond heat spreader using liquid capillary bonding technique. The heat spreader had a wedge of 2 degrees and was antireflection coated for both, pump and emission wavelengths.

A semiconductor saturable absorber mirror (SESAM) designed for 980 nm was grown by Molecular Beam Epitaxy (MBE). The absorbing section contained 2 layers of InGaAs quantum dots (QDs) sandwiched between GaAs barriers. The absorbing structure was resonant and grown on top of a DBR which had 28 pairs of ¼ lambda thick GaAs/AlGaAs layers. It had peak absorption at 967 nm. A QD SESAM was chosen for this experiment as it features low saturation fluence and faster recovery time as compared to its QW based counterparts [12, 13]. QD SESAMs previously were used to successfully mode-lock various types of lasers, including SDLs [14, 15]. Importantly to our experiment, QD absorbers also feature an α-factor which depends on the relationship between operation wavelength and spectral position of peak absorption [16]. It allows additional control of phase-amplitude coupling and played an important role in the presented experiment.

3. Experiment and results

To achieve a low repetition rate, a conventional multi-folded cavity was formed around the gain chip with a total cavity length of 1.76 m, shown in Fig. 1. Mirrors M1, M2 and M8 had a radius of curvature (RoC) of −200 mm, mirrors M5 and M6 had a RoC of −3000 mm and mirrors M3, M4 and M7 were flat. Mirror M5 was used as an output coupler and had transmission of 2%. The SESAM served as one of the cavity end mirrors.The temperature of heatsinks with gain and SESAM was set to 20 °C and 25 °C respectively. A commercially available fiber-coupled 808 nm diode laser was used as a pump source. The laser beam diameter was calculated to be 300 µm on the gain medium and 120 µm on the SESAM. The TEM00 mode output beam was linearly polarized. A stable mode-locked operation was achieved by pumping the gain chip with 14 W of 808 nm light which resulted in 360 mW average output power.

 

Fig. 1 A schematic drawing of the low repetition rate mode-locked SDL. A multi-folded cavity was formed using 8 dielectric coated mirrors and incorporating gain chip and SESAM.

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In order to investigate the dynamical properties of the device, we characterized time trace of laser output, radio frequency spectra and optical spectra. Importantly, two distinct, stable mode-locking regimes were observed: fundamental mode-locking and soliton bound state.

The temporal patterns of laser output representing two regimes were measured using a photodetector with 29 GHz optical bandwidth and are depicted in Fig. 2. Figure 2(a) shows a fundamental mode-locked operation with single pulse per cavity round-trip time of 12 ns. Meanwhile, Fig. 2(b) indicates the alternative regime of the soliton bound state where two pulses spaced by fixed time interval of 1 ns were circulating in the cavity. Narrow RF spectra were observed at cavity repetition rate for both regimes and are shown in Fig. 3 for (a) fundamental and (b) bound state mode-locking. Insets in the graphs show a number of subsequent RF harmonics indicating well-defined mode-locked operations. Pulse durations were measured to be 60 ps in the fundamental and 50 ps in the soliton bound state regimes as would be expected since the formation of the bound state requires a binding energy. Optical spectrum for fundamental mode-locking was centred at 989 nm (Fig. 4(a)). The strongly modulated spectrum of bound state was slightly blue-shifted to 988.5 nm due to the asymmetry provided by the non-zero and non-identical α-factors in the gain and absorption sections. The spectral blue-shifting has previously been reported for the harmonically mode-locked SDL [17], while the physical mechanisms for the spectral shifts in SDLs were discussed in [18].

 

Fig. 2 The trains of pulses measured from the mode-locked SDL indicating (a) fundamental mode-locking and (b) the soliton bound state regime. Red lines show the results of theoretical calculation matching experimental observations.

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Fig. 3 Radio frequency spectra of the semiconductor disk laser mode-locked at low repetition rate in (a) fundamental and (b) soliton bound state regimes. The insets show a number of RF harmonics indicating well-defined mode-locked regimes.

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Fig. 4 Optical spectra for (a) fundamental and (b) soliton bound state regimes in mode-locked SDL. The spectrum of bound state shows a strong modulation which is characteristic to such regime as also indicated by simulated spectrum shown in the inset.

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4. Discussion

Although the fundamental single pulse mode-locking in sub-100 MHz repetition rate is a significant improvement in the development of mode-locked SDLs, the observation of the double pulse regime is equally interesting. The state of multiple bounded solitons was first theoretically predicted as a possible solution in a nonlinear Schrödinger and Ginzburg-Landau equations [19, 20]. To our knowledge, previously such temporal pattern of multiple pulses spaced by fixed time interval was only observed in fiber lasers and attracted much attention in nonlinear and laser optics in terms of fundamental science and applications for high bit rate communications [21, 22]. In general, soliton bound state represents a pulse train with discrete, fixed, but non- identical time separations between multiple soliton-like pulses. The soliton bound state is, therefore, different from the harmonic mode-locking where pulses circulate in the cavity with constant separation.

The experimental observation of the two-soliton bound state coexisting with the fundamental mode locked pulse train is also important for understanding of the possible mechanism of the locking in our system since the bound soliton state is only possible if the interaction of the pulses to produce a duplet is phase sensitive [22]. It indicates importance of the phase-amplitude coupling for ultra-low repetition rate mode-locking in SDLs. The magnitude of the phase-amplitude coupling in semiconductor devices can be conveniently estimated by using α-factors [23].

To model the dynamics of our device, we use a system of delay differential equations (DDE) which has been successfully used to explain various dynamical phenomena [24]. The system reads:

The phase-amplitude coupling of the electric field is modeled by the α-factors. It is a crucial element in the appearance of the mode-locked regime and the bound state in our system. The other important aspect is the asymmetry of the α-factors,${\alpha }_g\ne {\alpha }_q$. This asymmetry is typical for SDLs and has already been discussed in [18] where it has been generally estimated to be${\alpha }_g>{\alpha }_q$. Our simulations confirm the existence of the mode-locked regime for the full ranges of ${\alpha }_{g,q}$discussed in [18].

The numerical results shown in red line in Fig. 2 display the fundamental pulse train and a train with double pulses, which are identical to the experimental observations. These regimes coexist with the patterns of multiple bounded pulses with well-defined discretely locked phases between the soliton multiplets. Some examples of these coexisting multiplets are shown in Fig. 5.

 

Fig. 5 Numerically-obtained time traces of different bound states. These regimes of stable soliton multiplets coexist with the regime of fundamental mode locking and duplet in Fig. 2. The parameters used in the simulation are: $J_g = 1.5$;$J_q = 2.5$;$s_q/s_g = 30$;${\alpha }_g = 4$;${\alpha }_q = 2$; $\kappa = 0.25$ and $\gamma T = 120$.

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In addition to the gain-loss interplay, generation of the solitonic trains in lasers usually requires a balance between nonlinearity and dispersion/diffraction [22]. The dispersion probably plays only a minor role in our ~50 ps pulse width device, but the asymmetry provided by non-identical α-factors can certainly be related to the diffractive effects. The possible large scale of the phase change in QD absorber demonstrated in [16] opens a new pathway for the investigation of the dissipative solitons in lasers. In addition, the numerical model formulated in terms of DDE allows new insights on the mathematical aspects of the problem.

5. Conclusion

In summary, we demonstrate a breakthrough in the lower repetition rate limit of mode-locked semiconductor disk laser with a record low operation at 85.7 MHz. We use numerical simulations to show that operation in such a regime is indeed possible if the phase-amplitude coupling effect is present. The achievement and subsequent developments will position SDLs as a feasible alternative to Ti:Sapphire lasers for 1 µm spectral range applications where high peak power or sub-100 MHz repetition rates are required. In addition, it was shown for the first time that low repetition rate mode-locked SDL can serve as a test-bed for bounded soliton state in semiconductor lasers.