We report on optically-pumped vertical-external-cavity surface-emitting lasers passively mode-locked with a semiconductor saturable-absorber mirror. The potential of harmonic mode-locking in producing pulse trains at multigigahertz repetition rates has been explored. The results present first systematic study of multiple pulse formation in passively mode-locked VECSELs.
©2007 Optical Society of America
Vertical-external-cavity surface-emitting lasers (VECSELs), also known as semiconductor disk lasers, offer unique combination of high average output power, high pulse repetition rate , short pulse width  and superb beam quality. Operation of an optically pumped VECSEL requires proper design of the gain structure with efficient transport of carriers from the pump absorbing regions into the active (quantum well or quantum dot) region producing the gain. The best VECSEL performance is achieved to date with optically pumped devices at 1-μm wavelength range. These lasers demonstrate an impressive power-scaling capability.
VECSELs passively mode-locked with semiconductor saturable absorber mirrors (SESAMs) typically use the broad gain bandwidth of the quantum-well material for generation of ultrashort pulses and can achieve gigahertz-level repetition rates in a short cavity or through harmonic mode-locking. VECSELs operating at high repetition rates (tens of gigahertz) can be used in high-speed communications, switching, sampling, and clocking. Since solid-state or glass fiber gain media have a low emission cross-section and high saturation fluence, these lasers may suffer from Q-switching instability particularly for high repetition rate mode-locking. In contrast, VECSELs have a high differential gain, low saturation fluence and are free from low-frequency instabilities even with low energy pulses.
Multi-GHz VECSELs reported to date were using short cavities [2, 3] or external feedback to provoke harmonic mode-locking . The mechanisms of high-repetition-rate pulse formation in VECSELs, especially harmonically mode-locked, are still to be thoroughly studied.
In this study, we systematically examine the regime of harmonic mode-locking in VECSELs and identify the main features associated with this operation mode. Particularly, we show both numerically and experimentally, that harmonic mode-locking is inherent attribute of VECSELs; the number of pulses circulating in the cavity is expected to increase with pump power. Strong saturation and fast recovery of the gain ensure efficient pulse ordering mechanism resulting in strong suppression of cavity fundamentals.
2. VECSEL gain mirror, SESAM and laser cavity
The GaAs-based laser gain structure consists of a quantum well gain section enclosed between a GaInP etch-stop layer and a distributed Bragg reflector (DBR). The structure was grown in a single step by molecular beam epitaxy (MBE). The gain section contains 15 compressively strained 7-nm thick GaInAs quantum wells sandwiched between 5-nm thick GaAs barrier layers and spaced with strain compensating GaInAsP layers. The thickness of the spacers was set to place each QW at an antinode of the optical field in the 8.75-λ long cavity defined by the DBR and the semiconductor-air interface. The distributed Bragg reflector includes 27.5 pairs of ¼-λ thick GaAs/AlAs layers and was grown last on top of the gain section.
The sample was attached with indium solder on a 2×2×0.3 mm3 diamond composite heat spreader, which in turn was bonded to a metallic heat sink with AuSn solder. After bonding, the GaAs substrate was removed using wet etching and a 2-layer SiO2-TiO2 antireflection coating was deposited on the sample.
The gain mirror was pumped by 808-nm radiation from a fiber-coupled diode focused onto a spot of about 165-μm in diameter. The barrier and spacer layers absorb the pump radiation creating the carriers that are trapped in the wells to generate gain at 1 μm.
The SESAM used as an end mirror in the mode-locked laser was grown by MBE. It comprises two 9-nm thick compressively strained GaInAs quantum wells separated by a 5-nm thick GaAs barrier and a GaAs/AlAs DBR with 27.5 pairs of quarter-wave thick layers. Figure 1 shows the low-intensity reflectivity of the SESAM. The SESAM has been irradiated with heavy ions to shorten the recovery time of the absorption. The recovery time estimated from measurements was found to be ∼2 ps.
Low single-pass gain in a VECSEL makes the cavity extremely sensitive to the cavity loss. Consequently, the modulation depth of the SESAM was limited here to ∼1 %. This value, however, was sufficient to ensure reliable start-up of the passive mode-locking. The saturation fluence of the SESAM was measured to be ∼50 μJ/cm2.
The asymmetric Z-shaped laser cavity, shown in Fig. 2, consisted of two curved folding mirrors and two semiconductor end-mirrors represented by the gain structure and the SESAM. This configuration provides a convenient option for setting the suitable mode size on the gain mirror and the absorber.
To achieve stable mode-locked operation, the mode area on the SESAM should be usually smaller than the mode area on the gain structure optimized to match the pump spot. An optical isolator was placed at the output of the laser to prevent back-reflection to the laser.
The laser described above typically generated 10–20 ps pulses at a wavelength between 1036 and 1040 nm, depending on pump power and the number of pulses circulating in the cavity.
Figure 3 shows the RF spectra of the current from a photodiode with bandwidth of 12 GHz illuminated with the output laser beam for several pump powers corresponding to different harmonics. The strong (≥50 dB) suppression of the cavity fundamentals (multiples of 350 MHz) indicates that the pulses are nearly equally spaced. In turn, this illustrates the high strength of the pulse ordering mechanism in passively mode-locked VECSEL.
Another feature observed regularly in the mode-locked VECSEL is an increase in the order of the oscillating harmonic with pump power. It was found that the number of pulses circulating in the cavity increases fairly linearly with pump power, as shown in Fig. 4.
This observation is in agreement with the theoretical model described below that confirms gradual increase in harmonic number with the pump power. The marker bars around data points in Fig. 4 denote pump power range for the stable mode-locked operation of a given harmonic. At the pump power of 2.35 W, mode-locked operation at the 6th harmonic corresponding to the repetition rate of 2.1 GHz could be achieved with proper alignment of the laser cavity. Generally, this means alignment for maximum power, which favors mode-locking at a higher harmonic until it does not violate the operation on fundamental mode.
The autocorrelation traces of the pulses corresponding to different harmonics are shown in Fig. 5.
The pulse width gradually decreases from 16.3 to 14.8 ps with an increase in the harmonic order, as seen from Fig. 6.
The corresponding spectra are shown in Fig. 7. In these measurements, the time-bandwidth product ranges from 1.5 to 1.9 exceeding the transform-limited value by factor of ∼5–6. The pulse energy was fairly constant revealing only a minor increase with increasing harmonic number from 38 pJ to 42 pJ.
The pulses generated by the passively mode-locked VECSELs acquire usually frequency chirp as a result of complex interplay between nonlinearity (phase effects) and saturation of the gain and absorption . The pulses could, however, be compressed close to the diffraction limit using an auxiliary delay line with anomalous dispersion. We have found that using a diffraction grating pair allowed for subpicosecond pulses with time-bandwidth product only slightly above the transform limit. Another possibility for producing chirp-free pulses directly from the mode-locked laser could be based on the “quasi-soliton” formation in the positive-dispersion regime and was discussed in Ref. .
The blue spectral shift observed with an increase in harmonic number (Fig. 7) could be understood assuming up-chirped pulses typical of mode-locked VECSELs . Indeed, the gain/absorption saturation model shows that up-chirped pulses acquire blue shift in SESAM due to suppression of the red-shifted spectral components in the leading edge of the pulse while gain saturation favors the leading edge thus provoking the red shift. At high repetition rate (≥ 1 GHz), when the gain cannot be fully recovered during pulse period, the red shift induced by the effect of gain saturation becomes less pronounced. Since the recovery time of the absorption is much faster than the gain recovery, blue spectral shift generated by the SESAM saturation remains largely unchanged with harmonic number (for repetition rate ≤ 100 GHz). Consequently, an effective “blue shift” could be observed with an increase of harmonic number. Another feature that supports indirectly this viewpoint is a decrease of the time-bandwidth product observed with an increase in the repetition rate (harmonic number), as shown in Fig. 8. The decrease in the frequency chirp induced by the gain saturation may be expected with weaker recovery of the gain for high pulse repetition rates.
In order to achieve shorter chirp-free pulses careful control of cavity dispersion would be necessary. It should be mentioned, however, that pulses with durations below 20 ps could be routinely obtained without additional efforts since the gain and SESAM structures were operated close to anti-resonance thus resulting in small overall cavity dispersion.
4. Numerical model
Strong repulsing or pulse interaction is needed to establish equal spacing between the pulses. The saturation and fast recovery of the gain are believed to be the main mechanisms responsible for pulse ordering in a harmonically mode-locked VECSEL. The ordering mechanism was investigated using the numerical simulations based on rate equations for the saturable gain and saturable loss. The simulations assume that the saturable absorber is highly oversaturated, which corresponds to experimental conditions.
The saturation of the gain g in the VECSEL is described by the rate equation 
The saturable absorption q is found from equation 
where t is the time, q0 is the modulation depth and g0 the small signal gain, which is proportional to the pump power. τg and τa are the recovery times, and Esat,g and Esat,q the saturation energies for the saturable gain and saturable loss, respectively. The rate equations are consecutively solved for saturable absorption and saturable gain. The model includes a dispersive element that accounts for second order chromatic dispersion and gain filtering.
The propagation through this element is carried out by a multiplication in the frequency domain:
Here E~a(ω) and E~b(ω) is the Fourier transform of the slow varying electric field amplitude before and after the dispersive element, respectively, ω the frequency, D2 the dispersion and ωg the gain bandwidth. The pulse is represented by 4096 complex amplitudes, which cover the whole roundtrip time range; the simulations start from white noise. Since the rate equations are scalable in time and energy, the dimensionless quantities for time, power and energy were used in the simulation. The bandwidth for the gain filtering was set to 5000×1/Tr, where Tr is the cavity roundtrip time. This resulted in pulse durations (τpulse∼0.0015/Tr) consistent with the experimental data.
To match closely the laser parameters, the recovery time of the gain was set to be equal to the cavity roundtrip time, τg =Tr (both characteristic times are of the order of 1 ns for our laser) and the recovery time of the SESAM to be τa =Tr/100. The gain saturation energy was assumed to be 100 times the SESAM saturation energy. The saturable loss of the SESAM was set to 2 % and additional losses of 6 % have been included representing the cavity loss and output coupling. The model was completed by a-factors, which account for phase effects proportional to the saturable gain (αgain=2) or loss (αSESAM=1) .
Figure 9 shows the results of the simulations performed with these parameters for 40000 roundtrips starting from white noise.
Figure 9 shows the time dependence of the pulsed output in Fig. 9(a), the VECSEL gain calculated with Eq. (1) in Fig. 9(b) and the saturable absorption modeled using Eq. (2) in Fig. 9(c). The simulations reveal that saturable gain results in a temporal pulse shift per round trip of the order of 3×10-6Tr, while the difference of the time shift between the strongest and the weakest pulse is ∼1×10-6Tr. These values correspond to the non-steady-state of the harmonic mode-locking after 40000 round trips. Calculations show that both values approach zero after 60000 round trips indicating the formation of the steady-state of the harmonic mode-locking. The arrows in Fig. 9(a) indicate direction and relative magnitude of the pulse temporal shift caused by the VECSEL gain recovery. The saturable absorber cannot contribute to the pulse ordering process due to its fast recovery and the large pulse separation.
The effect of cavity dispersion was then studied by adding negative or positive dispersion of the value of 2.0×10-9∙Tr 2. Without soliton shaping, the pulse duration is expected to be independent of the sign of dispersion due to the low values of the amplitude-dependent phase effects in the semiconductor materials [5, 6]. This resulted in an increase of the pulse width from τpulse∼0.0015∙Tr to τpulse∼0.003∙Tr. The pulse ordering mechanism, however, was found to be fairly independent on the cavity dispersion. The laser considered here operates essentially in non-soliton regime, contrary to the multiple pulse model used in Ref. . This conclusion is supported by the large time-bandwidth product of the pulses observed in the experiments. Consequently, the pulse quantization owing to soliton pulse formation  does not occur here and the steady-state pulse energy is determined mainly by the gain saturation and cavity loss. Figure 10 shows the number of ordered pulses in the laser cavity as a function of relative pump power obtained from numerical simulation. The average power in these calculations was adjusted by pump parameter in the gain-material rate equation.
As it is seen from the figure, the number of pulses increases linearly with increasing pump power in accordance with the experimental results presented in Fig. 4. Estimates of the nonlinear phase effects in the laser cavity derived from numerical simulations show that phase shifts associated with the saturation of the gain and SESAM absorption affect mainly the pulse width and quality, but they can be neglected when considering multiple-pulse ordering in the harmonically mode-locked VECSEL. Briefly, due to time-dependent gain, the pulse shifts on a time scale towards the region with higher gain resulting in pulse ordering . The strength of the drift force depends on the temporal gain slope ∂g/∂t, which, in turn, depends on gain magnitude and recovery time and pulse interval. With these assumptions, the gain and the absorber media have been modeled using rate equations that allow for monitoring multiple pulse evolution in a laser cavity. The pulse energy distributions in the laser cavity after 105 and 1.3×106 roundtrips are presented in Fig. 11(a) and 11(c), respectively. Figure 11(b) illustrates the evolution of the pulse ordering by plotting the temporal position of the pulse as a function of roundtrip number. After 106 round-trips from the mode-locking start-up, the pulse amplitude variation decreases from 40% to 2%, while uncertainty in the temporal pulse location started from 40% becomes negligible. It was found that adding either negative or positive dispersion to the cavity does not affect notably the pulse ordering mechanism, resulting both in a well ordered state after 106 cavity round-trips. The model described here implies ways to control the pulse energy and multiple pulsing. For instance, increasing the recovery time of the gain and absorber would reduce the pulse number. In contrast, the harmonic number can be increased using materials with shorter recovery times. The pulse energies can be scaled up by increasing the saturation energies, e.g. by increasing the beam spot sizes on both the absorber and the gain material.
This study shows the promising potential of VECSELs as practical sources of high repetition rate ultrashort pulses. It is demonstrated that the strong pulse ordering mechanism due to the dynamic gain saturation allows for efficient suppression of fundamental harmonic.
This research was supported in part by the European Commission through the FP6 research project NATAL, Jenny and Antti Wihuri Foundation, Nokia foundation and Emil Aaltonen Foundation.
References and links
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