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Abstract
Mode-locked vertical external-cavity semiconductor lasers (VECSELs) are a wavelength-versatile laser that relies on a semiconductor saturable absorber mirror (SESAM) to initiate pulsed emission while simultaneously significantly influencing the pulse’s properties. A SESAM can be characterized using a nonlinear reflectivity setup, realized here in the red spectral range around 660 nm and achieving a moderate peak-to-peak variation of 0.17%. We use our home-built mode-locked VECSEL to reach a high maximum fluence up to 430 µJ/cm2 with strongly chirped 7.5 ps pulses. This allows the first-of-its-kind characterization of GaInP quantum well SESAMs, thereby revealing saturation fluences of 38 µJ/cm2 and 34 µJ/cm2 with modulation depths of 5% and 10.3% for SESAMs comprising one or two active quantum wells, respectively. For all structures, a nonsaturable loss of 2.8% is found and attributed to scattering loss.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode-locked vertical external-cavity semiconductor lasers (VECSELs) represent a low-cost and wavelength-versatile source for delivering a single picosecond to subpicosecond pulse per round-trip in a near-diffraction-limited beam. For wavelengths around 1 $\mathrm {\mu }$m high average output powers of 5.1$\,$W [1] with picosecond pulses as well as short pulse durations down to 107$\,$fs [2] have been demonstrated. Through bandgap-engineering other spectral regions such as around 2 $\mathrm {\mu }$m [3] are also accessible where sub-400 fs pulse duration has been shown [4].
In these mode-locked VECSELs, typically a semiconductor saturable-absorber mirror (SESAM) is used as an end mirror to initiate fundamental mode locking. Knowledge of the SESAM’s nonlinearity offers a clear path towards optimized performance regarding stability and output power [5]. It is also required for numeric simulation of the laser’s dynamics [6] which in turn benefits the development of new mode-locked VECSELs with non-fundamental mode-locking behavior [7].
To this end, a straightforward nonlinear reflectivity setup was devised by Maas [8] in the year 2008 permitting the characterization of saturable absorber properties around 1 $\mathrm {\mu }$m. The needed stable high-power probe pulses are usually delivered by a mode-locked thin disk laser while at more exotic wavelengths expensive OPOs [3] can be used, especially to achieve subpicosecond pulses. As a compromise, a home-built mode-locked laser has also been used in [8,9]. A similar approach in the red spectral range was always limited by the performance of the home-built mode-locked laser which either shows more than one pulse per round-trip within a picosecond envelope [10,11] or indications of multi-pulse emission [12]. Only lately a stable fundamental mode-locked VECSEL was shown in the red-spectral range [13], enabling the usage of mode-locked emission for applications.
We implement a mode-locked VECSEL as a probe for a nonlinear reflectivity setup in the red spectral range. With this we show, to the best of our knowledge, the first nonlinear reflectivity measurement of GaInP QW SESAMs. These SESAMs differ in the number of GaInP quantum wells and their positioning relative to the standing electric field of our probe VECSEL.
2. Mode-locked VECSEL probe
Our VECSEL and SESAM structures are fabricated using metal-organic vapor-phase epitaxy with the standard sources trimethylgallium, trimethylaluminum and trimethyindium as well as arsine and phosphine in an Aixtron 3x2" close-coupled showerhead reactor. The samples are typically grown at a temperature of 640$^{\circ }$C at moderate pressures of 100 mbar. We use 2" n$^{+}$-GaAs substrates miscut 6$^{\circ }$ toward [111]$_{\text {A}}$ for all presented samples.
The gain chip comprises 5 packages, each with 4 compressively strained GaInP quantum wells, placed at the antinodes of the standing electric field in the overall antiresonantly coupled subcavity. The active region is grown on top of a 55 times $\lambda$/4 pair Al$_{0.50}$GaAs/Al$_{0.95}$GaAs DBR. The DBR as well as the quantum well position is optimized for oblique incidence at an angle of 20$^{\circ }$ for a wavelength of 660 nm. The gain chip is mechanically bonded to an anti-reflection coated 2$^{\circ }$ wedged diamond heatspreader.
The SESAM in the probe laser contains a single compressively strained quantum well which is located at the antinode of the electric field of an antiresonantly coupled active region. This AlGaInP active region is grown at a temperature of 560$^{\circ }$C and comprises a DBR optimized for normal incidence but otherwise similar to the VECSEL DBR.
The laser cavity is schematically shown in Fig. 1 and consists of three arms each including a curved mirror CM1 - CM3. CM1 has a radius of curvature $r_{\text {CM1}}=50\,\text {mm}$ and focuses on the SESAM with an average beam diameter of $d_{\text {SESAM}}=32.4\,\mathrm {\mu }$m. The arm with curved mirror 2 (CM2) with a curvature $r_{\text {CM2}}=100\,\text {mm}$ generates a narrower folding angle at the gain chip position, which allows outcoupling through curved mirror 3 (CM3) with $r_{\text {CM3}}=100\,\text {mm}$ and a transmission of 2.5%. On average, the individual passes on the gain are then separated by 625$\,$ps which is smaller than the typical recovery time of the VECSEL gain, usually assumed in the low nanosecond range [14]. Also, the beam diameter at the gain amounts to $d_{\text {VECSEL, I}}=66.6\,\mathrm {\mu }$m and $d_{\text {VECSEL, II}}=66.8\,\mathrm {\mu }$m, resulting in a mode area ratio of gain to absorber above 4 while the intracavity fluence on the SESAM is estimated as $F_{\text {SESAM}}=400\,\mathrm {\mu }\text {J}/\text {cm}^{2}$.
Fig. 1. Schematic cavity design with four gain-passes, allowing a total cavity length of $l_{\text {Cav.}}=41.2\,$cm. In contrast to typical VECSEL cavities, the additional folding angle created in the upper cavity arm allows additional amplification of the pulse during its cavity round-trip when it encounters the gain chip.
During laser operation, the gain chip is cooled to $T_{\text {gain}} = -20^{\circ }$C and pumped using 4.2 W at 532 nm which is focused on the gain chip using a f = 10 cm lens, leading to a focused pump beam diameter between 70 $\mathrm {\mu }$m-200 $\mathrm {\mu }$m, adjustable with a translation stage and adapted for maximum output power for a given pump power. The SESAM is heated to a temperature of $T_{\text {SESAM}} = 60^{\circ }$C to increase the absorption and promote stable mode-locked emission.
This results in an average output power of up to P$_{\text {avg}}$ = 32 mW in a fundamental mode-locked pulse train. A 10 ns part of the temporal trace is visible in Fig. 2(a) and shows single pulses with a separation of 2.75 ns on top of a stable zero baseline. The oscillation and negative overshoot after the pulse is an electronic artifact due to bandwidth limitations of the detection. The pulse train on a longer 200-$\mathrm {\mu }$s span in the inset of Fig. 2(a) shows stable emission where drop-outs or periodic modulations are absent.
Fig. 2. In a) a $10\,$ns span of the temporal trace is shown while the inset has a larger span of 200 $\mathrm {\mu }$s. b) shows the FFT-derived frequency spectrum in a 1 MHz range around the first harmonic. The inset of b) shows the full frequency spectrum where also the higher harmonics are visible. c) displays the non-collinear autocorrelation where a sech$^{2}$-fit shows a good overlap with the experimental data and results in a temporal pulse duration of 7.5 ps. The inset contains the optical spectrum which is centered at 662.2 nm with a FWHM of 1.3 nm.
Using the fast Fourier-transform algorithm results in a spectral representation with a resolution-bandwidth of RBW=5 kHz. The zoom-in around the fundamental cavity frequency with a 1 MHz window in Fig. 2(b) shows a single narrow peak just above 364 MHz corresponding to the cavity round-trip time of 2.75 ns. It has a large amplitude of more than 55 dB above the noise level and is free from a pedestal or side-peaks. The inset of Fig. 2(b) shows a larger span of the radio frequency spectrum where all harmonics are clearly visible and have low fluctuations of their peak amplitude below 3.3 dB up to the cut-off frequency of the photodiode around 12 GHz.
The non-collinear autocorrelation of Fig. 2(c) is recorded using an APE pulseCheck with a scan range of 150 ps. The measured pulse agrees well with a sech$^{2}$-fit from which we extract a temporal FWHM of ${\tau _{\text {p}} = 7.5\,\text {ps}}$.
The inset of Fig. 2(c) contains the optical spectrum which is centered at a wavelength of 662.2 nm and with a FWHM of 1.3 nm. This, in combination with the temporal width, results in a time-bandwidth-product of 6.6, which is 21 times the Fourier-limited value.
3. Nonlinear reflectivity setup
The setup to record nonlinear reflectivity is based on the principle initially presented by Maas [8] for the 1 $\mathrm {\mu }$m range which resembles a Michelson geometry, schematically shown in Fig. 4(a). For attenuation we use a zero-order half-wave plate in conjunction with a standard optical isolator, both with a design wavelength of 670 nm. The beam is then separated by an antireflection coated 50:50 beamsplitter. The reference arm always contains a high reflectivity (R = 99.8%) mirror while the sample arm contains an aspheric lens with a short focal length of f = 4.03 mm focusing the beam either on an identical highly-reflective mirror for calibration or a SESAM for measurement. The collimated beam area at the position of the lens is measured to $1.07\,$mm$^{2}$ with a beam profile camera, resulting in a focused beam area of $4.1\,\mathrm {\mu }\text {m}^{2}$ which is verified with a beam profile camera with microscope objective. The measured total transmission to the sample amounts to 22%. Both arms are temporally separated by a chopper and the back-reflected beam is detected using a switchable-gain photodiode. The photodiode is interfaced with a low-cost 14-bit analog-to-digital converter which is controlled by a PC. Then, a computer program sets the half-wave plate angle and performs 500 averages at each fluence level. We align the setup as proposed in [3], where we first overlap the beam from the sample and the reference arm at the detector position. Then the lens is introduced and matching beam profiles of the sample and reference arm at the detector position are established.
The reflectivity-curves are fitted using the typical description of SESAM dynamics based on a two level system [15]
4. Sample structure and nonlinear reflectivity
All investigated SESAMs comprise a 55 times $\lambda$/4 pair Al$_{0.50}$GaAs/Al$_{0.95}$GaAs DBR, optimized for 660 nm, on top of which different active region designs are grown. The refractive index profile as well as the standing electric field for a wavelength of 662.2 nm are depicted in Fig. 3(a-c) for the uppermost layers.
Fig. 3. In a) the refractive index profile and electric field distribution for 662.2 nm of the SESAM with a single quantum well in the field node is shown (’antiresonant QW’) while b) is for the SESAM with a single quantum well in the antinode (’resonant QW’) and c) for the SESAM with two quantum wells. The measured reflectivity spectrum (black) for the SESAM with a single quantum well in the field node is shown in d), for the single quantum well in field antinode in e) and for the two quantum well SESAM in f), each including the transfer-matrix simulation (red-dashed).
The first investigated SESAM’s active region in Fig. 3(a) comprises a single compressively-strained GaInP quantum well positioned in the node of the standing electric field (’antiresonant QW’). This results in a maximum normalized field amplitude below 0.04 at the position of the quantum well. This was achieved by reducing the thickness of the underlying Al$_{0.95}$GaAs heat spreading layer which also moves the arsenic-phosphidic transition into a node of the standing electric field. The corresponding reflectivity spectrum is shown in Fig. 3(d), where the simulation based on AlGaInP refractive index data from [16] reproduces the measurement well, also for the sidebands of the stopband.
The second SESAM in Fig. 3(b) comprises a single compressively-strained GaInP quantum well positioned in the antinode of the standing electric field (’resonant QW’). Here, the total thickness of the Al$_{0.95}$GaAs heat spreading layer is increased resulting in a completely resonant design with large field enhancement. This results in a dip in the stopband of the reflectivity spectrum in Fig. 3(e) where the reflectivity reaches a local minimum around 92%.
The third SESAM in Fig. 3(c) comprises a package of two compressively-strained GaInP quantum wells positioned in the antinode of the standing electric field. Similar to the second SESAM, a fully resonant design with a strong field amplitude at the position of the quantum wells is achieved. The associated reflectivity spectrum in Fig. 3(f) shows a stronger dip in the stopband where the reflectivity is reduced to approximately 81%.
The nonlinear reflectivity is shown in Fig. 4(b) where the measurement of a dielectric high reflector is also included for reference (black dots). The reference is used to calibrate the system, resulting in a peak-to-peak variation of ${\sigma _{\text {HR}}=0.17\%}$.
Fig. 4. In a) the schematic of the nonlinear reflectivity setup, adapted from [8]. The attenuation is realized by a combination of a half-wave plate (HWP) and a polarizing beamsplitter in the optical isolator. The Michelson geometry with the nonpolarizing 50:50 beamsplitter provides sample and reference arm which are detected at the photodiode with a temporal separation due to the chopper. In b) the nonlinear reflectivity for a dielectric high reflector (black), the single quantum well in the field node SESAM (red), the resonant single quantum well (brown) and resonant double quantum well (blue) SESAM. The continuous lines are fits using Eq. (1) adapted for a Gaussian beam profile.
The first SESAM with a quantum well in the field node shows a flat reflectivity across the available fluence range which amounts to $R_{\text {lin.}, 0\text {QW}} = 97.2\%$ when averaging all measured fluences. Using this value as a reference, we can fit the nonlinear reflectivity measurement using the saturation fluence as the only free fit parameter. The nonsaturable losses are fixed to 97.2%, as obtained from the SESAM with the quantum well positioned in the node of the electric field. The linear reflectivity is set to the value reached below $1\,\mathrm {\mu }\text {J}/\text {cm}^{2}$ since here no reflectivity dynamics are observed. Also, since we use picosecond pulses, the inverse-saturable absorption should be minimal and therefore the curves are fitted assuming infinite $F_2$.
For the SESAM with a single quantum well in the field antinode the reflectivity in Fig. 4(b) (brown dots) rises from a value of $R_{\text {lin.}, 1\text {QW}} =92.2\%$ to a maximum measured reflectivity of $R_{\text {max.}, 1\text {QW}} =96.7\%$. A fit based on Eq. (1) has a good agreement with the measured curve (adjusted R$^{2}$ = 0.991) and yields a saturation fluence of $F_{\text {sat.}, 1\text {QW}} = 38\,\mathrm {\mu }\text {J}/\text {cm}^{2}$ with a modulation depth of $\Delta R_{1\text {QW}}=5\%$.
The SESAM with a double quantum well package shows a more pronounced nonlinearity in Fig. 4(b) (blue dots). Here, the linear reflectivity amounts to $R_{\text {lin.}, 2\text {QW}} =86.9\%$ and increases to a maximum measured reflectivity of $95.3\%$. The fit based on Eq. (1) results in a saturation fluence $F_{\text {max.}, 2\text {QW}} = 34\,\mathrm {\mu }\text {J}/\text {cm}^{2}$, a modulation depth of $\Delta R_{2\text {QW}}=10.3\%$ with an adjusted R$^{2}$ = 0.995.
5. Discussion
The cavity of the VECSEL source is optimized to provide a fluence up to 430$\,\mathrm {\mu }\text {J}/\text {cm}^{2}$, easily exceeding 3$F_{\text {sat.}}$ of our investigated structures, a criterion for reliable parameter extraction through fitting [15]. To this end, the cavity realizes four gain-interactions of a single pulse per round-trip, which was also used at other spectral ranges to increase the pulse energy [17,18]. In addition, an antiresonant SESAM is used because the overall reduced loss is beneficial in terms of average output power. This allows twice the energy per pulse compared to a z-shaped cavity design previously used [12,13] in the red spectral range. The surprisingly large time-bandwidth product is difficult to explain. On the one hand, the antiresonant design of gain and absorber should provide only minimal dispersion and therefore support close to transform-limited emission. However, high values of dispersion could be introduced through the wedged intracavity diamond, depending on the strength of the Fabry-Perot effect. The oblique incidence of the intracavity beam on the wedged and ar-coated diamond heatspreader allows a reduction of the Fabry-Perot effect such that it is not visible in the autocorrelation in Fig. 2(c), where side-pulses with a separation around 10 ps would appear [10] that go along with a considerable Fabry-Perot modulation of the optical spectrum. Other VECSELs [19,20] with intracavity diamond heatspreader can also show a large time-bandwidth product despite a single pulse per round-trip, so that the diamond could still contribute residual group delay dispersion. This is, however, part of ongoing investigations.
The nonlinear reflectivity setup achieves a peak-to-peak variation of ${\sigma _{\text {HR}}=0.17\%}$ which is up to an order of magnitude larger (0.05% [8] to 0.02% [21]) than the best published results. This could in part be influenced by the larger electronics noise in our setup as well as the use of a short focal length lens, leading to a larger sensitivity for beam-pointing. Here, an increase of the available source power would probably also increase the measurement accuracy and could allow a clear identification of the reflectivity plateau. A further point is that for optimization of the nonlinear reflectivity of faster SESAMs, also a femtosecond VECSEL has to be used. For our structures, the average output power drops significantly, further limiting measurement and development of fast SESAMs.
Concerning the linear reflectivity, the stopband of Fig. 3(d) shows no discernible influence at the wavelength of investigation, despite the presence of a quantum well in the structure. This is different for the single quantum well SESAM which shows a cavity dip due to enhanced quantum well absorption. This dip is even more pronounced for the SESAM with two quantum wells and correlates to the higher number of excitable states.
This trend is also present in the nonlinear reflectivity measurement. Here, the single quantum well SESAM provides a significant modulation depth of $\Delta R_{1\text {QW}}=5\%$, while this is approximately doubled to $\Delta R_{2\text {QW}}=10.3\%$ for the two quantum well SESAM, in agreement with the trend in the linear reflectivity.
The saturation fluence of the single as well as the two quantum well SESAM have moderate values of $F_{\text {sat.}, 1\text {QW}} = 38\,\mathrm {\mu }\text {J}/\text {cm}^{2}$ and $F_{\text {sat.}, 2\text {QW}} = 34\,\mathrm {\mu }\text {J}/\text {cm}^{2}$. This is comparable to the InGaAs-GaAs material system where regularly saturation fluences below 100$\,\mathrm {\mu }\text {J}/\text {cm}^{2}$ are obtained [8,22,23].
For the nonlinear reflectivity characterization, a resonant sample amplifies the linear and nonlinear loss with a wavelength-dependence similar to the subcavity resonance [24]. In our case, this is beneficial because a large modulation for the same input powers can be observed, but requires exact analysis of the fabricated structures. This is the case for the investigated samples as a good agreement between measured and simulated reflectivity in Fig. 3(d-f) is obtained. Then, even a nonlinear reflectivity setup with larger peak-to-peak variation can be used to extract the nonlinear reflectivity.
The amount of nonsaturable loss in our SESAMs is rather high, although high loss SESAMs have previously been used in mode-locked VECSELs [25] where more than 5% of nonsaturable loss were found. In contrast, usually mode-locked VECSELs use absorbers with lower nonsaturable losses of 1.94% [26], 1.23% [8] or even as low as 0.3% [24] for resonant SESAMs.
Concerning the origin of losses, we currently expect that losses introduced through strain-related defects of the quantum wells would scale with the quantum well number and position, while a similar behavior is expected for losses occurring at the arsenic-phosphidic transition between the AlGaAs DBR and the AlGaInP active region. However, the constant nonsaturable loss of $\Delta R_{\text {ns.}}=2.8\%$ of all presented SESAM designs allows us to exclude this option. Subsequent investigations of substrate-removed and green-pumped VECSEL and substrate-removed SESAM chips show that the transmission through the DBR accounts only for T$_{\text {loss}}$<0.1% loss. Similarly, Hall measurements of nominally-undoped layers suggest a very low background-doping below $10^{15} \text {cm}^{-2}$, a value that should only lead to absorption loss in the <0.1% range [27,28] much smaller the our observed losses of 2.8%.
We therefore currently assume that all interfaces, as well as the surface, are responsible for scattering loss. Actually, for VCSELs in the red spectral range it is well known that surface-roughness can have a comparably large influence on the overall DBR reflectivity [29]. Assuming a reduced DBR reflectivity of 99.5 %, this would lead to cavity-enhanced losses on the same order of magnitude as the losses observed in the nonlinear reflectivity. Furthermore, such scattering-losses do not introduce an inverse-saturable absorption mechanism [30] in agreement with the good fitting in Fig. 4(b) assuming infinite $F_2$. In the mode-locked VECSEL high nonsaturable loss mainly reduces the optical output power.
6. Conclusion
We have presented, to our best knowledge, the first nonlinear reflectivity characterization of SESAMs in the red spectral range. The laser source is a home-built mode-locked VECSEL with four gain passes as well as an antiresonant GaInP quantum well SESAM. This enables an average output power of P$_{\text {avg}}$ = 32 mW in fundamental mode-locked operation with 7.5 ps sech$^{2}$-shaped pulses at a repetition rate of 364 MHz.
The nonlinear reflectivity setup achieves a peak-to-peak variation of 0.17% and a maximum fluence of 430$\,\mathrm {\mu }\text {J}/\text {cm}^{2}$. We use this to characterize resonant single and double GaInP quantum well SESAMs with saturation fluences of $34\,\mathrm {\mu }\text {J}/\text {cm}^{2}$ and $38\,\mathrm {\mu }\text {J}/\text {cm}^{2}$ and modulation depths of 10.3% and 5%, respectively. These results show a nice inter-comparability and are overall similar to the InGaAs-GaAs material system. We find high and identical nonsaturable loss of 2.8% for all investigated SESAMs which is attributed to surface and interface roughness induced scattering, in agreement with the absence of inverse-saturable absorption for picosecond pulses.
Funding
Deutsche Forschungsgemeinschaft (JE 422/9-1).
Acknowledgments
The authors would like to thank S. Vollmer for technical assistance with the XRD and MOVPE systems, J. Elling for help in SEM analysis and M. Seibold for introduction into wet-chemical processing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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