Abstract

Optical frequency combs based on mode-locked lasers have revolutionized many areas of science and technology, such as precision metrology, optical frequency synthesis, and telecommunications. In recent years, a particular kind of frequency comb has been observed in edge-emitting semiconductor lasers where the phase difference between longitudinal laser modes is fixed but not zero. This results in a linearly chirped output in the time domain with nearly constant intensity. Here, by using coherent beatnote spectroscopy, we show that such a comb regime can also exist in vertical-external-cavity surface-emitting lasers, as evidenced for a specific part of the laser spectrum. Our findings may not only lead to a better understanding of the physics of frequency-modulated combs but also enable comb applications with high optical power per comb line and flexible emission wavelengths.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

An optical frequency comb consists of equidistantly spaced laser lines. What distinguishes it from a free-running multi-mode laser is the fact that there exists a fixed phase relationship between adjacent longitudinal modes oscillating in the laser resonator. This guarantees that the frequency spacing between different modes does not change with time. Historically, such mode locking has been achieved by the use of strongly intensity-dependent elements in the laser cavity where saturable absorption provides a coupling mechanism between laser modes, which typically results in ultrashort pulses in the time domain and can be understood as in-phase synchronization of laser modes [1,2]. However, frequency-comb generation in a semiconductor laser can also occur in the absence of a saturable absorber [3,4]. In this case, it is understood that the beating of different laser modes leads to oscillations of the carrier density in the gain medium at multiples of the repetition frequency (corresponding to longitudinal mode spacing), which in turn again couple with the laser modes. This provides a locking mechanism that can compensate for dispersion and noise that otherwise prevent equidistance and phase coherence of the modes, respectively. These combs have been primarily observed in interband and quantum cascade lasers, which have a short gain recovery time compared to the cavity round trip time, as a slow gain medium with a long gain recovery time cannot respond efficiently to fast intermode beating and thus results in negligible mode coupling [5]. However, also in interband diode lasers, where the round trip time is typically somewhat smaller than the carrier lifetime of around 1 ns, this effect has been observed in a variety of material systems [2,6,7]. This has been supported by recent theoretical work that suggests that comb formation is principally determined by the interplay of group delay dispersion (GDD) and carrier-induced refractive index changes leading to soliton-like states with a characteristic linear chirp or frequency modulation (FM) in the time domain [8,9].

Optically pumped semiconductor disk lasers or vertical-external-cavity surface-emitting lasers (VECSELs) can be passively mode-locked by use of a semiconductor-saturable-absorber mirror (SESAM) with ultrashort pulse emission down to the sub-100 fs regime [10,11], and even saturable-absorber-free mode locking was discussed [1215]. Whether this class of lasers supports FM combs similar to their edge-emitting counterparts remains an exciting question to address, as both types of semiconductor lasers differ in some aspects fundamentally. The mode spacing (i.e., free spectral range), which relates directly to the cavity round trip time, is typically an order of magnitude smaller, in the few gigahertz range. This provides a setting where gain recovery time and round trip time are very similar. Also, the spatial hole burning process of a Fabry–Perot cavity, which triggers multi-mode operation in edge-emitting lasers, is absent in VECSELs, as gain-contributing quantum wells (QWs) overlap only at nearly discrete positions in the sample structure with the standing optical field. In addition, the typically centimeter-long external resonator leads to the storage of optical power away from the gain medium.

From a practical point of view, FM combs in VECSELs might be useful for dual-comb spectroscopy with high power per comb line and consequently increased SNR of the measurement, as they are unrivaled in terms of output power among semiconductor lasers, reaching more than 100 W in cw operation [16]. Moreover, advanced III-V semiconductor technology enables great flexibility with respect to the emission wavelength, ranging from the visible to the mid-infrared [17]. Recently, dual-comb spectroscopy with mode-locked VECSELs has been demonstrated [18]. However, when pushing the pulse length below 100 fs, one observes a dramatic decrease in peak and average power [10], which is possibly caused by fundamental non-equilibrium carrier dynamics such as kinetic hole burning [19]. For increased average power and thus more power per comb line, one would have to increase the pulse length, which means generating chirped pulses for a given bandwidth. A frequency-modulated comb, being the extreme case of a maximally linearly chirped “pulse,” would lead to quasi-cw operation and thus highest average power. Remarkably, the existence of FM combs in lasers with fast gain media has been explained with the so-called maximum-emission principle, which states that the phase—amplitude relations of the laser modes will organize in a way to extract the maximum amount of power from the gain medium, which corresponds to the FM state [5].

 figure: Fig. 1.

Fig. 1. (a) Measured and simulated group delay dispersion (GDD) of the investigated sample. The error bars indicate the standard deviation when averaging over 997 subsequent measurements/interferograms. (b) Experimental setup used for coherent beatnote spectroscopy. PD, photodiode; LO, local oscillator.

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In this work, we investigate whether FM combs can also be supported in VECSELs by using a coherent beatnote spectroscopy technique, referred to as shifted wave interference transform spectroscopy (SWIFTS) [20]. This allows us to directly measure the intermode phase relation of the laser and assess its phase stability (coherence) over the laser spectrum. Our results show that such comb states can indeed exist in VECSELs, and we discuss its spectral and pump-power dependence.

2. SAMPLE PROPERTIES AND EXPERIMENTAL SETUP

For our investigations, we use a VECSEL gain chip, which has been designed for ultra-short pulse emission and low dispersion. To ensure good crystalline quality, the VECSEL layer structure was grown by metal organic vapor phase epitaxy (MOVPE) using an Aixtron AIX 2600 G3 reactor. The active laser structure consists of four double (GaIn)As QWs with surrounding Ga(AsP) strain-compensating barriers. Each QW pair was placed around a maximum of the longitudinal optical field. The distributed Bragg reflector contains 23.5 (AlGa)AlGaAs mirror pairs with $\lambda /4$ layers for a VECSEL lasing wavelength at 980 nm and additional 13 pairs for a pump wavelength at 808 nm to increase pump efficiency. The final GaAs layer is for phase matching and oxidation protection. The detailed chip structure and layer composition are provided in Supplement 1.

We have performed measurements with a white-light Michelson interferometer to determine the GDD of the sample [21]. As can be seen in Fig. 1(a), the GDD at the lasing frequencies around 303 THz is flat and lower than $500\;{{\rm fs}^2}$ in magnitude as expected for an anti-resonant design, i.e., a design that suppresses a strong microcavity resonance for optimized broadband operation at the cost of reduced gain [22]. Also, the measured dispersion is close to the calculated dispersion obtained by transfer-matrix simulations of the layered chip structure. More details on the dispersion measurement and calculation are provided in Supplement 1.

For laser operation, we mount the chip on a temperature-controlled copper heat sink and construct a simple linear cavity of approximately 9 cm length with an output mirror of 100 mm radius of curvature, minimized dispersion and 0.6% outcoupling rate. The chip is pumped with a fiber-coupled 808 nm multi-mode diode laser and the pump-spot diameter is adjusted to 200 µm to match the fundamental transverse mode on the chip. The temperature of the heat sink is kept at 18°C throughout all investigations.

To investigate whether the modes of the laser are phase-stable and locked, we use the SWIFTS technique, which resolves the beatnote coherently over the laser spectrum by use of a Michelson interferometer [20]. A sketch of our experimental setup is shown in Fig. 1(b). Part of the laser light is branched off into a fast photodiode while the other part is sent into a home-built Michelson interferometer, the output of which is recorded by another fast photodiode. The signal of both photodiodes is subsequently amplified (by around 25 dB) and mixed down with a local oscillator (LO) with a frequency of 1.58 GHz, which is close to the fundamental beatnote frequency of 1.6 GHz. The downconverted signal of the first photodiode is again amplified (by around 30 dB) to serve as a reference signal for a fast lock-in amplifier (SR844, Stanford Research Systems). The downconverted signal of the fast photodiode after the Michelson interferometer is taken as signal input. Consequently, the lock-in amplifier serves as a phase-sensitive detector, which records two interferograms when the arm of the Michelson interferometer is scanned. One interferogram, $X(\tau)$, corresponds to the in-phase component with respect to the reference signal, and the other interferogram, $Y(\tau)$, corresponds to the quadrature (90° shifted) component. It can be shown (see Supplement 1) that, by Fourier transforming these interferograms with respect to the interferometer delay, the intermode phase difference (SWIFTS phase) can be retrieved by $\arg (X(\omega) - iY(\omega))$, where $X(\omega)$ and $Y(\omega)$ are the complex spectra of $X(\tau)$ and $Y(\tau)$, respectively [2,20]. The magnitude of the combined spectra, the SWIFTS intensity spectrum $|X(\omega) - iY(\omega)|$, indicates over which spectral regions the modes are locked. By comparing this spectrum to the normal intensity spectrum obtained by Fourier transforming the interferogram recorded by a slow photodiode, one can assess which parts of the spectrum are phase coherent, and to what degree. When the shapes of both spectra match exactly, the emission consists of perfectly phase-coherent and equidistant laser modes.

 figure: Fig. 2.

Fig. 2. Coherence characterization of the VECSEL at 3.7 W pump power. (a) Fundamental beatnote at 1.6 GHz recorded with a resolution bandwidth of 1 kHz over a span of 500 kHz. The 3 dB bandwidth is indicated by the arrows. (b) Intensity interferogram recorded with a slow photodiode (“Intensity”) and the interferograms of the in-phase (“SWIFTS X”) and quadrature component (“SWIFTS Y”) of lock-in detection. (c) Magnitude of the Fourier transforms of the intensity interferogram (solid lines) and of the combined SWIFTS interferograms (dashed lines). Ten subsequently recorded measurements are shown. (d) Corresponding frequency-resolved intermode (SWIFTS) phase. The dots indicate the resolution of the measurement and do not represent individual modes.

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3. EXPERIMENTAL RESULTS

A first indicator of phase locking in a laser is provided by a narrow RF beatnote. Figure 2(a) shows the fundamental RF beatnote measured at 1.6 GHz with a 25 GHz photodiode at an optical pump power of 3.7 W. The 3 dB width of the beatnote is approximately 2.2 kHz. The noise pedestal is nearly 30 dB below the peak. Figure 2(b) displays the envelope of the raw interferograms recorded with the slow photodiode and the SWIFTS setup. The regular intensity interferogram exhibits a maximum at zero delay of the interferometer. The beating on the envelope is caused by the two-color operation of the laser. One notices that the envelope beatings of the intensity interferograms and the SWIFTS interferograms are phase shifted to each other by 180°. This is a consequence of the fact that each lobe (color) exhibits a total intermode phase difference of $\pi$ [as can be seen in Fig. 2(d)]. A derivation of this relation is provided in Supplement 1. The fact that the laser operates on two spectral lobes is probably a consequence of the anti-resonant design of the gain chip, for which the cavity resonance is designed in a way that there is no strong cavity resonance at one specific wavelength but rather two smaller resonances centered around the maximum material gain (see Supplement 1). In contrast to the intensity interferogram, both SWIFTS interferograms show a characteristic minimum at zero delay. This minimum is attributed to the presence of FM in the laser [3] and can be understood by regarding the intermode beating as complex phasors that cancel each other out when summed up [2]. Finally, Fig. 2(c) shows the retrieved normalized intensity and the two SWIFTS spectra as well as the intermode (SWIFTS) phase for 10 subsequent measurements [Fig. 2(d)]. Interestingly, for the lobe at larger frequencies, the intensity and SWIFTS spectrum match very well, whereas for the lobe at smaller frequencies, the amplitude of the SWIFTS spectrum is considerably smaller than the intensity spectrum and does not span over the whole range towards smaller frequencies. Accordingly, the SWIFTS spectrum is here normalized with respect to the intensity of the higher-frequency lobe. The intermode phase in Fig. 2(d) is well defined wherever the SWIFTS spectrum contains significant intensity. All SWIFTS phase measurements have been aligned with respect to their phase at 303.6 THz. As a result, the phases of the low-frequency lobe will also be aligned, although some phase measurements exhibit an offset of $2\pi$ from each other. This is a consequence of the unwrapping procedure and was corrected by shifting the phases at frequencies smaller than 303.3 THz by $2\pi$, so that all phases also match exactly at the low-frequency lobe of the spectrum. Interestingly, while the SWIFTS phases between the lobes are not (well) defined and thus are different for different subsequent measurements, the phase offset between high- and low-frequency lobes is constant for all subsequent measurements, and the total phase difference over both lobes amounts to about $2\pi$ as expected for a frequency-modulated comb. As a result of these investigations, we average both the intensity spectrum and SWIFTS (phase) spectra over multiple subsequent measurements in the following investigations. For the SWIFTS phase, we also plot the corresponding standard deviation as error bars to indicate where it is well defined.

To gain further insights into the coherence properties of our laser, we investigate the pump power dependence of the fundamental beatnote, as well as of the intensity and SWIFTS spectra. In Fig. 3(a), the pump-power-dependent evolution of the beatnote at 1.6 GHz is displayed. At 3.2 W pump power, corresponding to an output power of the laser of 111 mW, a detectable but small beatnote close to the noise level is measured. At pump powers ranging from 3.2 to 3.6 W, the beatnote is so small that it cannot be used as a reference for SWIFTS measurements. However, at a pump power of 3.6 W, the beatnote suddenly increases by more than 20 dB in magnitude. Strikingly, this coincides with the separation of the optical spectra in Fig. 3(b) into two lobes. Here, as already observed in Fig. 2(b), the intensity and SWIFTS spectra of the lobe at larger frequencies match perfectly over the pump power range from 3.4 to 4 W corresponding to output powers of 135 to 188 mW. In this range, the lobe at lower frequencies exhibits only partial coherence with nearly no coherence towards the lower frequency side. At a pump power of 4.1 W, the beatnote “explodes” into strong and broad noise pedestals around its peak within the frequency range of 500 kHz. The phase coherence is lost, and the SWIFTS intensity spectrum consequently drops to zero. For larger pump powers, the beatnote remains broad. Thus, no data for pump powers beyond 4.1 W are shown.

 figure: Fig. 3.

Fig. 3. (a) Pump-power dependence of the beatnote at 1.6 GHz measured with 1 kHz resolution bandwidth and 500 kHz span. (b) Pump-power-dependent intensity spectra (blue solid line) and SWIFTS intensity spectra (dashed line). The respective pump-power value is indicated in each subfigure. All spectra have been obtained by averaging over 10 subsequent measurements. (c) Corresponding SWIFTS phase. The power level is indicated to the right of the phase spectrum. The dots indicate the spectral resolution, and the error bars indicate the standard deviation when averaging over 10 subsequent measurements.

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All the retrieved intermode (SWIFTS) phases [Fig. 3(c)] show a phase difference of approximately $2\pi$ over the total spectrum. Thus, while the phases in-between the lobes are not very well defined and display a large standard deviation when averaging over multiple measurements, the two lobes are not completely decoupled and can still exhibit linearly chirped anti-phase synchronization. This is evidenced by an approximately linear trend of the intermode phase over the laser spectrum and a total phase difference of $2\pi$ [2,8,23].

It is worth mentioning that one witnesses here the existence of one higher-order transverse mode with a broad RF line (several tens of kilohertz) in the long-span RF spectrum, as shown in Fig. S3 of Supplement 1 when the photodiode is placed in a way that the contribution from the higher-order transverse mode (${{\rm TEM}_{10}}$) is detected. Attempts to suppress this mode by reducing the pump spot size on the chip were not successful. In fact, the existence of a higher-order transverse mode seems to coincide with the appearance of a narrow beatnote for the fundamental mode, similar to the behavior observed in Ref. [24]. This might hint to a possible connection between the frequency-modulated comb state we observe here and the self-mode-locking reports for VECSELs, where coherence of the laser emission was evidenced by autocorrelation measurements [14,24]. Nonetheless, we point out that the excellent correspondence of SWIFTS and intensity spectrum for the high-frequency lobe demonstrates that this part of the spectrum must principally consist of phase-locked longitudinal modes of the fundamental mode.

Furthermore, we investigated the effect of suppressing externally the partially incoherent lobe at lower frequencies with an angle-tunable short-pass filter (Semrock TSP01-1116) on the beatnote and SWIFTS interferograms. For a valid comparison, we adjusted the power in front of the photodiode to 2.2 mW for both the investigation with the filter inserted and without a filter (for the measurements in Fig. 2, the power in front of the photodiode was significantly larger). The result is shown in Fig. 4. Without the filter, the fundamental beatnote at 1.59 GHz is below 60 dBm [Fig. 4(a)], and the two SWIFTS interferograms [“X” and “Y” in Fig. 4(b)] show a pronounced minimum at zero delay position. However, when the low-frequency lobe is suppressed with the filter, the beatnote increases by approximately 16 dB, and the SWIFTS interferograms show no minimum at zero delay position anymore. This illustrates nicely the frequency-modulated nature of the laser emission. In the unfiltered case, the phases of the locked longitudinal modes organize in a way to minimize amplitude fluctuations, and therefore, the result is a small beatnote as well as a minimum at zero delay position in the SWIFTS interferograms. Both features result from destructive interference of the intermode beatings. In contrast, when part of the phase-locked laser spectrum is removed by the filter, the remaining intermode beatings will not cancel each other out very well anymore. This explains the strong increase in the magnitude of the beatnote as well as the disappearance of the minima at zero delay position in the SWIFTS interferograms.

 figure: Fig. 4.

Fig. 4. (a) Fundamental beatnote (measured at 1.59 GHz center frequency with 1 kHz resolution bandwidth and 500 kHz span), (b) intensity and SWIFTS interferograms, and (c) intensity (blue solid line), SWIFTS spectrum (orange dashed line), and SWIFTS phase $\Delta \varphi$ of the unfiltered laser emission at a pump power of 3.2 W (sample spot different from that in Fig. 3 used here). The corresponding measurements with spectral filtering are shown in (d), (e), and (f). For measurement of the fundamental beatnote in (a) and (d), the power in front of the photodiode is adjusted to 2.2 mW in both cases.

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The lobe in Fig. 4(f) has a 3 dB width of around 0.13 THz, thus containing more than 82 longitudinal laser modes, which is more than twice the number of modes that have been used in the pioneering first dual-comb spectroscopy experiment with VECSELs [18]. This highlights the importance of our results. Even though not the whole unfiltered laser spectrum is perfectly phase locked, a combination of spatial and spectral filtering can render it effectively coherent.

We believe that with a detailed understanding of the locking mechanism, it will be possible in the future to obtain FM combs in VECSELs that are fully coherent over the whole laser spectrum. Then they might provide a very simple and at the same time high-power source for dual-comb spectroscopy. To reach this goal, two open questions need to be addressed in future works: what limits the coherence over a broad spectrum, and what is the optimal amount of GDD in the cavity (see Ref. [8])?

Moreover, FM combs may become a useful alternative to SESAM-mode-locked VECSELs for some applications, particularly in the context of novel material systems targeting new spectral emission wavelengths where SESAM mode locking might be difficult to achieve. An example can be seen in the recently demonstrated type-II VECSELs [25], which have not been SESAM mode locked yet.

4. CONCLUSION

By measuring the intermode phase relation and the phase coherence with the SWIFTS technique, we have demonstrated that a VECSEL can run in a frequency-modulated regime, whereas at the moment, this occurs over a certain part of its spectrum. With an optical filter, the incoherent part can be suppressed, and phase-coherent light is obtained. This establishes optically pumped semiconductor disk lasers as a new platform where the physics of FM combs can be studied. In fact, VECSELs offer unique characteristics such as a very similar gain recovery time and cavity round trip time as well as the absence of spatial hole burning as a driver for multi-mode emission. Given future optimization efforts, it can be anticipated that these comb sources may prove themselves useful for dual-comb spectroscopy in application scenarios where a particular high power per comb line or specific target wavelengths are required.

Funding

Deutsche Forschungsgemeinschaft (DFG RA 2841/1-1, DFG RA 2841/1-3).

Acknowledgment

We thank C. Schindler for expert design of the RF amplifiers and mixers and for useful discussions.

Disclosures

The authors declare no conflict of interests.

Supplemental document

See Supplement 1 for supporting content.

REFERENCES

1. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000). [CrossRef]  

2. J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019). [CrossRef]  

3. A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012). [CrossRef]  

4. E. Escoto and G. Steinmeyer, “Pseudo mode-locking,” Proc. SPIE 11263, 1126306 (2020). [CrossRef]  

5. M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019). [CrossRef]  

6. M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020). [CrossRef]  

7. R. Rosales, S. G. Murdoch, R. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20, 8649–8657 (2012). [CrossRef]  

8. N. Opačak and B. Schwarz, “Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr nonlinearity,” Phys. Rev. Lett. 123, 243902 (2019). [CrossRef]  

9. D. Burghoff, “Unraveling the origin of frequency modulated combs using active mean-field theory,” Optica 7, 1781–1787 (2020). [CrossRef]  

10. D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016). [CrossRef]  

11. A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018). [CrossRef]  

12. L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012). [CrossRef]  

13. A. R. Albrecht, Y. Wang, M. Ghasemkhani, D. V. Seletskiy, J. G. Cederberg, and M. Sheik-Bahae, “Exploring ultrafast negative Kerr effect for mode-locking vertical external-cavity surface-emitting lasers,” Opt. Express 21, 28801–28808 (2013). [CrossRef]  

14. M. Gaafar, P. Richter, H. Keskin, C. Möller, M. Wichmann, W. Stolz, A. Rahimi-Iman, and M. Koch, “Self-mode-locking semiconductor disk laser,” Opt. Express 22, 28390–28399 (2014). [CrossRef]  

15. M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked semiconductor disk lasers,” Adv. Opt. Photon. 8, 370–400 (2016). [CrossRef]  

16. B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012). [CrossRef]  

17. A. Rahimi-Iman, “Recent advances in VECSELs,” J. Opt. 18, 093003 (2016). [CrossRef]  

18. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017). [CrossRef]  

19. I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014). [CrossRef]  

20. D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs,” Opt. Express 23, 1190–1202 (2015). [CrossRef]  

21. A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. Am. B 22, 1868–1874 (2005). [CrossRef]  

22. A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30, 1–43 (2006). [CrossRef]  

23. M. Singleton, P. Jouy, M. Beck, and J. Faist, “Evidence of linear chirp in mid-infrared quantum cascade lasers,” Optica 5, 948–953 (2018). [CrossRef]  

24. C. H. Tsou, H. C. Liang, C. P. Wen, K. W. Su, K. F. Huang, and Y. F. Chen, “Exploring the influence of high order transverse modes on the temporal dynamics in an optically pumped mode-locked semiconductor disk laser,” Opt. Express 23, 16339–16347 (2015). [CrossRef]  

25. C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016). [CrossRef]  

References

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  1. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
    [Crossref]
  2. J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
    [Crossref]
  3. A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
    [Crossref]
  4. E. Escoto and G. Steinmeyer, “Pseudo mode-locking,” Proc. SPIE 11263, 1126306 (2020).
    [Crossref]
  5. M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
    [Crossref]
  6. M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
    [Crossref]
  7. R. Rosales, S. G. Murdoch, R. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20, 8649–8657 (2012).
    [Crossref]
  8. N. Opačak and B. Schwarz, “Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr nonlinearity,” Phys. Rev. Lett. 123, 243902 (2019).
    [Crossref]
  9. D. Burghoff, “Unraveling the origin of frequency modulated combs using active mean-field theory,” Optica 7, 1781–1787 (2020).
    [Crossref]
  10. D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016).
    [Crossref]
  11. A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
    [Crossref]
  12. L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
    [Crossref]
  13. A. R. Albrecht, Y. Wang, M. Ghasemkhani, D. V. Seletskiy, J. G. Cederberg, and M. Sheik-Bahae, “Exploring ultrafast negative Kerr effect for mode-locking vertical external-cavity surface-emitting lasers,” Opt. Express 21, 28801–28808 (2013).
    [Crossref]
  14. M. Gaafar, P. Richter, H. Keskin, C. Möller, M. Wichmann, W. Stolz, A. Rahimi-Iman, and M. Koch, “Self-mode-locking semiconductor disk laser,” Opt. Express 22, 28390–28399 (2014).
    [Crossref]
  15. M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked semiconductor disk lasers,” Adv. Opt. Photon. 8, 370–400 (2016).
    [Crossref]
  16. B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
    [Crossref]
  17. A. Rahimi-Iman, “Recent advances in VECSELs,” J. Opt. 18, 093003 (2016).
    [Crossref]
  18. S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
    [Crossref]
  19. I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
    [Crossref]
  20. D. Burghoff, Y. Yang, D. J. Hayton, J.-R. Gao, J. L. Reno, and Q. Hu, “Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs,” Opt. Express 23, 1190–1202 (2015).
    [Crossref]
  21. A. Gosteva, M. Haiml, R. Paschotta, and U. Keller, “Noise-related resolution limit of dispersion measurements with white-light interferometers,” J. Opt. Soc. Am. B 22, 1868–1874 (2005).
    [Crossref]
  22. A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30, 1–43 (2006).
    [Crossref]
  23. M. Singleton, P. Jouy, M. Beck, and J. Faist, “Evidence of linear chirp in mid-infrared quantum cascade lasers,” Optica 5, 948–953 (2018).
    [Crossref]
  24. C. H. Tsou, H. C. Liang, C. P. Wen, K. W. Su, K. F. Huang, and Y. F. Chen, “Exploring the influence of high order transverse modes on the temporal dynamics in an optically pumped mode-locked semiconductor disk laser,” Opt. Express 23, 16339–16347 (2015).
    [Crossref]
  25. C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
    [Crossref]

2020 (3)

E. Escoto and G. Steinmeyer, “Pseudo mode-locking,” Proc. SPIE 11263, 1126306 (2020).
[Crossref]

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

D. Burghoff, “Unraveling the origin of frequency modulated combs using active mean-field theory,” Optica 7, 1781–1787 (2020).
[Crossref]

2019 (3)

N. Opačak and B. Schwarz, “Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr nonlinearity,” Phys. Rev. Lett. 123, 243902 (2019).
[Crossref]

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

2018 (2)

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

M. Singleton, P. Jouy, M. Beck, and J. Faist, “Evidence of linear chirp in mid-infrared quantum cascade lasers,” Optica 5, 948–953 (2018).
[Crossref]

2017 (1)

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref]

2016 (4)

A. Rahimi-Iman, “Recent advances in VECSELs,” J. Opt. 18, 093003 (2016).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016).
[Crossref]

M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked semiconductor disk lasers,” Adv. Opt. Photon. 8, 370–400 (2016).
[Crossref]

2015 (2)

2014 (2)

2013 (1)

2012 (4)

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
[Crossref]

R. Rosales, S. G. Murdoch, R. Watts, K. Merghem, A. Martinez, F. Lelarge, A. Accard, L. P. Barry, and A. Ramdane, “High performance mode locking characteristics of single section quantum dash lasers,” Opt. Express 20, 8649–8657 (2012).
[Crossref]

2006 (1)

A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30, 1–43 (2006).
[Crossref]

2005 (1)

2000 (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
[Crossref]

Accard, A.

Albrecht, A. R.

Alfieri, C. G. E.

Auth, D.

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

Balakrishnan, G.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

Barry, L. P.

Beck, M.

Belyanin, A.

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

Berger, C.

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

Blaser, S.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
[Crossref]

Breuer, S.

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

Burghoff, D.

Butkus, M.

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

Capasso, F.

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

Cederberg, J. G.

Chen, Y. F.

Chevalier, P.

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

Cundiff, S. T.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Day, M. W.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Dong, M.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Escoto, E.

E. Escoto and G. Steinmeyer, “Pseudo mode-locking,” Proc. SPIE 11263, 1126306 (2020).
[Crossref]

Faist, J.

M. Singleton, P. Jouy, M. Beck, and J. Faist, “Evidence of linear chirp in mid-infrared quantum cascade lasers,” Optica 5, 948–953 (2018).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
[Crossref]

Fedorova, K. A.

Fuchs, C.

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

Gaafar, M.

Gaafar, M. A.

Gao, J.-R.

Ghasemkhani, M.

Gini, E.

Golling, M.

Gosteva, A.

Hader, J.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Haiml, M.

Hamilton, C. J.

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
[Crossref]

Hayton, D. J.

Heinen, B.

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Hillbrand, J.

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

Hoogland, S.

A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30, 1–43 (2006).
[Crossref]

Hu, Q.

Huang, K. F.

Hugi, A.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
[Crossref]

Jouy, P.

Kazakov, D.

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

Keller, U.

Kerber, G. C.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Keskin, H.

Kilen, I.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

Koch, M.

M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked semiconductor disk lasers,” Adv. Opt. Photon. 8, 370–400 (2016).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

M. Gaafar, P. Richter, H. Keskin, C. Möller, M. Wichmann, W. Stolz, A. Rahimi-Iman, and M. Koch, “Self-mode-locking semiconductor disk laser,” Opt. Express 22, 28390–28399 (2014).
[Crossref]

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Koch, S. W.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Kornaszewski, L.

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

Kunert, B.

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Laurain, A.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

Lelarge, F.

Liang, H. C.

Link, S. M.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref]

D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016).
[Crossref]

Liu, H. C.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
[Crossref]

Ludewig, P.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

Ma, T.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Maas, D. J. H. C.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref]

Maker, G.

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

Malcolm, G. P.

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

Mangold, M.

Martinez, A.

Merghem, K.

Möller, C.

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

M. Gaafar, P. Richter, H. Keskin, C. Möller, M. Wichmann, W. Stolz, A. Rahimi-Iman, and M. Koch, “Self-mode-locking semiconductor disk laser,” Opt. Express 22, 28390–28399 (2014).
[Crossref]

Moloney, J. V.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

I. Kilen, J. Hader, J. V. Moloney, and S. W. Koch, “Ultrafast nonequilibrium carrier dynamics in semiconductor laser mode locking,” Optica 1, 192–197 (2014).
[Crossref]

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Murdoch, S. G.

Opacak, N.

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

N. Opačak and B. Schwarz, “Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr nonlinearity,” Phys. Rev. Lett. 123, 243902 (2019).
[Crossref]

Owen, R. C.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Paschotta, R.

Perez, A. R.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

Piccardo, M.

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

Rafailov, E.

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

Rafailov, E. U.

Rahimi-Iman, A.

Ramdane, A.

Reno, J. L.

Richter, P.

Rosales, R.

Schwarz, B.

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

N. Opačak and B. Schwarz, “Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr nonlinearity,” Phys. Rev. Lett. 123, 243902 (2019).
[Crossref]

Seletskiy, D. V.

Sheik-Bahae, M.

Singleton, M.

Smith, B. C.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Sparenberg, M.

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Steinmeyer, G.

E. Escoto and G. Steinmeyer, “Pseudo mode-locking,” Proc. SPIE 11263, 1126306 (2020).
[Crossref]

Stolz, W.

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

M. A. Gaafar, A. Rahimi-Iman, K. A. Fedorova, W. Stolz, E. U. Rafailov, and M. Koch, “Mode-locked semiconductor disk lasers,” Adv. Opt. Photon. 8, 370–400 (2016).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

M. Gaafar, P. Richter, H. Keskin, C. Möller, M. Wichmann, W. Stolz, A. Rahimi-Iman, and M. Koch, “Self-mode-locking semiconductor disk laser,” Opt. Express 22, 28390–28399 (2014).
[Crossref]

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Strasser, G.

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

Su, K. W.

Tilma, B. W.

Tropper, A. C.

A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30, 1–43 (2006).
[Crossref]

Tsou, C. H.

Villares, G.

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
[Crossref]

Waldburger, D.

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref]

D. Waldburger, S. M. Link, M. Mangold, C. G. E. Alfieri, E. Gini, M. Golling, B. W. Tilma, and U. Keller, “High-power 100 fs semiconductor disk lasers,” Optica 3, 844–852 (2016).
[Crossref]

Wang, T.-L.

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Wang, Y.

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

A. R. Albrecht, Y. Wang, M. Ghasemkhani, D. V. Seletskiy, J. G. Cederberg, and M. Sheik-Bahae, “Exploring ultrafast negative Kerr effect for mode-locking vertical external-cavity surface-emitting lasers,” Opt. Express 21, 28801–28808 (2013).
[Crossref]

Watts, R.

Weber, A.

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

Wen, C. P.

Wichmann, M.

Winful, H. G.

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Yang, Y.

Adv. Opt. Photon. (1)

APL Photon. (1)

M. W. Day, M. Dong, B. C. Smith, R. C. Owen, G. C. Kerber, T. Ma, H. G. Winful, and S. T. Cundiff, “Simple single-section diode frequency combs,” APL Photon. 5, 121303 (2020).
[Crossref]

Appl. Phys. Lett. (2)

A. Laurain, I. Kilen, J. Hader, A. R. Perez, P. Ludewig, W. Stolz, G. Balakrishnan, S. W. Koch, and J. V. Moloney, “Modeling and experimental realization of modelocked VECSEL producing high power sub-100 fs pulses,” Appl. Phys. Lett. 113, 121113 (2018).
[Crossref]

C. Möller, C. Fuchs, C. Berger, A. R. Perez, M. Koch, J. Hader, J. V. Moloney, S. W. Koch, and W. Stolz, “Type-II vertical-external-cavity surface-emitting laser with Watt level output powers at 1. 2 µm,” Appl. Phys. Lett. 108, 071102 (2016).
[Crossref]

Electron. Lett. (1)

B. Heinen, T.-L. Wang, M. Sparenberg, A. Weber, B. Kunert, J. Hader, S. W. Koch, J. V. Moloney, M. Koch, and W. Stolz, “106 W continuous-wave output power from vertical-external-cavity surface-emitting laser,” Electron. Lett. 48, 516–517 (2012).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
[Crossref]

J. Opt. (1)

A. Rahimi-Iman, “Recent advances in VECSELs,” J. Opt. 18, 093003 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

L. Kornaszewski, G. Maker, G. P. Malcolm, M. Butkus, E. Rafailov, and C. J. Hamilton, “SESAM-free mode-locked semiconductor disk laser,” Laser Photon. Rev. 6, L20–23 (2012).
[Crossref]

Nature (1)

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492, 229–233 (2012).
[Crossref]

Opt. Express (5)

Optica (4)

Phys. Rev. Lett. (3)

N. Opačak and B. Schwarz, “Theory of frequency modulated combs in lasers with spatial hole burning, dispersion and Kerr nonlinearity,” Phys. Rev. Lett. 123, 243902 (2019).
[Crossref]

J. Hillbrand, D. Auth, M. Piccardo, N. Opacak, G. Strasser, F. Capasso, S. Breuer, and B. Schwarz, “In-phase and anti-phase synchronization in a laser frequency comb,” Phys. Rev. Lett. 124, 023901 (2019).
[Crossref]

M. Piccardo, P. Chevalier, B. Schwarz, D. Kazakov, Y. Wang, A. Belyanin, and F. Capasso, “Frequency-modulated combs obey a variational principle,” Phys. Rev. Lett. 122, 253901 (2019).
[Crossref]

Proc. SPIE (1)

E. Escoto and G. Steinmeyer, “Pseudo mode-locking,” Proc. SPIE 11263, 1126306 (2020).
[Crossref]

Prog. Quantum Electron. (1)

A. C. Tropper and S. Hoogland, “Extended cavity surface-emitting semiconductor lasers,” Prog. Quantum Electron. 30, 1–43 (2006).
[Crossref]

Science (1)

S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, “Dual-comb spectroscopy of water vapor with a free-running semiconductor disk laser,” Science 356, 1164–1168 (2017).
[Crossref]

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. (a) Measured and simulated group delay dispersion (GDD) of the investigated sample. The error bars indicate the standard deviation when averaging over 997 subsequent measurements/interferograms. (b) Experimental setup used for coherent beatnote spectroscopy. PD, photodiode; LO, local oscillator.
Fig. 2.
Fig. 2. Coherence characterization of the VECSEL at 3.7 W pump power. (a) Fundamental beatnote at 1.6 GHz recorded with a resolution bandwidth of 1 kHz over a span of 500 kHz. The 3 dB bandwidth is indicated by the arrows. (b) Intensity interferogram recorded with a slow photodiode (“Intensity”) and the interferograms of the in-phase (“SWIFTS X”) and quadrature component (“SWIFTS Y”) of lock-in detection. (c) Magnitude of the Fourier transforms of the intensity interferogram (solid lines) and of the combined SWIFTS interferograms (dashed lines). Ten subsequently recorded measurements are shown. (d) Corresponding frequency-resolved intermode (SWIFTS) phase. The dots indicate the resolution of the measurement and do not represent individual modes.
Fig. 3.
Fig. 3. (a) Pump-power dependence of the beatnote at 1.6 GHz measured with 1 kHz resolution bandwidth and 500 kHz span. (b) Pump-power-dependent intensity spectra (blue solid line) and SWIFTS intensity spectra (dashed line). The respective pump-power value is indicated in each subfigure. All spectra have been obtained by averaging over 10 subsequent measurements. (c) Corresponding SWIFTS phase. The power level is indicated to the right of the phase spectrum. The dots indicate the spectral resolution, and the error bars indicate the standard deviation when averaging over 10 subsequent measurements.
Fig. 4.
Fig. 4. (a) Fundamental beatnote (measured at 1.59 GHz center frequency with 1 kHz resolution bandwidth and 500 kHz span), (b) intensity and SWIFTS interferograms, and (c) intensity (blue solid line), SWIFTS spectrum (orange dashed line), and SWIFTS phase $\Delta \varphi$ of the unfiltered laser emission at a pump power of 3.2 W (sample spot different from that in Fig. 3 used here). The corresponding measurements with spectral filtering are shown in (d), (e), and (f). For measurement of the fundamental beatnote in (a) and (d), the power in front of the photodiode is adjusted to 2.2 mW in both cases.