We present analytical considerations of “self-mode-locked” operation in a typical vertical external-cavity surface-emitting laser (VECSEL) cavity geometry by means of Kerr lens action in the semiconductor gain chip. We predict Kerr-lens mode-locked operation for both soft- and hard-apertures placed at the optimal intra-cavity positions. These predictions are experimentally verified in a Kerr-lens mode-locked VECSEL capable of producing pulse durations of below 500 fs at 1 GHz repetition rate.
© 2013 Optical Society of America
In recent years, VECSELs have been utilized in several applications requiring high power, good beam quality lasers at a variety of wavelengths. Record continuous-wave (CW) output powers in excess of 100 W  have been demonstrated in the infrared and at the same time the emission wavelength can be tailored for specific applications, for example laser cooling of Yb-doped solids at 1020 nm [2, 3]; several hard-to-reach wavelengths in the visible  and ultra-violet  wavelength regimes have been demonstrated using intracavity frequency conversion.
Mode-locked VECSELs are of particular interest and have advanced from picosecond  to sub-100 fs pulse widths  at repetition rates typically in the GHz regime . Almost all of those results rely on a semiconductor saturable absorber mirror (SESAM)  to passively mode-lock the VECSEL, although more recently, graphene  and carbon nanotubes  have been utilized as well.
A few recent publications describe observations of SESAM-free or self-mode-locked VECSELs [12–14], with some hinting at Kerr lensing as the mechanism behind the unexplained behavior. Kerr lensing has been successfully used to mode-lock solid-state lasers, most notably, Titanium-Sapphire lasers [15, 16]. In this paper, we show that the negative ultrafast Kerr effect in the VECSEL gain chip can explain mode-locking and our current experimental results show the expected behavior.
2. Kerr-lensing in VECSEL gain chip
Kerr-lens mode-locking (KLM) is essentially a process of mimicking a fast saturable absorber inside a laser cavity by a combination of self-action of the laser beam due to the optical Kerr effect together with spatial aperturing [15–17]. The latter can be either due to the pump/laser mode overlap (soft aperture) or a physical (hard) aperture. In most solid state lasers, KLM originates from the optical Kerr effect in the gain medium host crystal (example: Ti:Sapphire lasers), while it is possible that the Kerr medium be separate from the gain structure. Here we analyze the potential for KLM operation in a simple VECSEL cavity due to the ultrafast Kerr nonlinearity in the semiconductor gain chip itself. What distinguishes this from conventional solid-state systems is that the optical Kerr coefficient n2 is negative and many orders of magnitude larger than in host crystals such as sapphire. This large value of n2 is however compensated by the small thickness of the semiconductor gain (Kerr) medium, which is typically of the order of a few µm. The gain structure considered here is a multiple quantum well (MQW) structure containing periodic layers (12) of InGaAs quantum wells embedded in a 2 µm thick GaAs barrier. Theoretical [18, 19] and experimental [20–22] investigations in the early 90’s have shown that an ultrafast (sub-picosecond) nonlinear response from bound electrons gives rise to a large negative n2, of the order of -(1-10)x10−12 cm2/W, at wavelengths extending from just below the band gap (e.g. in the barrier layers of GaAs) to the gain region (e.g. in the InGaAs QWs).
To model KLM process, without loss of generality we consider a typical linear VECSEL cavity, of length d consisting of a curved mirror (radius R), and a flat end mirror with the gain (Kerr) medium situated at a distance zK from the flat mirror as shown in Fig. 1.This configuration captures either a simple two-mirror cavity when zK = 0 or a folded 3-mirror v-cavity geometry.
The Kerr lens focal length is taken to be  where L is the Kerr medium thickness, Ppeak is the intracavity peak power, w(zK) is the beam waist for a given location zK. The factor a~4-6 is a correction term in aberration-free approximation.
For the simple cavity shown in Fig. 1, we derive an expression for the mode perturbation due to Kerr lensing using standard textbook ABCD matrix formalism. We find that the deviation of the Rayleigh range of the nonlinear cavity () from that of the linear cavity, to the first order in Ppeak can be given as:
Next, we explore the feasibility of KLM operation in VECSELs for typical experimental parameters (see section 3) of Ppeak = 10 kW, L~2 µm (Leff = 4 µm for double pass), and n2~-1x10−12 cm2/W. This peak power is inferred by assuming 10 W intracavity average power (100 mW output power), pulse width Δtp~1 ps, and a roundtrip time of T~1 ns. The cavity parameters are taken as R = 15 cm and d/R = 0.9994, corresponding to a configuration which is near the edge of the stability regime, where the cavity spot-size (hence z0) reduces leading to enhancement of Kerr lens modulations, as given by the functional form of γ parameter. Figure 2 depicts essentially an intracavity z-scan, where the calculated change in the beam radius (from Eq. (3)), at the locations of gain chip and the curved mirror are shown as a function of position of the Kerr medium. The negative sign, implying beam narrowing, can therefore be exploited for mode-locking. Reversing the sign of n2 (i.e. to a positive sign) will also change the sign of beam-radius modulation in Fig. 2. We note that the beam narrowing due to negative Kerr effect at the gain chip occurs for all positions of the gain chip. It is maximum (~10%, under the given parameters) for zK = 0 corresponding to a simple plano-concave resonator where the gain chip acts as an active end-mirror. For our current experimental conditions, beam-radius modulation of as much as 0.5% is possible for the gain chip placed at ~5z0 away from the flat mirror. Conversely, a positive n2 will not lend itself to KLM operation in the given cavity geometry. Figures 2 and 3 also indicate that with the gain chip positioned at |zK| >z0, a hard aperture at the curved mirror or anywhere between the curved mirror and the gain chip will favor KLM operation.
The VECSEL gain chip used in our experiments was originally designed for high power CW operation for laser cooling of a Yb:YLF crystal at 1020 nm [2, 3]. The active region consists of 12 single InGaAs QWs aligned with the antinodes of the standing wave in the sub-cavity, which consists of GaAsP for strain compensation. A 25-pair AlAs/GaAs DBR is used to optimize thermal conductivity. The DBR is grown last and mounted to a CVD-grown diamond heat spreader using indium solder. The GaAs substrate is then etched off using a selective wet etch which stops at the InGaP window layer. Details of the structure, growth, and high power CW performance can be found in [24, 25].
The schematic of our V-shaped VECSEL cavity is shown in Fig. 4(a). It consists of a 15 cm radius of curvature high-reflection (HR) mirror, is then folded on the gain chip and ends at a 1% transmission output coupler. The length of the two arms can be adjusted independently, with the distance between gain chip and output coupler in the range of 2.5-5 cm, and the total cavity length usually close to, but just below the stability limit of 15 cm (see section 2). The spot size of the pump laser, an 808 nm fiber coupled diode laser, focused onto the sample by a pair of 50 mm focal length lenses is adjusted for maximum output power. The gain chip is mounted onto a water-cooled heat sink with a water temperature of 15°C. To explore the mode-locking of our laser, we supplement the setup with a high speed InGaAs photodiode (>15 GHz) to monitor the transmitted light after the curved HR end mirror and analyze the signal using an 8-GHz high speed oscilloscope.
To check the origin of self-mode-locking, we investigated two possibilities for pulsed operation of our laser. In the first approach, we deliberately placed a hard aperture inside the cavity just before the curved mirror, a position motivated by the analysis reported in the previous section. For a given pump power, CW operation would commence with the hard aperture in a fully-open position, as verified on the oscilloscope trace of Fig. 4(b) (bottom trace). As expected from our analysis, mode-locking operation could be initiated by slight closure of the aperture, as evidenced by the formation of a stable pulse train in the time domain in Fig. 4(b) (top trace) and a commensurate increase in the average output power. At this point, opening of the aperture would return the laser to back to CW operation. In the second approach, with the hard aperture fully open, the pump spot size on the gain chip could be slightly decreased by moving the pump focusing lens closer to the semiconductor surface. This perturbation in the soft aperture would also initiate mode-locking operation and in practice proved to be much more reliable and robust in comparison to the manually controlled hard aperture near the external mirror. Therefore, the soft aperture method is used in the remainder of this paper.
A third cavity geometry corresponds to using the VECSEL gain chip as the end-mirror in a two-mirror plan-concave resonator. From the analysis given in section 2, this corresponds to zK = 0. As predicted by the model, hard-aperture KLM is not possible in this configuration while soft aperture effect is at its maximum. We have been able to routinely observe KLM operation using this configuration with similar characteristics as described below for the folded V-cavity.
A typical time trace of our self-mode-locked VECSEL is shown in Fig. 5(a), where a pulse train with approximately 1 GHz repetition rate can be observed. Since we currently do not have access to a high bandwidth spectrum analyzer, Fig. 5(b) shows an RF spectrum as obtained by Fourier transform of a 100,000 data point (4 ms long) time trace from the oscilloscope. It should be noted that in most cases a relatively small amount of CW (or quasi-CW) power was present in the mode-locked VECSEL output, especially at higher pump powers, as is evident from the pulse train observed on the oscilloscope, as seen in Fig. 5(a). In some cases, we also observed some instability in the amplitude of the pulse train on timescales of a few to several tens of microseconds, which we have not been able to completely stabilize yet.
Figure 6(a) shows the VECSEL output power versus pump power in a cavity adjusted for optimal soft-aperture KLM operation, with a 12.7 mm fused silica window inserted into the cavity under Brewster’s angle for dispersion compensation (see below). Pulses in the VECSEL output could be observed for all pump powers above 2W. For pump powers above 13 W (not shown), the laser would revert to mostly CW operation. The insets in Fig. 6(a) show optical spectra of the VECSEL at two different pump powers. The full widths at half maximum are 1.7 nm and 2.3 nm, corrected for the resolution of the spectrometer (Ocean Optics HR4000, 0.75 nm resolution).
To characterize the pulse width of the mode-locked laser, the light from the output coupler is directed to a homemade rapid-scan intensity autocorrelator with 10 mm of travel, using a 0.5 mm thick beta barium borate second harmonic crystal. Sample intensity autocorrelation traces corresponding to different output powers in Fig. 6(a) are shown in Fig. 6(b), along with sech2 fits, corresponding to pulse durations from above 1 ps at low power to below 500 fs at high power. In addition to the main peak at the zero delay point, we observed a residual background or pedestal. This can be attributed to CW or quasi-CW background , which was observed to increase for higher pump powers. It could also arise from small mode-locking instabilities or from a residual chirp of our uncompressed femtosecond pulse train. Further experiments are required to analyze this in more detail.
The demonstrated initiation of mode-locked operation by either hard- or soft-apertures serves as direct evidence of Kerr-lens mode-locking due to ultrafast negative Kerr effect in the VECSEL chip. This demonstration is supported by the analysis presented in previous section and positions of the apertures are in full agreement with the calculation. In a typical Kerr-lens mode-locked solid-state femtosecond oscillator, the combined normal (positive) group velocity dispersion (GVD) and positive self-phase-modulation (SPM) experienced in the gain crystal (n2>0) needs to be compensated by introduction of negative GVD intracavity element , such as a prism pair or a chirped mirror with an appropriate spectral phase. Our finding contrasts this case with the mode-locked VECSEL, where in fact negative SPM is introduced by the nonlinear gain element  and positive GVD of the end-mirrors is used for partial intracavity GVD compensation. Preliminary measurements of pulse duration versus the thickness of a fused silica glass Brewster-plate inserted near the curved mirror, as shown in Fig. 7, further support this point. A clear minimum in pulse duration is observed for an increasing amount of added positive GVD, consistent with compensation of the negative SPM. Such a clear variation however can only be observed in a certain power range as it is indicative of the balance between GVD and SPM. At higher powers variation with GVD insertion is less visible. Further understanding of the interplay between SPM, GVD, and gain dynamics are key to utilizing these phenomena towards a reliable and practical self-mode-locked device . This system with such unique characteristics can also serve as an excellent platform to study the operation of solitary mode-locked lasers and the dynamics of dissipative solitons .
The highly nonlinear nature of a mode-locked laser is further complicated in a VECSEL by the fast lifetime of the semiconductor gain, which is in fact comparable to or shorter than the repetition rate. Nontrivial many-body effects and carrier dynamics in the semiconductor add additional complexity to the story of mode-locking in VECSELs. While these facts warrant further parametric investigation into the detailed nature of the dynamics of formation of mode-locking in these lasers, we emphasize that our analysis and experiments directly verify the picture of Kerr-lens mode-locking in a VECSEL. Further detailed studies of nonlinear interplay between intracavity dispersion, pump power dependence, and gain saturation are currently underway. Since our gain chip was not anti-reflection coated, the linear and non-linear optical effects due to the sub-cavity formed by the DBR and semiconductor-air interface may influence the mode-locking process as well.
In this work we have presented analytical considerations of “self-mode-locked” operation in a typical VECSEL cavity geometry by means of Kerr lens action in the semiconductor gain chip. Strong negative nonlinear contribution to the refractive index in the gain medium and the resulting increase in the differential gain favors short pulse operation. For a typical cavity geometry, we predict optimal intracavity positions for both soft- and hard-apertures. Furthermore, our supporting experiments demonstrate self-mode-locking in a VECSEL with pulse durations between 2 ps to below 500 fs and with both soft- and hard-apertures, as predicted in the analysis. While this work unambiguously demonstrates the possibility of Kerr-lens mode-locking in VECSELs, it presents interesting opportunities and challenges for further investigation into the nonlinear gain/phase dynamics as well as dispersion management in these systems in order to render stable and background free short pulse operation.
Work at UNM was partially supported by grants from US Air Force Research Laboratory (AFRL). DVS acknowledges support by the National Science Foundation under Grant No. 1160764. VECSEL growth was supported by Sandia’s Laboratory Directed Research and Development Office. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
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