Self−Mode−Locked 2−μm GaSb−Based Optically Pumped Semiconductor Disk Laser

Abstract

We present a mode−locked GaSb−based optically pumped semiconductor disk laser operating at 2 µm based on the self−mode−locked mechanism. Using the delay differential equation model, we discuss the influence of cavity length on the stability of self−mode−locking and design a Z−shaped long cavity for self−mode−locking. Employing an aperture and an F−P etalon in the cavity length of ~365 mm, we obtain stable self−mode−locking at a center wavelength of 2034.5 nm, with a pulse duration of 255.48 ps and average output power of 173 mW at a repetition rate of 404 MHz.

1. Introduction

Optical pumped semiconductor disk lasers (SDLs), also known as vertical−external−cavity surface−emitting lasers (VECSELs), are versatile lasers in applications requiring both high power and good beam quality at a variety of wavelengths [1,2,3,4]. Gallium−antmonide (GaSb) material systems can be used to fabricate SDLs that operate at wavelengths of 2~4 μm [5,6,7,8]. High−pulse−energy lasers with a short pulse at the mid−infrared wavelength region have particularly important applications for time−resolved molecular spectroscopy, remote sensing, infrared countermeasures, medical, and optical free−space communications [9,10,11,12,13]. At present, the methods of generating short pulses at mid-infrared wavelengths [14] mainly include Kerr−lens mode−locking (KML), nonlinear polarization rotation (NPR), and intracavity semiconductor saturable absorption mirror (SESAM). GaSb−based materials are more used as SESAMs with ~2 μm wavelength in applications [15,16,17,18]. Studies on mode−locking of GaSb−based disk lasers are relatively sparse [19,20,21]. The main challenge to achieving mode−locking operation in the GaSb−based SDLs is the high quality and reliable epitaxial growth of GaSb−based SDLs and SESAMs wafers. More details of the passively mode−locked GaSb−based SDLs with SESAM can be found in

Table 1. Passively mode−locked GaSb−based SDLs with SESAM at 2 μm wavelength. τ_p is the pulse duration. f₀ is the pulse repetition rate. λ₀ is the center wavelength of the laser. P_out is the average output power.

Laser Gain	τp	f0	λ0	Pout	References
InGaSb Multi−QWs	1.1 ps	881.2 MHz	1950 nm	25 mW	[19]
	384 fs	890.4 MHz	1960 nm	25 mW	[20]
	324 fs	3.03 GHz	2061 nm	65 mW	[21]
	4.52 ps	3.03 GHz	2072.8 nm	260 mW

. Obviously, the lower performance index means that there is still a great possibility of progress in the research of this field.

One intriguing phenomenon that has been observed in near−infrared GaAs−based SDLs is so−called self−mode−locking (SML) [22,23,24,25,26], which forms a stable mode−locked pulse laser output without an intracavity SESAM. The origin of self−mode−locking is conjectured to result from the nonlinear Kerr lens effect from the semiconductor epitaxial structure itself [22]. In this way, the SML SDLs can more easily realize mode−locked pulse operation with simplified system design and broader spectrum coverage. The physical mechanism of SML was described as Kerr lens mode−locking has been widely studied in semiconductor materials such as GaAs and InP [27,28,29,30,31], and soli−state crystal lasers such as Ti: Sapphire [32,33,34,35]. The strong self−focusing of the laser beam combined with either a hard aperture or a soft aperture in Kerr medium is employed to produce a self−amplitude modulation [36]. In addition to mode−locked lasers, devices developed based on this mechanism also include wavelength/frequency division multiplexing [37,38,39], optical frequency comb [40,41,42,43], supercontinuum generation [44,45,46], and so on. However, there are currently no relevant reports on the Kerr effect in GaSb−based gain materials, nor have there been corresponding reports on self−mode−locked GaSb−based lasers.

Inspired by the self−mode−locking effect observed in GaAs−based SDLs [22,23], this paper validated and implemented continuous−wave (CW) mode−locked GaSb−based SDLs employing self−mode−locking. Based on the pulse dynamics simulated by delay differential equations (DDE), we designed a Z−shaped cavity with a long cavity length for SML GaSb−based SDLs. Then, we systematically measured the pulse characteristics of the SML GaSb−based SDLs.

2. Experiment Design and Setup

Self−mode−locked pulses of SDLs are realized by the nonlinear Kerr lens effect of the pump spot, and it has been demonstrated that the nonlinear refractive index n₂ is large enough to cause perturbations of the cavity beam profile [47,48,49]. The Kerr lens effect has been explored both experimentally and theoretically in solid−state crystal lasers. In most cases, Haus master equations can explain the pulse dynamics [50]. However, it cannot describe mode−locking in semiconductor lasers satisfactorily because it is based on small changes of gain and losses in laser pulse shape within one round trip. Instead, the delay differential equation (DDE) model is widely used to describe the pulse dynamics in semiconductor lasers [51,52,53].

According to Refs [25,26], the DDE equations can be expressed as:

$$\frac{1}{\gamma }\frac{\partial A}{\partial t}+A\left(t\right)=\sqrt{\kappa }exp\left[\left(1-i{\alpha }_g\right)g\left(t-{\tau }_r\right)/2-\left(1-i{\alpha }_q\right)q\left(t-{\tau }_r\right)/2\right]A\left(t-{\tau }_r\right)$$

(1)

$$\frac{\partial g}{\partial t }={\gamma }_g\left[g_0-g\left(t\right)\right]-\exp \left(-q\right)\left[\exp \left(\mathrm{g}\right)-1\right]{\left|A\left(t\right)\right|}^2$$

(2)

$$\frac{\partial q}{\partial t}={\gamma }_q\left[q_0-q\left(t\right)\right]-s\left[1-\exp \left(-q\right)\right]{\left|A\left(t\right)\right|}^2$$

(3)

where A is the laser field amplitude. g and q are saturable gain and loss. γ is the corresponding bandwidth of the spectral filtering element. The gain bandwidth of quantum wells (QWs) is usually about 10 nm, so here we set γ as 200. κ is the linear nonresonant attenuation factor per round−trip pass; in SDLs, κ can be expressed as κ = √(R₁R₂). Based on our experimental conditions, the reflectivity of the two end mirrors of the cavity R₁ = 99.9%, R₂ = 95%, and the value of κ is 0.9742. α_g and α_q are the linewidth enhancement (self−phase modulation) factors; for simplicity, we restrict our numerical analysis to the case in α_g = α_q = 0. g₀ and q₀ are the small−signal gain and loss, and also the initial value of g and q. γ_g and γ_q are the carrier density relaxation rates in the gain and absorbing sections; here, we set the relaxation time γ_g⁻¹ and recovery time γ_q⁻¹ as 10 ns and 10 ps, respectively. s is the ratio of saturation energy of gain and absorber. Referring to the value in Refs. [26,52], we set s as 25. The delay parameter τ_r is the cavity round trip time. All the time in the calculation was normalized. The traditional way to obtain higher single pulse energy is to reduce the pulse repetition rate and compress the pulse width. The pulse repetition rate is inversely proportional to the cavity length. A longer cavity length means a larger τ_r, which may have a negative impact on the mode−locked pulse. In the DDE model, the threshold condition can be expressed as g = q − ln(κ). By selecting a pair of q₀ = 1.0 and g₀ = 2.0, which are low power levels slightly higher than the threshold value, to achieve mode−locked resonance, we can calculate the time−dependent variation trend of A, g, and q under different cavity lengths. Figure 1 and

Table 2. Parameters used in the calculation.

γ	κ	γg−1	γq−1	s	q0	g0
200	0.9742	10 ns	10 ps	25	1.0	2.0

show the calculation results when the cavity length was set as 200 mm, 400 mm, 600 mm, and 800 mm, respectively.

As shown in Figure 1, the relative value of loss caused by saturated absorption will decrease with the increase of cavity length and the cavity round−trip time. An unstable jitter occurs after the loss drops to the bottom in a single pulse cycle of the long cavity length. This phenomenon began to appear when the cavity length was 400 mm, but it did not significantly affect the pulse waveform. When the cavity length is extended to 600 mm and 800 mm, a single pulse will be irregularly broadened and the pulse waveform will become irregular too. This instability may be due to the long cavity length increasing the round−trip time τ_r and approaching the gain relaxation time, and the long cavity length will also increase the loss of the resonator. If we want to offset the loss fluctuation caused by this cavity length, we can only increase g₀ by increasing the pump power continuously. However, it is difficult to achieve SDLs in the GaSb which have an obvious upper heat dissipation limit [8]. Therefore, we believe that it is more reliable to select a cavity length of less than 400 mm for verification of self−mode−locking in GaSb−based SDLs.

A Te−doped 2″ (001) GaSb wafer was grown in a VECCO Gen−II solid source molecular beam epitaxy system at ~430 °C for the SDLs chip structure. First, a buffer layer of GaSb was grown on the substrate. A Distributed Bragg Reflector (DBR) comprising 21.5 pairs of GaSb/AlAs_0.08Sb_0.92 quarter wavelength layers follows. The DBR has a broadband reflectance of ~99.9%, centered at a wavelength of 2 μm. The active regions were grown directly on top of DBRs with resonant periodic gains (RPG) and symmetric structures. Ten In_0.2Ga_0.8Sb QWs with a thickness of ~10 nm, arranged in five groups of two QWs each, make up the active region. The QWs are separated by 20 nm thick layers of GaSb and equally enclosed by λ/2 GaSb barrier layers. In comparison with Al_0.3Ga_0.7As_0.02Sb_0.98, the GaSb barrier layer can provide relatively high thermal conductivity. In addition, the pump source with a wavelength of 1470 nm can be used to reduce quantum defects, therefore reducing heat generation and improving laser performance. An Al_0.8Ga_0.2As_0.03Sb_0.97 confinement layer was grown on top of the gain region to prevent carrier nonradiative recombination. The surface was protected from oxidation with a thin GaSb cap layer. We cleaved the chip into 3 × 3 mm² pieces, which were then liquid−capillary−bonded [54] to an uncoated 400 μm thick 6H−SiC intracavity heat spreader of 5 × 5 mm² dimensions. The SDLs chip package was then mounted on a copper heat sink cooled by Peltier elements. The heat sink temperature was controlled at 10 ± 1 °C.

The gain chip was set up in a Z−shaped laser resonator, as shown in Figure 2a. The cavity was formed by the DBR, curved high−reflectivity mirror M₁ with a radius of curvature r = 200 mm, plane high−reflectivity mirror M₂, and output coupler M₃ with a reflectivity R = 95% at 2 μm wavelength. The pump laser we used was a DILAS M1F4S22 with an emission wavelength of 1470 nm. The 400 μm core diameter fiber−coupled pump beam was focused into a spot on the SDLs chip with a diameter of ~400 μm. The incident angle of the pump beam was ~30°. The reflectivity of the incident pump laser was measured to be 48 ± 2% on the SiC–air interface. To make the transmission mode in the cavity close to circular, the folding angle of the Z−shaped cavity should be as small as possible. While ensuring that the resonator is in a steady state, it is also necessary to consider that the spatial positions between mirrors cannot conflict with each other. Here, we set L₁ to 110 mm, which is slightly larger than half of the radius curvature of M₁. Additionally, the length of L₂ was set as 75 mm. For spectral control, an F−P etalon was inserted into the cavity. Based on the configuration of the resonator, we used the transmission matrix to calculate the fundamental transverse mode size in the cavity, as shown in Figure 2c. For the F−P etalon, any position after M₂ can be set because the size change of the transmission mode is very small. Here, we set L₃ to 70 mm. The mode size on the chip surface was an ellipse close to a circle, with the major axis ω_y = 252 μm and the minor axis ω_x = 243 μm. The design of this Z−shaped cavity allows us to change the cavity length only by lengthening the L₄ arm without moving other components. At this condition, the pump spot diameter was larger than the mode. Therefore, we introduced a variable aperture at the L₄ arm to suppress the resonance of higher−order transverse modes [55,56] and assist the self−mode−locking process to initiate. The aperture will not be adjusted to smaller than the size of the fundamental mode, so the mode−locking essentially operates in the soft aperture mode [24,57]. Based on the simulation results in the previous section, we set two groups of experiments as controls. One was a relatively stable cavity with a cavity length of less than 400 mm (L₄ = 110 mm and the total length was ~365 mm, as shown in Figure 3), and the other one was a relatively unstable cavity with a cavity length of more than 800 mm (L₄ = 645 mm and the total length was ~900 mm). The laser output through the plane output−coupling mirror M₃ will incident in a wedged plane beamsplitter with AR coating at 2 μm, as shown in Figure 2a. About 99% of the laser transmission incident into the optical power meter kits. Two beams of weak reflected laser with different angles were used: one beam was coupled into the optical spectrum analyzers, and the other beam incident into the high−speed photodetector connected to the digital oscilloscope.

3. Results and Discussion

First, to measure the temporal characteristics of the self−mode−locked pulses, a high−speed 2 µm InGaAs photodetector (EOT, ET−5000, 12.5 GHz, Walnut, CA, USA) combined with a 59 GHz digital storage oscilloscope (Tektronix, DPO75902SX, Beaverton, OR, USA) was used. Figure 3a,b show the typical time trace of our SML GaSb−based SDLs measured at the cavity length of ~365 mm and ~900 mm, respectively. Their average output power is 168 mW. The pulse separation of ~2.47 ns and ~6.03 ns corresponds right to the round−trip time of their cavity length. The pulse train with ~404 MHz and ~166 MHz repetition rate can be calculated. A representative 1 μs long−span pulse train is shown in the insertion of Figure 3a,b. The intensity fluctuation of the mode−locked pulses in Figure 3a is obviously more stable than in Figure 3b. This experimental result is consistent with our previous prediction of the cavity length. Based on the DDE model, we also calculated the pulse train with a 365 mm and a 900 mm cavity length. As shown in Figure 3c,d, the measured pulse repetition frequency is consistent with the calculated result. The smaller error within tolerance may be due to the error in device installation and adjustment. Subsequent experiment results were measured under a relatively stable cavity length of ~365 mm.

The mode−locked pulse duration was also directly measured by the high−speed photodetector and oscilloscope. The pulse duration was ~255.48 ps with a near−Lorentz shape, as shown in Figure 4a. The experimentally measured pulse duration was much larger than our simulation results because we did not consider the nonlinear effects, such as group delay dispersion, in our calculations. A strong nonlinear has been observed in GaSb−based SESAMs which have a similar multi−QW epitaxial structure to GaSb SDLs [58]. Positive intracavity roundtrip group delay dispersion of 2030 nm GaSb SDLs is on the order of 1000 fs², which has an intense negative impact on the pulse duration and the laser performance [21]. Considering the nonlinear effects introduced by quartz F−P etalon, SiC heat spreader, and GaSb gain chip, it is difficult to accurately simulate the pulse duration of SML GaSb SDLs. The spectral filtering element in the resonant cavity also affects the pulse duration. Further study is required to analyze these in more detail.

The radio frequency (RF) spectrum was measured by a mixed−domain oscilloscope with 1 GHz bandwidth (Tektronix, MPO3104, Beaverton, OR, USA). At the repetition rate of ~404 MHz, the RF spectrum shows a clean peak without side peaks, as shown in Figure 4b. This reveals the GaSb SDLs operating in a stable SML mode and a near−fundamental transverse mode. As shown in the insert of Figure 4b, the 1 GHz wide−span RF spectrum measurement indicated the single−pulse operation of the mode−locked GaSb SDLs.

The laser output power characteristics were measured with a power meter (Thorlabs, S425C−L, PM100D, Newton, NJ, USA). Without the aperture and the F−P etalon, the laser operated in CW mode could reach 560 mW with the incident pump power of 10.7 W, as shown in Figure 5a. This value is lower than our previous work [59], mainly because we used a longer cavity and an output coupling mirror with higher transmittance. The laser spectra were measured using a Fourier transform optical spectrum analyzer (Thorlabs, OSA207C, Newton, NJ, USA), as shown in the insert of Figure 5. Without other components in the cavity, the uncoated SiC heat spreader on the chip surface acted as an F−P etalon. The emission spectra have multiple equally spaced peaks simultaneously, which is not conducive to realizing the mode−locking. Self−mode−locking of the GaSb−based SDLs was accomplished by inserting an aperture and an F−P etalon in the cavity. The output power of the SML GaSb SDLs is shown in Figure 5b. The additional etalon filters the spectrum into a single peak with a width of 1.1 nm. At a low output power of ~42 mW, the laser switched immediately to self−mode−locked operation. With the increase of pump power, the emitting wavelength switched from 2031.8 nm to 2034.5 nm, as shown in the insert of Figure 5b. The maximum average output power achieved for the SML GaSb SDLs amounted to 173 mW at an incident pump power of 11.2 W.

4. Conclusions

In conclusion, we have presented analytical considerations of self−mode−locking semiconductor disk laser operation in different cavity lengths configuration by the DDE model. For self−mode−locking, the cavity length cannot be increased unboundedly for a low repetition rate. It needs to be configured according to the gain, loss, and thermal limits of the actual device. Furthermore, we demonstrated the self−mode−locked operation of GaSb−based SDLs based on an optimized long cavity length of ~365 mm and obtained stable self−mode−locking at a center wavelength of 2034.5 nm. During mode−locked operation, the pulse duration of GaSb−based SDLs was 255.48 ps with a repetition rate of 404 MHz. The maximum average output power was 173 mW. Further optimization of the epitaxial structure of the SML GaSb−based SDLs and compensation of the intracavity nonlinear dispersions are expected to generate shorter pulses and higher single−pulse energy.