AlGaAs/GaAs asymmetric‐waveguide, short cavity laser diode design with a bulk active layer near the
 p
 ‐cladding for high pulsed power emission

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| INTRODUCTION
High power broad area diode lasers operating in the quasicontinuous-wave (quasi-CW) pulsed regime (with pump pulses long enough to achieve steady state from the laser dynamics point of view yet short enough to not cause substantial current heating, in practice corresponding to the nanosecond region) are important components of Lidars [1] as well as for a number of other applications. With regard to the spectral range of laser emission, two strategies are possible. One involves working in the eye-safe spectral range of 1300-1600 nm, allowing high output power to be used, and requiring InGaAsP/InP [2][3][4] or AlGaInAs/InP [5][6][7][8][9] based sources and photodetectors. The other involves working at shorter wavelengths and can be further subdivided in two spectral regions: λ ∼ 0.9-1.1 µm [10][11][12][13] and λ < 0.9 µm, used [14,15] for the case of nanosecond pump pulses resulting in picosecond pulse emission under gain-switched operation. The latter spectral range makes use of the efficient and reliable GaAs/AlGaAs emitters and, crucially, the relatively mature technology of Silicon Single-Photon Avalanche Photodetectors [16] which have a high sensitivity at the operating wavelengths below 900 nm.
Traditionally, the design of high-power laser structures in both InGaAsP/InP and (InGaAs)GaAs/AlGaAs material systems used almost exclusively thin active layers (ALs), including 1-3 Quantum Wells (QWs). In the latter case, this was at least because the research largely concentrated on the λ = 0.9 −1.1 μm range, where the use of Indium containing components is necessary and growing thick ALs is impossible due to lattice mismatch induced strain. For lattice matched structures, such as In-free GaAs/AlGaAs system and the eyesafe wavelength InGaAsP/InP lasers, there is no such technological limitation. Hence in our work, asymmetric laser designs with a bulk AL in a gain-switched GaAs/AlGaAs λ ≈ 0.85 µm laser [14,15] and, later, in a quasi-CW operated InGaAsP/InP λ ≈ 1.5 µm devices [3,4,17] have been proposed and realised. The results on the long-wavelength lasers compared favourably with the best published results, with considerable scope for further optimisation. Here, we show that the same strategy can also be applied in the design of quasi-CW operated GaAs/AlGaAs lasers, compatible with silicon photodetectors. wavelength lasers. The most important parameter to be maximised in high-power lasers is the quantum efficiency, which is the product of injection and output efficiencies: η = η i η out . Some compromise in the form of an increased threshold current may be required, and is justified in order to achieve an increased η, so long as the threshold increase is not drastic.
In modern laser structures, the leakage of electrons into the p-cladding is very small so that the injection efficiency, at nottoo-high temperatures, can be η i ≈ 1 [10]. The goal then becomes increasing with the output efficiency η out ¼ α out α out þα in , α in and α out ¼ 1 2L ln 1 R HR R AR being, respectively, the internal optical losses and the outcoupling losses, R HR and R AR standing for the high-reflection and anti-reflection coated facet reflectances, respectively. Substantial research effort has gone into minimising α in both near the threshold [10,19,20] and at high injection level (see e.g. [17,[21][22][23]). A potentially very efficient complementary way of increasing η out in pulsed lasers is to reduce the effect of α in by decreasing the cavity length L and hence increasing α out . However, if the thickness of the active region and, accordingly, the confinement factor of the active region (Γ a ), are small, the decreased L can drastically increase the threshold carrier density N th . If this parameter is allowed to reach values of N th ∼ 10 19 cm −3 , in addition to the risk of compromising the threshold current beyond the acceptable level, the carrier escape from the active region into the OCLlayer by increasing α in and thus compromising η out, as well as current leakage into the p-cladding affecting η i , can become significant even at room temperatures.
Thus, efficient operation of a short cavity laser with the AL near the p-cladding as in Figure 1a is possible only with an active region of a relatively large thickness (d a ∼ 1000 Å in the case under consideration) and the corresponding substantial value of Γ a , avoiding excessive increase in N th. In principle, this can be either a bulk or Multiple Quantum Well (MQW) structure. However, for a given total thickness d a of the AL, the bulk AL gives a larger overlap with the purely active material than the MQW, in which some of the AL is occupied by the barriers between the wells.
Thus, the design proposed, like that of the long-wavelength laser [3,4,17,18], is intended to use a bulk AL to provide substantial values of Γ a , whilst keeping α in relatively low. The limit to how short the cavity can be, assuming quasi-CW operation without heating can be ensured, is set by the requirement that N th is not excessively high.
The proposed laser waveguide structure is shown in Figure 1a.
As in the work on long-wavelength lasers [18], the doping levels and thicknesses of the layers of the structure are selected to obtain high injection efficiency, low α in at both low and high injection levels, minimum series and thermal resistances. Most importantly, minimising the modal overlap with the p-cladding (to ensure low α in at low injection) requires a substantial refractive index step at the p-OCL/p-cladding interface, whereas avoiding a strong carrier accumulation and α in increase at high injection levels means that the distance between the AL and the p-cladding needs to be small. To further decrease the carrier accumulation in the OCL, high doping of the n-OCL can be used [17,18], which is one of the differences between the current design and the gain-switched one of [14,15] (the other one being the position of the AL with respect to the peak of the modal profile, which is optimised somewhat differently for gain-switched and quasi-CW applications). Furthermore, a small refractive index step at the n-OCL/n-cladding interface provides good fundamental mode selection (see below) and a broad near field fundamental (TE 0 ) mode distribution (quantified by the modal field profile ψ 0 (x) or a modal intensity profile ψ 0 2 (x), also illustrated in Figure 1a). This makes for a narrow far field and hence potentially high brightness. This is illustrated in Figure 1b which shows the far field ΨðθÞ as well as the efficiency η of coupling the light into a given one-dimensional numerical aperture θ (in this case, this may approximately represent the LIDAR collimation optics) estimated as The parameters that were fixed in the studies below were the refractive index steps, the thicknesses of n-OCL and p-OCL layers (d n-OCL = 1.8 μm >> d p-OCL = 0.04 μm as in Figure 1), and the doping levels of the layers, in particular N The parameters that were varied were the width of the AL d and the cavity length L.

| ANALYSIS OF LASER PERFORMANCE
We first analyse the threshold behaviour of the laser.
Similarly, with regard to long-wavelength lasers [18], we consider pulsed (quasi-CW) operating regime, with the injection current pulse short enough (<<100 ns) to not cause appreciable laser heating, as is typically the case in LIDAR applications. Thus room-temperature dependences of peak gain g on carrier density N can be used in calculations. To analyse what may be, in general, large variations of the threshold carrier density N th , we use the three-parameter logarithmic gain-carrier density dependence gðNÞ ¼ G 0 ln NþN 1 N tr þN 1 [24] , rather than the simpler linear approximation used in [17,18] following [25]. Then, the threshold carrier density is determined from the transcendental equation where, as in [17,18], the internal losses at threshold contain just two contributions The first term in Equation (2) is the built-in losses α ðbuilt−inÞ in ≈ 3:0cm -1 , of which the main part (≈2.6 cm −1 for d a = 800 Å as in Figure 1) is associated with free carrier absorption in the doped n-OCL and n-cladding, calculated using the modal profile of Figure 1 and the common doping level N D = 10 18 cm −3 ; the rest accounts for the (weak) overlap of the mode with the (also highly doped) p-OCL and p-cladding. This is quite different from earlier work on InGaAsP materials, in which the n-doped layers made very little contribution to α ðbuilt−inÞ in due to the very low values of the free-electron absorption cross-section in those materials. The second term in Equation (2) is the free carrier absorption in the AL at threshold where σ ea and σ ha are free electron and free hole absorption cross-section in the AL material. Similar to the previous work, Equation (2) neglects the presence of non-equilibrium carriers in all the non-active parts of the waveguide, which is justified at the relatively low threshold current. Figure 2 shows the calculated value of the confinement factor Г а , as well as the threshold current density for several values of the cavity length L, as functions of the AL thickness d a . For a thin AL (d a <∼ 400 Å), the value of Г а is approximately proportional to d a ; for thicker AL, the dependence Г а (d a ) becomes super-linear reflecting the increasingly important waveguiding properties of the AL itself. At d a >∼ 900 Å, the waveguide is, strictly speaking, not in a single mode, but the calculated confinement factor for the second (TE1) mode (shown as a dashed line in the figure) is much smaller than that of the fundamental TE0 mode, so there is never any doubt about the single transverse mode operation of this structure.
As can be expected from Equation (1), the strongly increasing Г а leads to a dramatic decrease in the threshold carrier density with increasing d a ; for the shortest cavity analysed (L = 0.5 mm) the value of N th at d a = 800 Å (as in Figure 1) is substantial but realistic whereas d a <∼ 600 Å makes N th for such a short cavity impractically high. For longer cavities (L = 1-3 mm), starting with d a ≈ 600-700 Å and greater, the main contribution to the threshold carrier density is the transparency carrier density N tr = 1.85 � 10 18 cm −3 [24] (N th − N tr < N tr ).
We proceed next to analyse the power output of the laser. Similar to the previous work, [3,17,18] the light-current characteristics P(I ) was calculated self-consistently alongside the power-dependent internal loss α in ðI; PðIÞÞ and the effective threshold current I th ðIÞ, using the transcendental equation Here, similar to the previous work, I th ðIÞ ¼ I th ðN th ðIÞÞ is the current expended on creating the AL carrier density N th ðIÞ necessary for the gain to compensate the total losses α out þ α in ðI; PðIÞÞ, and the internal loss α in ðI; PðIÞÞ is calculated using the approach of Equation (2) with added  The details of calculating individual contributions are described in [17]. An important difference from the numerical results of [17,18] (which dealt with InGaAsP materials), is the more complex effect of high n-doping of the n-OCL (N D = 10 18 cm −3 ) in the current study. As already mentioned above, the fact that in AlGaAs materials the free-electron absorption cross-section is smaller than the free-hole value by only a factor of ≈3 (as opposed to more than an order of magnitude difference in InGaAsP materials) means that the heavy n-doping of the n-OCL leads to a substantial α ðbuilt−inÞ in . Thus at modest injection levels, the predicted power output of lasers studied here is below those with lightly doped n-OCL (in which α ðbuilt−inÞ in may be down to <0.5 cm −1 ) However, at high currents, the high level of n-OCL doping makes for strong suppression of α ðFCÞ j ðIÞ (which is important for lasers with a small cavity length L, since α ðFCÞ j ðIÞ scales with the current density j = I/(wL)) and also to some (modest) extent reduces α ðFCÞ T PA ðPðIÞÞ [16]. Thus, at I >∼ 40-50 A, the n-doping of the n-OCL becomes beneficial.
These considerations are illustrated in Figure 3, which shows the current dependences of the total internal loss as well as the contributions to it for the case of high ( Figure 3a) and low (Figure 3b) n-OCL doping.
As in [3,4], the p-OCL contribution to the current-induced carrier absorption α ðIÞ dominates at high currents as discussed above; in the structure with a highly doped n-OCL (Figure 3a) this contribution, too, is suppressed by doping, at the expense of a higher built-in loss as discussed above. Also, important is the indirect TPA effect which is of a similar magnitude in both designs. Note that, in spite of a substantially smaller value of the TPA coefficient in AlGaAs OCL (β 2,OCL = 1 � 10 −8 cm/W [26]) as compared with the value in InGaAsP OCL (β 2,OCL = 6 � 10 −8 cm/W [27]), the TPA effects remain significant in the lasers studied here due to the large intracavity powers generated.
At I ∼ 100 A, the laser with a large N ðn−OCLÞ D has an advantage of about 5%-7% in power output over that with a lightly doped n-OCL; both are predicted to achieve power outputs that compare favourably with the results in the literature.
As was anticipated, despite the non-linear loss increase being somewhat higher in the shorter laser cavities, the increase of η out ¼ α out α out þα in by decreasing the cavity length is a robust enough mechanism of increasing the power output to ensure a substantial (up to >50%) advantage of power output from a laser with L = 0.5 mm at high currents over the lasers with longer cavities as illustrated in Figure 4.
The absolute values of the predicted output power at I = 100 A reach more than 100 W for short cavities (L = 0.5 mm), whereas for the relatively long 3 mm cavity, the value is about 60 W. The latter is similar to the 50 W achieved experimentally at similar currents in an advanced wavelength stabilised λ = 905 nm laser (with the same stripe width of w = 100 μm) utilising an asymmetric structure with a Single Quantum Well AL [13].
We note finally that, although the absolute values of output power discussed above are the most important advantage for LIDAR applications, the proposed structure design can be expected to decrease the series resistance of the device also, and hence its wall-plug efficiency, compared to many currently used designs. This is, firstly, because the bulk AL can be expected to virtually eliminate the recently put forward [28] extra series resistance mechanism which is associated with finite capture time in QWs and determined essentially by the excess density of OCL carriers N bj due to the finite capture time τ cap , evaluated [28,29] as N bj ≈ j ed a τ cap ¼ I ewLd a τ cap , where j is the current density and w the stripe width. Indeed, in case of a bulk heterostructure, besides the straightforward effect of a lower N bj due to the larger d a , a lower N bj can also be expected due to the fact that τ cap is identified as just the time of carrier thermalisation, which is well known to be sub-picosecond and thus substantially shorter than τ cap in QW structures (which depend in a complex way on the QW parameters [30,31] and can reach picosecond values [28,31]). The second reason for the reduced series resistance is that the high n-OCL doping reduces the resistance of the thick n-OCL. Both effects are most pronounced at low to moderate currents-in the case of the OCL resistance effect, this is because the OCL resistance in weakly to moderately doped structures is non-linear, decreasing with the current so that at very high injection levels, the layer doping level makes relatively little difference [32]. A qualitatively similar nonlinearity was also established for the extra resistance because of finite capture time [28].

| CONCLUSIONS
We have analysed the design of single transverse mode AlGaAs/GaAs λ ≈ 850 nm diode lasers with an asymmetric resonator and a bulk AL located very near the p-cladding for high-power pulsed (quasi-CW) operation. It was shown that optimisation of power output at high currents can be achieved using short cavity lengths, and also, to a smaller extent, by high n-doping of the n-side of the waveguide.