In-Well and Barrier Coupling Pump of Semiconductor Disk Laser

We report an in-well and barrier coupling pump scheme of semiconductor disk laser (SDL). An in-well-absorbed (940 nm) and a barrier-absorbed (808 nm) pump source were used to measure laser output characteristics. The output power of the coupling pump can be significantly improved compared to the in-well pump only scheme under similar thermal load conditions. The power scaling of the coupling pump SDL is caused by the interaction dynamics of the photoexcited carrier between quantum-well and barrier. The results are discussed with a rate equation model that considers the injected into the quantum-well carrier and the barrier carrier in the active region.


I. INTRODUCTION
V ERTICAL-external-cavity surface-emitting lasers (VEC-SELs), also called semiconductor thin disk lasers (SDLs), incorporate many attractive features of both semiconductor lasers and solid-state lasers. Owing to the wavelength flexibility obtained by properly designing the gain region and quantum well (QWs), SDLs have demonstrated the continuous wave (CW) and pulsed operation with wavelength spanning from UV to mid-IR via the fundamental wavelength and frequency mixing methods [1], [2], [3], [4], [5]. For the purpose of high power, reduced selfheating and enhanced heat-dissipating ability were expected. Hence, two kinds of pump approaches were developed. The conventional one is barrier pump with a pump wavelength shorter than the absorption edge of the barrier to ensure that the pump light is absorbed by the barrier/spacer regions between the QWs [6], [7]. The quantum defect, defined as the energy difference between pump-and lasing energy, typically is ∼20% in near-IR devices, and ∼50% in mid-IR devices [8], [9]. Such a large quantum defect aggravated the heat generation in SDL. The other pump approach is in-well pump [9], [10], in which the barrier/spacer regions are transparent for the pump light and absorption only occurs in the QW region. It has been applied so far to GaN-based SDL emitting at blue-violet wavelength [11], [12], [13], GaAs-based SDL emitting at red [14], [15], and near-IR [9], [10], GaSb-based SDL emitting at around 2 μm [8], [16], [17].
For in-well pumping, the main issue is the thin QWs lead to the low absorption of pump light. To enhance the absorption, the multi-pass pump scheme and the epitaxial structure with resonant wavelengths of both lasing and pump source are employed in the SDLs [9], [15]. The decrease in slope efficiency with a nonlinear increase in the threshold power density when the pump spot size was increased [18] limits the in-well pump scheme to operate with high power. These factors make it difficult for in-well pumping to reach the power level of barrier pumping although it has higher quantum efficiency, and the increased system complexity also damaged the original advantages. Obviously, the dynamics of photoexcited carriers in QWs play an important role in the performance of in-well pumped SDL, which includes the generation, relaxation, escaping, and radiative recombination process of carriers in QWs and determined the threshold, power, and efficiency of SDL. More carriers were expected to be confined in the QW to involving in the process of forming laser output instead of escaping from QW. The carrier escape process may be inhibited by barrier pump photoexcited carriers in the QW barrier. In this way, the output performance under large pump spots of the in-well pumping SDL may be improved.
In this paper, we proposed an in-well and barrier coupling pump to improve the performance of SDL unitizing the dynamics of photoexcited carriers in QWs. Based on a structure that was originally designed for conventional barrier pumping, an in-well-absorbed (940 nm) and a barrier-absorbed (808 nm) continuous-wave pump source were used to measure laser output characteristics. We studied the output power scaling and lasing threshold as a function of the additional incident laser power and the relaxation pathways are considered. The lasing spectrum reflecting the transport mechanism and temperature characteristics of the carriers was investigated.

II. EXPERIMENTAL SETUP
The investigated active medium of the SDL chip was grown by metal-organic vapor phase epitaxy (MOVPE) on a GaAs substrate in reverse order. The active region consists of ten inverted 8 nm InGaAs QWs, equally spaced by GaAsP barrier layers with optimized anti-node positions of the standing wave in the optical cavity (a resonant periodic gain placement) to ensure a low threshold and homogeneous gain. 20 pairs of AlAs/GaAs layer form the distributed Bragg reflector (DBR), which has a reflectivity higher than 99.9% at 1050 nm. The gain chip was cut into 3 mm × 3 mm pieces. In order to minimize the effect of waste heat generated by pump laser, thermal management of the gain medium was achieved by bonding to a pre-metalized diamond heat spreader via solid-liquid-interdiffusion bonding [19]. After the packaging step, the semiconductor substrate is removed by selective wet etching. No anti-reflective coating is applied to fully exploit the resonant gain enhancement by the sub-cavity mode [20], [21], [22]. The sample was further mounted to a copper heatsink which was cooled by a Peltier element. Fig. 1 shows the laser setup used in the experiments. The laser cavity was formed by the SDL chip's DBR as one end mirror and a plane output coupler on the other end. In order to take into account the transmittance of the barrier pumping output coupling mirror, we choose the conventional 3% instead of 0.8% which is more suitable for in-well pumping [9]. A plano-convex lens was set in the cavity to cooperate with the flat output coupler to form a stable resonant cavity. The cavity length L 1 = 102 mm and L 2 = 210 mm. The diameter of the mode size on the gain chip is ∼127 μm so that the laser can operate in multi-mode with high output power.
A barrier-absorbed 808 nm wavelength pump source and a 940 nm wavelength in-well-absorbed pump source were selected for the verification experiment. For in-well pumping, the shorter wavelength of the pump light, the larger photon energy, and the greater the intrinsic absorption coefficient of QW to the pump light. However, large pump photon energy will also lead to large quantum defects, an obvious thermal effect, and a weaker confinement effect of QW on excited carriers [9], [23]. Due to the pump photon being absorbed in the QW and creating an electron-hole pair, the conduction band and valence band have the same number of electrons and holes. Here we only consider the electron relaxation process. Therefore, we chose a 940 nm laser as the in-well pump source, which electron energy level is about half of the QW conduction band depth. Both beams of the pump light were imaged at the same point onto the SDL chip surface. At a near 30°angle of incidence, a slight angle difference was introduced to prevent the two pump beams from reflecting into each other. The main difference between the pump laser was the pump-spot size. The barrier-absorbed 808 nm pump laser was focused into a spot with a diameter of ∼400 μm and the in-well-absorbed 940 nm pump laser was ∼300 μm. This is so that the in-well pumping area can be completely covered by the barrier pumping area.
For the SDL optimized for high power operation, the heatspreader was measured in a temperature range of 10 ± 1°C. Because the epitaxial structure is designed for conventional barrier pumping, the DBR is optimized only for the emission wavelength. The reflectance of the DBR around 940 nm is only ∼60%, and any transmission of the remaining pump light through the DBR below the gain region would lead to further heating of the structure [10]. The absorption efficiency of the 940 nm pump laser by QW η wa is ∼20%. The reflectance of the DBR around 808 nm is ∼40%, and the absorption efficiency of the 808 nm pump laser by active region η ba is ∼87%.

III. THEORETICAL BACKGROUND
For in-well pumping, the barrier/spacer regions are transparent to the pump wavelength and the absorption of pump light only occurs in the QW region. We use a simple model to discuss the dynamics of photo-excited carriers in QW. As shown in Fig. 2, three relaxation pathways of the in-well excited states were considered.
The carrier loss rate for QW photoexcited carrier density N w at a given con-fined sub-band can be expressed as where τ escape , τ rad , and τ nonrad are the escape, radiative recombination, and non-radiative relaxation times, respectively. When in-well pumped SDL operates in continuous wave (CW) mode, the carriers were injected directly into the QW and relaxed to the ground state of QW through non-radiative relaxation. Then carriers located at the ground state recombined to generate the photons. This process dominates the entire carrier dynamics injected into the QW. The carrier escape and radiation recombination processes are relatively weak and negligible. However, when the pump power increases and the QW temperature rises, the carrier escape process cannot be ignored. Especially in the SDL, a number of 8 to 18 QWs are used in the gain structure for high modal gain. The amount of escaped carriers due to the thermal effect becomes enriched at high temperatures and high-power operation. In the undoped SDL epitaxial structure, the rate of carriers' escape from the QW can be expressed by [24]: where τ th is the thermal escape time, L w = 8 nm is the QW width, m ω = 0.057m 0 is the effective mass of carrier in the QW, and ΔE is the energy barrier height of QW. L w is fixed for a single QW. ΔE and m ω are also determined at a fixed in-well pump wavelength. The escape rate of photoexcited carriers in the QW is mainly determined by the QW temperature T and the injected carrier density N w . Based on the parameters used in our experimental conditions, we can calculate the carrier escape time τ escape for in-well pumping, the result is shown in Fig. 3. The τ escape decreases with the increase of temperature and will be less than 100 ps above 320 K. It is close in value of τ bg (∼20 ps), the carrier capture time from the barrier into the ground states of QW [25]. Therefore, the carrier thermal escape effect may be one of the reasons why the pump spot size and pump power cannot be increased in the in-well pumping, thereby limiting its performance improvement.
In the QW, recombination and escape are two competing processes whereby one increases at the expense of the other one [26], [27]. For the carrier escape process, the barrier energy state that would otherwise be occupied by the escaped carriers will be occupied by the carriers excited by the barrier pump light, and the competition between them will inhibit the escape of the carriers. On the other hand, the carriers that have escaped the QW are counted in N b and will be re-captured by the QW. With the increase of N b , the N b /τ bg rate will also increase. Both above processes will increase the number of carriers injected into the QW ground state N g , and the non-radiative relaxation of carriers is reduced. In terms of laser performance, the threshold of coupling pump power will be reduced and the output power will be improved.
Assuming the carriers injected into the QW can directly relax to the QW ground state through non-radiative relaxation and participate in the radiation recombination process of the ground state, τ nonrad = τ wg , as shown in Fig. 2(b). The rate equations for in-well and barrier coupling pump SDL can be written as where g is the optical gain, S is the photon density of laser, Г is the optical confinement factor, v g is the group velocity of the photon, τ p is the photon lifetime, β s p is the spontaneous emission factor, R sp is the spontaneous emission rate, τ b and τ w are the carrier recombination lifetime in the barrier state and in-well bound state, τ bw is the carrier capture time by the in-well bound states of the QW from the barrier states, τ bg and τ wg are the approximate value of the carrier capture time by the ground states of the QW from the barrier states and the in-well bound states, respectively. The laser and material parameters for the calculation are summarized in Table I [6], [25]. When we study the threshold characteristics, the pump power injection efficiency of barrier and in-well pumping are η bp = η ba α bp (A mode /A b ) and η wp = η wa (A mode /A w ) respectively. V b = L b A b and V w = n w L w A w are the volumes of the barrier and the QW layers. A mode , A b , and A w are the area of laser-mode, barrier pump, and in-well pump. n w , L w , and L b are the number of QW and the thickness of the QW, and the barrier layers. The carrier recombination lifetime of the ground state of the QW τ g (N g ) = 1/(A+BN g +CN g 2 ), where A, B, and C are the monomolecular, bimolecular, and Auger recombination coefficients. The thresh-old carrier density N th = N 0 (R 1 R 2 T loss ) -1/(2Гg0nwLw) [6], where R 1 and R 2 are the DBR and the output coupler mirror reflectivity, T loss is the round-trip loss transmission factor, g 0 is the material-gain parameter, N 0 is the transparency carrier density. Except for the thermal escape carrier, other temperature variables are approximate to the N th Ý exp(T/T 0 ) and the characteristic temperature T 0 ≈ 100K. The laser and material parameters for the calculation are summarized in Table I. Through the rate equation (3)-(6), we can calculate the relationship between the threshold of pump power P bp and P wp in the coupling pump process, as shown in Fig. 3(b). In the coupling pumping, the threshold for the P bp and the P wp decrease as one of them increases. While the overall threshold rises with the increasing temperature.
The laser output power P out can be calculated by the differential efficiency η d . For the in-well/barrier pumping, η (w/b)d = η out η (w/b)q η (w/b)abs . The output efficiency is determined by the external cavity parameters, η out = ln(R 2 )/ln(R 1 R 2 T loss ), and the quantum efficiency is determined by the pump wavelength, η (w/b)q = λ (w/b)p /λ laser . Here we can get the differential efficiency η wd = 0.0813 and η bd = 0.304. The low absorption efficiency of the in-well pump is the main reason for the low η wd . Compared with the in-well pump, the absorption efficiency and temperature characteristics of the barrier pump are more linear, so when calculating the P out of the coupling pump, we set the CW P bp to a fixed value. The P out can be divided into the in-well pump and barrier pump contribution, P out = P wout + P bout . The temperature of the heat sink set by the controller in the experiment is approximately 280 K. The output power contributed by the barrier pump can be described as P bout = η bd (P bp -P bth ), only when P bp is greater than the threshold of barrier pump P bpth . The initial temperature and threshold of the in-well pumped part P wout will vary with the injection of the P bp . The temperature rise caused by the injection of P bp is calculated according to thermal impedance R th = 1.25 K/W, as shown in our previous work [19]. The P wout can be approximately given by P wout = η wd (P wp -P wpth ) + η bd (P bp -P bpth ) (P wp /(P bp +P wp )), and thus get P out versus P wp at different P bp and temperatures. The result is shown in Fig. 4(b). In addition to increasing the P out , the injection of a barrier pump laser in the coupling pump will also introduce more serious quantum defects and thermal effects. The thermal rollover effect is not considered in the calculation results.

IV. EXPERIMENTAL RESULTS AND DISCUSSION
At first, the operation of the SDLs was pumped at in-wellabsorbed 940 nm wave-length, the output power versus incident pump power curves was shown in Fig. 5(a). With 940 nm pumping only (black line), we achieve a maximum output power of 2.11W. This output power level is comparable to previous experimental and theoretical reports [9], [15], [23]. At the end of the power curve, the slope of the curve tends to remain constant. Meanwhile, the carrier escape rate increase until it is balanced with the radiative and nonradiative rate as given by (1).
In the coupling pump, we first consider the in-well pump leading case, a barrier-absorbed 808 nm pump laser with fixed power as an additional injected pump source in the in-well pump process. For the resonator configuration of this experiment, if only an 808 nm pump laser was injected the threshold of P bp is 16.8 W. With the P bp level upping from zero to 16.8 W, the threshold of P wp has significantly decreased, and the slope and the maximum output power P out have significantly increased. The maximum P out increased from 2.11 W to 5 W, as shown in Fig. 5(b). As given by (5), the carrier density N g contributed mainly by N w /τ wg from the in-well pumping and N b V b /τ bg V w from the barrier pumping. For the coupling pump, the additional injection N b increases both N w /τ wg and N b V b /τ bg V w , as given by (3)-(5). The carriers escaping from the QW will make N b larger than that excited by the barrier pump laser alone. For in-well pumping, the increase in N b and N b V b /τ bg V w makes less N w /τ wg required for N g to reach the threshold condition. The suppressed carrier escape process and a small amount of N b V b /τ bw V w will increase the N w /τ wg . The above reasons together lead to the increase of N g and P out . The overall optical-optical efficiency η opt-opt has been significantly improved, as shown in Fig. 5(c). That means under the same total pump power P wp + P bp , more carriers relax to the ground state of the QW and involve in radiative recombination than using the only in-well pump. The intrinsic efficiency is improved [9]. Fig. 5(d) shows the peak emission wavelength of the output laser pumped by P wp only and the coupling pump with an additional P bp = 16.8 W, corresponding to the black and purple curves in Fig. 5(a) and (c). When the total pump power is close in value, the output power of the coupling pump is 5 W greater than that of the in-well pump is only 2.11 W, but the difference between the peak emission wavelength is only about 0.4 nm. This means that the additional P bp injected below the threshold in the coupling pump does not produce too much additional heat, but improves both η opt-opt and P out .
With the incident 808 nm P bp raising from 16.8 W to 29.4 W, the maximum P out is also increased. Under this condition, P bp is already higher than its own threshold, as shown by the negative part of the black line in Fig. 5(b). For the coupling pump, the contribution of in-well pumping to output power decreases, and the pumping process gradually changes to barrier pump dominant, as shown by the red dash line in Fig. 5(b). With the further increase of the P bp level, the overall optical-optical efficiency η opt-opt drops rapidly after reaching the peak, as shown in Fig. 5(c). Because the heat generated by the quantum defect of N b V b /τ bg V w increases accordingly with the P bp . Meanwhile, as the temperature of the QW increases, the carrier escape rate also increases. An increase in the number of carriers escaping from the QW and subsequently re-captured by the ground state of the QW will generate more heat. Therefore, a higher P bp above the threshold will compete and displace the in-well pumping, and bring about more severe thermal effects. For in-well pumping, an additional barrier pump source with power below the threshold will effectively suppress the carrier escape effect and improve the laser output performance.
In the relative case of the 808 nm barrier pump leading coupling pump, a 940 nm in-well-absorbed pump laser as an additional pump source was injected into the active region. The P out versus incident 808 nm P bp is shown in Fig. 6(a). With 808 nm pumping only (black line), we can achieve a maximum P out = 12.19 W. When the P bp is less than 40 W, the additional injected P wp enables a lower threshold and a higher output power. Because the carriers excited by P wp and relaxed through N w /τ wg directly increase the N g , then the N g can achieve threshold carrier density by capturing fewer barrier carriers. When the P bp is more than 40 W, the maximum P out decrease is mainly caused by the thermal effect. The high temperature brought by high P bp makes the device thermal rollover. Under this condition, the carrier escape rate of N w will be too large to be ignored and the escaped carriers re-captured by the ground state of the QW will generate more heat. The total amount of heat dissipation capacity is constant, so the additional injected P wp will advance the rollover point. The same result is also shown in Fig. 6(b).
Similar optical-optical efficiency results induced by thermal effects are shown in Fig. 6(c). Under the same total pump power  P wp + P bp , in addition to the thermal effect of carrier relaxation, the decrease of efficiency η opt-opt is also due to the additional heat generated by the low absorption efficiency of P wp . Fig. 6(d) shows the peak emission wavelength of the output laser pumped by P bp only and the coupling pump with an additional P wp = 19.8 W, corresponding to the black and brown curves in Fig. 6(a) and (c). The peak emission wavelength of the coupling pump is overall longer than the P bp pump only. Their average difference is greater than 1.2 nm, especially at low pump power. This indicates that the heat load brought by the P wp injection is greater than the gain contribution in the barrier pump leading coupling pump. The thermal effect reduces the achievable output power.
We compared the threshold results of the concept of coupling pump (red line in Fig. 4(a)) with the experimental value at 280 K (positive part of black curves in Figs. 5(b) and 6(b)). The results are shown in Fig. 7(a). The threshold variation trend of coupled pumping is basically in line with the predictions of our theoretical simulations. The simulated and experimental P out of the coupling pump at different fixed P bp and temperatures are shown in Fig. 7(b). The experimental values are the same as the corresponding curves given in Fig. 5(a). According to the actual P bp values used in the experiments, we fine-tune the simulated values in Fig. 4(b). As explained above, the relative error of P out is caused by the carrier thermal effect and rollover. Overall, the measurement is a demonstration of the applicability of the coupling pump rate equations for the output characterization.

V. CONCLUSION
In summary, we have presented an in-well and barrier coupling pump scheme of semiconductor disk laser. We have investigated the carrier dynamics characteristics of the coupling pump and give a reliable rate equation model. As a mechanism to limit the improvement of the output performance of in-well pump SDL, the carrier thermal escape effect will be significantly improved by the coupling pump scheme. In the in-well pump leading coupling pump case, the optical-optical efficiency and output power can be significantly improved by introducing a barrier absorption pump source under a similar thermal load. The threshold of the in-well/barrier pump can be significantly reduced by introducing a barrier/in-well absorption pump source. Although the improvement brought by the coupling pump is obvious, it is still a difficult task and the overall optical efficiency is relatively low, primarily due to the low absorption of the in-well pump source. We believe that combining the coupling pump approach with existing methods for improving the absorption efficiency of the in-well pump laser, such as resonant pumping and multi-pass pumping [9], [15], [28], can achieve more efficient pumping and higher output power simultaneously. Furthermore, for some visible and mid-IR wavelength SDL devices which have no commercial high power pump source with a suitable wavelength, our approach can also provide a potential solution.