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Abstract
We present a detailed analysis of multiphysics simulation results to evaluate the threshold for catastrophic optical damage (COD) of high-power laser diodes under misaligned external optical feedback. Three different chip designs are investigated: the non-injecting mirror concept, the non-absorbing mirror concept and the introduction of an additional energy barrier within the waveguide near the front facet. Furthermore, a modification of the external resonator that promises a lower sensitivity towards misalignments is considered. The dependence of the COD threshold on the additional design parameters (bandgap change, modification length, focal length) and the impact of the different approaches on electro-optical efficiency as well as beam quality are analyzed. Compared to the initial design, the different chip design concepts promise an increase of the achievable output power by 8%, 27% and 27% respectively, whereas the modified resonator fully prevents feedback-induced failure.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The output power of state-of-the-art high-power laser diodes is limited by thermal rollover and catastrophic optical damage (COD). Especially for spectrally stabilized, external cavity laser diodes (ECDL) used in direct diode laser systems [1] or for pumping of Ytterbium-based fiber or disc lasers at 976 nm [2], feedback-induced COD represents a serious issue. In this case, the COD threshold of a laser diode is significantly reduced when a portion of the feedback radiation, e.g. by a volume Bragg grating (VBG), hits the highly p-doped cap layer or even the metal layers on the p-side of the device [3]. The absorption in these layers causes a strongly confined heat source creating the initial temperature rise required to trigger the damage mechanism. This was confirmed by several experimental studies using thermoreflectance imaging [3,4]. Due to the small size of the p-side epistructure of less than 2 µm such a misalignment is hard to avoid and can e.g. be caused by the smile error of a laser bar soldered to a submount. In a previous work, we were able to confirm these results with a multiphysics model of an ECDL, which self-consistently computes its electrical, optical and thermal properties [5]. Furthermore, it was shown that the model is also able to accurately predict the experimentally measured COD thresholds when the COD is triggered by an increasing overhang between diode chip and submount [6]. Finally, usage of this model clarified the decisive impact of thermo-optically generated leakage currents from the quantum well on the thermal runaway process during COD [7]. Here, we use this numerical model to analyze three different chip design approaches to increase the COD threshold of laser diodes under misaligned external feedback with respect to their impact on the maximum achievable output power, electro-optical efficiency as well as beam quality. Furthermore, a bi-telecentric external resonator setup is investigated which enables feedback into the waveguide irrespective of the shift of the fast axis collimation (FAC) lens and thus circumvents feedback-induced failure.
2. Design approaches for increased COD threshold
The four approaches considered in this paper are summarized in Fig. 1. Due to nonradiative recombination at surface states the two facets are usually weak points of the device, where COD is likely to start. Furthermore, due to the packaging on the submount with overhang and the maximum optical intensity, the temperature at the front facet is especially elevated. The absorption of misaligned feedback radiation at the metal layers and the resulting surface heat source causes another increase in temperature and makes the front facet the primary point for the occurrence of COD [5]. Therefore, all considered modifications presented in this paper are restricted to the front facet of the device.
Fig. 1. Overview of the three different considered chip design modifications and the adaption of the external resonator. Adapted from [8,9].
The different approaches all try to mitigate a certain driver on the route to COD:
- 1) The non-injecting mirror (NIM) aims at a reduction of the current and carrier density at the facet by blocking the current injection from the p-side on a length ${d_{\textrm{unp},\textrm{f}}}$.
- 2) The non-absorbing mirror (NAM) shifts the onset of absorption at the initial COD site in the active region to higher temperatures by locally increasing the bandgap of the quantum well by $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$.
- 3) The energy barrier within the waveguide suppresses leakage currents from the quantum well into the waveguide by locally increasing the bandgap of the waveguide material by $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}}$.
- 4) The bi-telecentric external resonator makes the setup less sensitive to misalignments of the optical components and enables stable feedback into the waveguide irrespective of a potential smile error by introducing an additional imaging lens.
The concepts are compared by computing the COD thresholds with the previously mentioned multiphysics model for an FAC lens shifted by $\mathrm{\Delta }{x_{\textrm{FAC}}} = $ -2 µm towards the p-side. In this case the feedback radiation is completely absorbed within the metal layers on the p-side of the device and leads to a strong reduction of the COD levels [5]. The model is part of the semiconductor laser simulation software (SEMSIS), which was developed at the Fraunhofer Institute for Laser Technology ILT, Fig. 2. It incorporates the solution of the drift-diffusion equations including an additional thermoelectric current on a vertical-longitudinal slice of the device [10]. The coordinate system is chosen in a way that $x = $ 0 corresponds to the center of the quantum well and $z = 0$ to the rear facet of the laser diode. The electrical model is coupled self-consistently to a two-dimensional wave-optical model, which consists of the wide-angle beam propagation method (WA-BPM) with Padé approximation of order (2,2) [11] for the computation of the optical field within the semiconductor heterostructure and a GPU-accelerated Fourier optical model for the external resonator [12]. The computed electrical and optical heat sources are then homogeneously extrapolated over the injection stripe width and the temperature is computed on a three-dimensional domain considering the semiconductor chip as well as the submount. For the thermal model we use bulk values for the thermal conductivity of the different layers and do not consider a reduction due to the low dimensionality of the quantum well or thermal boundary resistances. Subsequently, temperature dependent material properties like bandgap, carrier mobility, recombination coefficients for spontaneous, Shockley-Read-Hall and Auger recombination as well as gain, free carrier absorption and thermal conductivity are updated.
Fig. 2. Multiphysics model of an external cavity laser diode (ECDL), where the electro-optical problem is solved in the vertical-longitudinal plane of the device and the thermal model considers the full 3D structure of chip and submount [5].
These two stationary models (electro-optical and thermal) are solved iteratively until convergence is achieved. If the iteration loop becomes unstable and leads to ever increasing temperatures, this is interpreted as a thermal runaway, leading to catastrophic damage of the device. More details on the model are presented in [7,8]. The basic device parameters and properties of the external resonator are listed in Table 1. The laser diode uses a single quantum well active region with a separate confinement heterostructure waveguide with constant bandgap throughout the waveguide layers and is very similar to the one described in [13]. The additional imaging lens shown in Fig. 1 is only considered in section 2.4.
Table 1. Device parameters considered for the simulation
2.1 Non-injecting mirror (NIM)
The first ansatz is the well-known concept of non-injecting mirrors (NIM) [14]. The current injection into the device is suppressed near the front facet by depositing an insulating material before the metal contacts are evaporated. This makes it possible to reduce carrier as well as current density at the facet and leads to lower surface recombination heat, lower Joule heating and in turn to a lower facet temperature. The impact of the length of this unpumped section ${d_{\textrm{unp},\textrm{f}}}$ on the COD level was previously investigated using our model in [15], and is displayed in Fig. 3. When ${d_{\textrm{unp},\textrm{f}}}$ increases from 0 to 30 µm the COD level is increased by about 7%. However, when ${d_{\textrm{unp},\textrm{f}}}$ is further increased to 100 µm, the COD level reaches saturation and only small improvements are visible.
Fig. 3. Computed COD threshold for misaligned feedback ($\mathrm{\Delta }{x_{\textrm{FAC}}} = $ -2 µm) as a function of the unpumped section length. Adapted from [15].
To further investigate this result, the influence of the NIM on the regular operation of the device, i.e. with aligned feedback ($\mathrm{\Delta }{x_{\textrm{FAC}}} = $ 0 µm), is analyzed in Fig. 4 for an injection current of 15 A. This avoids that the impact of the NIM on physical properties is obscured by the strong feedback induced temperature gradients and the resulting additional leakage currents. Due to current spreading the current density at the facets is not vanishing for small values of ${d_{\textrm{unp},\textrm{f}}}$, Fig. 4(a), but around 30 µm it decreases to almost 0, which constitutes the major portion of the increase in COD level. For ${d_{\textrm{unp},\textrm{f}}} \ge $ 30 µm, the COD level increases only slightly due to the further decreasing facet temperature, Fig. 4(b). However, the maximum temperature saturates in this regime and becomes larger than the facet temperature, which can be attributed to the electrical isolation of the front facet resulting in reduced Joule heating and smaller carrier density. In this case, the maximum device temperature is reached in the bulk, at the edge of the electrically pumped section, where the intensity reaches its maximum and thus strong heating by free carrier absorption and Joule heating occurs.
Fig. 4. For $I = \textrm{}$ 15 A and aligned feedback ($\mathrm{\Delta }{x_{\textrm{FAC}}} = $ 0 µm): (a) vertical component of the current density near the front facet within the quantum well, (b) temperature at the front facet and maximum temperature within the quantum well, (c) electro-optical efficiency and average temperature of the active region as a function of the unpumped section length. Adapted from [15].
When choosing the optimum length of the unpumped section, the electro-optical efficiency has to be considered as well. As the electrically unpumped section is absorbing for the propagating laser field, it is optically pumped to a value close to the transparency of the active medium. For increasing ${d_{\textrm{unp},\textrm{f}}}$ this leads to a decreased efficiency as a longer region needs to be optically pumped. On the other hand, for a fixed injection current an increase of ${d_{\textrm{unp},\textrm{f}}}$ leads to an increasing current density within the pumped region and thus to an increasing average temperature of the active region, which further decreases the efficiency. The computed mean temperature and electro-optical efficiency are shown in Fig. 4(c). For ${d_{\textrm{unp},\textrm{f}}} \le $ 10 µm no changes are visible as due to current spreading, the whole resonator length is still electrically pumped and no optical pumping is required. For larger values of ${d_{\textrm{unp},\textrm{f}}}$ the expected increase of the mean temperature and the decrease in efficiency is visible, but the computed changes for ${d_{\textrm{unp},\textrm{f}}} = $ 100 µm are quite small with approximately 1 K temperature increase and 0.8% efficiency drop.
An approach related to the NIM is the multi-section waveguide structure recently described in [16], where the current flow close to the facet is not completely blocked, but separately adjusted by an additional contact. By electrically pumping this section close to transparency, the previously mentioned optical pumping and the resulting efficiency drop can be avoided while simultaneously keeping the Joule heating and carrier density at the minimum required value. We might consider this approach in a future analysis.
2.2 Non-absorbing mirror (NAM)
The temperature-induced decrease of the quantum well bandgap in the active region is usually considered as the main cause for the onset of the positive feedback loop leading to thermal runaway and finally to COD. In a previous study, we demonstrated that even though other temperature dependent material properties are relevant as well, this one is the most important factor triggering a COD event [6]. The shift of the peak of the gain spectrum towards larger wavelengths leads to an absorption of the laser radiation at the heated front facet and consequently to a local increase in carrier density and nonradiative recombination. If the bandgap of the active region near the facets is increased, this section becomes transparent for the emitted laser radiation at moderate temperatures, which is known as a non-absorbing mirror (NAM) [17,18]. Elevated facet temperatures will finally also lead to absorption in this region, but the onset of absorption is shifted towards higher temperatures. The increase in bandgap for the NAM can be realized e.g. by using quantum-well intermixing, where point defects from an evaporated dielectric material or from ion implantation enhance the self-diffusivity of atoms between the quantum well and the waveguide layers leading to a washed-out quantum well [19].
To describe the NAM in our model, we simply decrease the indium content within the quantum well in a region of 30 µm around the front facet to cause a bandgap change $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ of 60 meV, 120 meV and 180 meV. The length of 30 µm is assumed to be sufficient as the longitudinal range where leakage currents are caused by the misaligned feedback is limited to approximately 10 µm [5]. The gain spectra for TE polarization of the original quantum well design and the three aforementioned modifications were computed using a quantum-mechanical model considering Coulomb interactions and correlation effects within the electron-hole plasma [20]. The results for different carrier densities are shown in Fig. 5(a). As expected, the gain spectra shift to smaller wavelengths with increasing $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$. Furthermore, the peak gain for fixed carrier density decreases due to the reduced mechanical strain with decreasing indium content. Increasing temperatures at the facet might still lead to absorption for the NAM when the temperature-induced bandgap shrinkage compensates $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$. The gain coefficient for a fixed wavelength and carrier density but varying temperature illustrates this, Fig. 5(b). A constant wavelength can be assumed as the radiation propagating within the waveguide will not be influenced by the narrow, heated region near the front facet. It can be stated that the temperature range without absorption increases from around 410 K for the original design to approximately 550 K for the bandgap change of 180 meV. The onset of absorption leads to an optical pumping near the facet and thus an increasing carrier density until a stationary value close to the transparency carrier density is reached. The transparency value is displayed in Fig. 5(c) and indicates that even in the presence of absorption a larger $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ leads to a lower carrier density near the facet for a given temperature. This lower carrier density is accompanied by a lower nonradiative recombination rate and thus a higher threshold for the onset of COD compared to a device without NAM or a device with smaller $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$.
Fig. 5. (a) Computed gain spectra of the four quantum well designs for different carrier densities, (b) gain coefficient at fixed carrier density and wavelength as a function of temperature, (c) transparency carrier density as a function of temperature. Adapted from [8].
The computed COD thresholds and efficiencies are shown in Fig. 6. Between 0 and 120 meV only a moderate increase of the COD level by about 5% is visible, before a stronger increase of 27% is shown for 180 meV. As expected, the electro-optical efficiency is not affected by the NAM. The small changes that are visible in the plot are caused by the numerical tolerances of the algorithms to compute the model.
Fig. 6. Computed COD threshold as a function of the bandgap change in the NAM and electro-optical efficiency for an injection current of 8.3 A (applied voltage of 1.6 V).
The computed hole density in the active region close to the front facet demonstrates the working principle of the NAM, Fig. 7. Whereas in the initial design without the NAM, Fig. 7(a), the electrically unpumped part is optically pumped to transparency as soon as the threshold current is reached, the designs with NAM show a carrier density close to zero for small currents, Fig. 7(b)-(d). The hole density does not drop to zero because of current spreading and carrier diffusion. However, the latter one is expected to decrease with increasing energy barrier between the active part of the quantum well and the NAM, which is in agreement with the simulation results. With increasing injection current the hole density increases close to the facet, which is caused by the temperature increase due to the feedback radiation that is absorbed in the metal layers. However, for a larger bandgap change $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ these peaks are less pronounced and their occurrence is shifted towards larger currents due to the later onset of absorption predicted by the gain spectra in Fig. 5.
Fig. 7. Computed hole density close to the front facet as a function of the longitudinal position and injected current for different bandgap changes in the NAM.
For the largest considered value of $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}} = $ 180 meV no absorption or increase of carrier density is visible in the whole considered range of currents. This fits well the computed facet temperatures for an injection current of 8.3 A in Fig. 8(a) where due to the temperatures above 450 K absorption is expected for all quantum well designs except for the one with $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}} = $ 180 meV, Fig. 5(b). Despite the well visible decrease in carrier density and the decreasing facet temperature, the leakage current (vertical component of the hole current density in the n-waveguide of the device) for a bandgap change of 60 meV is still comparable to the original design, Fig. 8(b). This can be explained by the decreasing energy depth of the quantum well in the non-absorbing mirror which makes an escape of the optically generated carriers from the quantum well more likely. The previously shown small increase of the COD thresholds for a $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ of 60 meV and 120 meV is thus caused by a quantum well design, which is more prone to leakage currents. Only the largest considered value of 180 meV promises a significant increase of feedback resistance, as in this case the carrier density becomes so small that this drawback is overcompensated.
Fig. 8. (a) Temperature at the front facet within the quantum well as a function of $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$, (b) hole current density close to the facet in the n-waveguide (500 nm above the quantum well), adapted from [8], both for an injection current of 8.3 A.
In [17] an increase of the COD level by a factor of 2.6 is presented for a $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ of 80 meV. However, these results are obtained with a completely different device design (1 mm cavity length, 60 µm long NAM regions, two quantum wells) and under different operating conditions (pulsed mode, no heating of the facet due to feedback) so a direct comparison is difficult in this case. The same applies to the results shown in [18], where lifetime tests for different values of $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ are performed. The laser diodes are operated at an output power below their unaged COD levels until gradual degradation lowers the COD level to the set output power. This leads to a combined measurement of gradual and catastrophic degradation in contrast to the situation considered here, where misaligned feedback and local heating of the facet allows to directly access the catastrophic degradation alone. Nevertheless, a similar trend is shown in a way that values of $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ smaller than a certain threshold value (between 30 meV and 80 meV) only slightly increase the lifetime, whereas values above this threshold completely avoid COD. In [18] this is attributed to tail states of the bandstructure, which are not included in the presented simulation results, but the previously mentioned leakage currents could be another cause.
In conclusion, to optimize the feedback-resistance the bandgap change $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ should be chosen as large as technologically feasible by the intermixing technique. Limits are given by the introduction of point defects during the intermixing process and ultimately by the bandgap of the surrounding waveguide material.
2.3 Energy barrier within the waveguide
As we stated in previous publications [5,7], the onset of leakage currents from the quantum well represents a crucial contribution to thermal runaway, the second phase of COD. The temperature-induced bandgap shrinkage in a section heated by the feedback radiation causes an accumulation of optically generated carriers in the active region, which finally start diffusing out of the quantum well. The analyzed heterostructure consists of a single quantum well active region surrounded by a single waveguide layer on each side with a constant bandgap. By increasing the bandgap of these two waveguide layers close to the facet, the energy barrier between the quantum well and the neighboring waveguide increases. This should lead to a suppression of leakage currents from the quantum well and represents a novel approach to alleviate COD. The additional barrier can be created by an intermixing process between the waveguide and cladding layers, leading to an increase of the bandgap in the waveguide and a corresponding decrease within the cladding. Another option would be to etch away the heterostructure near the front facet and epitaxially regrow a heterostructure with increased bandgap in the waveguide layers similar to the two-step epitaxy process for buried-mesa lasers described in [21]. As for the case of the non-absorbing mirror, a longitudinal range of 30 µm should be sufficient to suppress the onset of leakage currents. Furthermore, due to the additional unpumped section of 30 µm near the front facet, no negative influence of the barrier on the injection of carriers into the active region is expected. The computed power characteristics for different changes of the waveguide bandgap $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}}$ is shown in Fig. 9. An increase of the COD threshold by approximately 27% can be observed, but for the largest considered value of 180 meV the slope efficiency is slightly decreased.
Fig. 9. Computed light-current (L-I) curve for different values of the energy barrier in the waveguide. Adapted from [8].
The decreasing efficiency is caused by the weaker index guiding as the refractive index contrast between the waveguide and cladding layers decreases with increasing bandgap of the waveguide in the modified section. Finally, this even leads to a widening of the waveguide when the bandgap of the waveguide equals the bandgap of the cladding layer. For $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}} = $ 120 meV and 180 meV the forward propagating optical intensity profile in the vertical-longitudinal plane for an injection current of 8 A is displayed in Fig. 10(a) and (b). On the last 30 µm along the propagation direction, diffraction into the larger waveguide near the front facet is visible. For the larger bandgap change the influence on the intensity distribution is much stronger. This diffraction causes on the one hand a decreasing beam quality in the fast axis and on the other hand an additional loss when this broadened field is coupled back into the original, smaller waveguide. The backpropagating intensity distributions are shown in Fig. 10(c) and (d). For $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}} = $ 120 meV only slight diffraction ripples are visible and the expected loss is small. However, for a bandgap change of 180 meV a fraction of the power reflected at the front facet propagates in a parasitic waveguide within the cladding and is thus not amplified. This leads to the previously mentioned decrease of the slope efficiency.
Fig. 10. Forward (a), (b) and backward (c), (d) propagating intensity distributions at $I = $ 8 A for $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}} = $ 120 meV (a), (c) and $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}} = $ 180 meV (b), (d), respectively. The dashed lines in (a) and (b) indicate the boundaries of the waveguiding layers.
COD threshold, beam quality factor ${M^2}$ and the electro-optic efficiency as main parameters influenced by the additional barrier in the waveguide layer are displayed in Fig. 11. The latter two quantities were evaluated at a current of 8 A, as this value represents a useful pre-COD point for all considered devices. ${M^2}$ increases from an almost diffraction limited beam with a value of 1.1 for 0 meV and 60 meV to around 1.8 for 180 meV. The loss due to propagation in the parasitic waveguide, Fig. 10, leads to a distinct efficiency drop by 1.5% between the last two data points. However, on the transition between 0 meV and 120 meV the barrier enables a higher electro-optic efficiency due to the suppressed leakage of carriers from the quantum well in the heated region near the front facet. In conclusion, to choose the optimum barrier height a tradeoff between these three parameters has to be carefully made.
Fig. 11. COD threshold, ${M^2}$ and electro-optic efficiency as a function of the bandgap change in the waveguide.
2.4 Bi-telecentric resonator
The observed reduction of the COD threshold due to external feedback originates from the absorption within the metal layers of the device, which can be caused by slight misalignments in the external resonator. If these are assumed to be statistically distributed, an external resonator with a smaller sensitivity to misalignments promises a higher yield of devices, which are not prone to feedback-induced failure. A possible approach to this is given by a bi-telecentric optical setup. By introducing a second lens into the external optical resonator, which images the emitted field distribution on the VBG surface, and choosing the distances between the optical elements as shown in Fig. 12, bi-telecentricity is achieved and enables feedback into the waveguide, irrespective of a smile error or vertical shift of the FAC lens [22].
In contrast to the previously investigated setup, where a collimated beam hits the VBG, the bi-telecentric resonator shows a feedback field without image reversal. The second lens is in the following modelled as a thin lens, which only introduces a quadratic phase term on the optical field. For the FAC, a focal length of ${f_{\textrm{FAC}}} = $ 1.1 mm is used as before, whereas the focal length of the imaging lens ${f_{\textrm{Im}}}$ represents a new parameter, which has to be defined for the setup. On the one hand, larger focal lengths enhance the size of the overall system. On the other hand, small focal lengths decrease the effective reflectivity from the VBG, as the VBG with its small angular selectivity is illuminated with a beam containing a wide angular spectrum. The angular selectivity of the VBG as well as the angular intensity distribution along the fast axis are shown in Fig. 13(a) for different focal lengths ${f_{\textrm{Im}}}$. For a focal length of 10 mm the angular distribution of the incoming beam is larger than the angular bandwidth of the VBG with a FWHM of approximately 2°.
Fig. 13. Angular intensity distribution on the VBG and angular diffraction efficiency of the VBG (a), feedback intensity distribution (rescaled by the maximum diffraction efficiency) on the front facet of the laser diode (b), both for different focal lengths ${f_{\textrm{Im}}}$. Adapted from [8].
The resulting feedback field has lower power and is broadened due to the selective feedback of certain angular contributions from the VBG, Fig. 13(b). For longer focal lengths like 50 mm the angular intensity distribution on the VBG becomes smaller than the angular selectivity of the VBG and leads to a narrow feedback field with large overlap to the waveguide eigenmode along the fast axis.
To identify an optimum value for the focal length, the overlap between the emitted eigenmode profile and the feedback field as a measure of the coupling efficiency is displayed in Fig. 14(a) together with the effective reflectivity of the VBG (feedback power divided by emitted power). For focal lengths larger than 50 mm overlap and reflectivity reach their maximum value. However, a focal length of 50 mm leads to a total resonator length of more than 100 mm, which corresponds to an increase by a factor of 20 compared to the previously considered resonator with a distance of 5 mm between laser diode and VBG. Additionally, after the VBG another lens would be required to collimate the beam again, which would further increase the total size of the setup. Apart from the size, the complexity and cost of the whole module would be higher as two additional optical elements have to be aligned. The computed feedback field at the front facet of the laser diode for a vertical misalignment of the FAC lens is shown in Fig. 14(b). For the non-telecentric setup a shift of the FAC lens by $\mathrm{\Delta }{x_{\textrm{FAC}}}$ leads to a shift of the feedback field by 2$\mathrm{\Delta }{x_{\textrm{FAC}}}$ due to the reversed image. In contrast, for the telecentric resonator the feedback field is independent of $\mathrm{\Delta }{x_{\textrm{FAC}}}$.
Fig. 14. Overlap integral and effective VBG reflectivity as a function of ${f_{\textrm{Im}}}$ (a), feedback field for different misalignments of the FAC lens in telecentric and non-telecentric configurations (b). Adapted from [8,9].
As expected, the computed power characteristics for a focal length of the imaging lens of 50 mm is identical to the one for the non-telecentric resonator without misalignment, Fig. 15. The output power is limited only by thermal rollover and no sign of feedback-induced COD is visible. This corresponds to an achievable increase of the output power by about 72%.
Fig. 15. L-I curve for different external resonators (with and without misalignment, with and without telecentricity). Adapted from [8,9].
3. Comparison
The results that were obtained in the previous section by separately adjusting single parameters to obtain a higher COD threshold are summarized and compared in this section. Furthermore, a device which combines all three considered chip modifications is investigated. A non-injecting mirror at the front facet with a length of ${d_{\textrm{unp},\textrm{f}}} = $ 100 µm is used in conjunction with a non-absorbing mirror with a bandgap shift in the quantum well of $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ = 180 meV and a barrier in the waveguide with a bandgap enlarged by $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}}$ = 120 meV. The value of 120 meV is chosen to avoid the reduced efficiency and the lower beam quality seen at 180 meV. The power characteristics of the devices with different design concepts for an FAC lens misaligned by $\mathrm{\Delta }{x_{\textrm{FAC}}} = $ - 2 µm are displayed in Fig. 16(a). For each concept the free parameter was chosen to achieve the optimum value of the COD threshold, i.e., ${d_{\textrm{unp},\textrm{f}}} = $ 100 µm, $\mathrm{\Delta }{E_{\textrm{G},\textrm{QW}}}$ = 180 meV and $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}}$ = 180 meV. The additional non-absorbing mirror and the longer non-injecting mirror in the combined approach lead to COD occurring approximately at the same current as for the larger barrier height but yield a higher output power and slope efficiency. Besides the avoided feedback-induced COD, the bi-telecentric resonator shows an increased slope efficiency as no additional loss occurs due to feedback radiation hitting the metal layers. The electro-optic efficiency at an injection current of 8 A, Fig. 16(b), decreases with the elongation of the NIM and remains almost unchanged when the NAM is introduced. The barrier of $\mathrm{\Delta }{E_{\textrm{G},\textrm{WVG}}}$ = 180 meV leads to lower efficiency because of the additional losses during backpropagation, whereas the combined approach with a barrier of 120 meV displays an even higher efficiency than for the original design due to the additional suppression of leakage currents, see Fig. 11. But the largest efficiency with a value of 63% can be observed if the bi-telecentric resonator concept is used to completely avoid losses during backpropagation.
Fig. 16. (a) L-I curve, adapted from [9], (b) electro-optical efficiency at 8 A for the original design, the four different design concepts and the combined approach.
Finally, the different approaches are again compared in Fig. 17. The maximum possible output power ${P_{\textrm{COD}}}$ before damage occurs only slightly increases when the non-injecting mirror length is increased from the original value of 30 µm to 100 µm. The introduction of a non-absorbing mirror or the additional barrier within the waveguide allows for an increase of the output power by 27%. By combining these three methods, a further increase by 10% is demonstrated within the simulation. The highest advancement is possible by completely avoiding any absorption in the metal layers on the p-side by using a bi-telecentric external resonator. In this case, the output power is only limited by thermal rollover. Moreover, this leads to the highest efficiency as no loss occurs due to misaligned feedback fields. A second positive aspect of this is the expected lower gradual degradation which would otherwise be accelerated by the high facet temperatures occurring in the device. The only disadvantages to be considered are the footprint of the setup and its increased complexity.
Fig. 17. Maximum achievable output power and critical temperature for the different approaches (no COD occurs in the grey area and the output power is only limited by thermal rollover). Adapted from [8].
A comparison of the critical temperature ${T_{\textrm{crit}}}$ allows to judge the actual feedback-resistivity of the investigated devices. The critical temperature is defined as the largest stable temperature in the semiconductor heterostructure observed within the simulations. For slightly larger temperatures the onset of the positive feedback loop leading to thermal runaway and finally COD is visible. All measures modifying the chip structure in sections 2.1 to 2.3 are aiming to shift this onset to larger temperatures or equivalently higher output powers. This makes it possible to expose the laser diode to higher levels of misaligned feedback power and thus really improves the feedback-resistivity. Again, the non-absorbing mirror as well as the barrier within the waveguide lead to a significant improvement compared to the original design. The system with a telecentric resonator does not show any improvement in the critical temperature as an unchanged heterostructure is investigated. In this case, where misaligned feedback from the laser diode itself is not possible due to the structure of the resonator, feedback robustness has to be interpreted as robustness against other parasitic reflections e.g. from the workpiece in materials processing or from other laser diodes within a pump module, which are not imaged onto the waveguide by the external resonator. In this scenario, the telecentric resonator provides no additional protection of the laser diode. So in conclusion, a combination of the telecentric resonator with the other three approaches promises the highest protection of a device with respect to its own feedback for spectral stabilization as well as any other parasitic feedback.
4. Summary & outlook
In this work, we have evaluated four different approaches to increase the feedback-resistance of high-power laser diodes with a multiphysics simulation and compared them with respect to the achievable output power, efficiency and beam quality. By combining the three chip design approaches an increase of the output power by 37% is possible. A bi-telecentric external resonator which makes the system insensitive towards a misalignment of the FAC lens completely avoids feedback-induced failure.
Future work will include the experimental validation of the proposed design concepts. If the additional barrier in the waveguide leads to the predicted increase of the COD level this could be seen as a further evidence of the importance of leakage currents from the quantum well during COD. Additionally, further refinements of the model including an extension to a full three-dimensional model by including the lateral direction would allow to consider the impact of filamentation. The inclusion of scattering between the quantum well states and bulk states would be a suitable extension to allow for a more accurate description of the leakage currents. Apart from applications in laser materials processing feedback-resistant high-power laser diodes will also be a key technology for reliable, efficient and economically viable inertial fusion power plants in the future [23].
Acknowledgments
The authors would like to thank Trumpf Photonics Inc., Cranbury, New Jersey, for funding this work. Portions of this work were presented at the SPIE LASE High-Power Diode Laser Technology XX in 2022, “Multiphysics modeling of feedback-induced catastrophic optical damage in 9xx-nm high-power laser diodes” (paper number: 119830E), CLEO Science and Innovations 2022: Power Scaling in Semiconductor Lasers, “Analysis of the Non-Injecting Mirror Concept for Feedback-Resistant High-Power Laser Diodes with a Multiphysics Model” (paper number: SS2D.1) and SPIE LASE High-Power Diode Laser Technology XXI in 2023, “Evaluation of design concepts for feedback-resistant 9xx-nm high-power laser diodes” (paper number: 124030B).
Disclosures
MA, MT, HDH, CH: Trumpf Photonics Inc. (F), SR: Trumpf Photonic Components (E).
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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