Raman spectroscopy plays an important role in nondestructive testing. Portable, efficient, and convenient devices are preferred by consumers. Semiconductor lasers have garnered significant research attention due to their small size, light mass, and high electro-optical conversion efficiency, and can be used as Raman light sources when their excitation wavelength is 785 nm^[1-3]. Raman detection requires high power (shortened detection time) and narrow linewidth (high spectral purity), which requires the product to have sufficient gain and the grating to have a high coupling coefficient κ, forcing the grating to have a high etching depth^[4-5].

However, the ordinary wide-stripe laser has a wide gain spectrum, which makes multiple longitudinal modes to be excited and broadens the spectrum. As a wavelength selection element, the Bragg grating filters the needless wavelengths and only retains the required Bragg wavelength. Such wider linewidths are not sufficiently applicable for Raman spectroscopy. Generally speaking, narrow linewidth lasers are categorized as external cavity lasers, distributed feedback lasers (DFB), and distributed Bragg reflector lasers (DBR). External cavity lasers necessitate Bragg gratings designed outside the cavity according to the diffraction conditions, which poses challenges in terms of mounting and light output efficiency. Consequently, inner-cavity design is a more appropriate choice. Regardless of whether it's DFB or DBR lasers, there's a need for sufficient etching depth to ensure an appropriate coupling coefficient. This presents numerous difficulties in laser fabrication. Shallow etching depth will lead to inadequate mode filtering, large threshold current and deep etching depth will cause enhanced mode scattering and increased optical loss in the waveguide. In the meanwhile, excessively deep etching depth may also result in the formation of a V-groove, altering the effective duty cycle of grating and thereby affecting its coupling coefficient. To the author's knowledge, the vast majority of published papers related to epitaxial design usually keep the transverse mode profile as far away from the p-type region as possible, because the free carrier absorption coefficient of holes is higher than that of electrons (about three times higher). However, some articles do report that symmetric epitaxial structures yield higher reflectivity as well as optical confinement factors. Specially, the epitaxial structure adopted by the reported dual wavelength laser, taking Germany's FBH as an example, adopts a symmetrical waveguide and a 1 μ m wide cladding layer structure. This structure not only causes significant internal losses, but also requires deep etching to achieve the expected reflection effect^[6-7]. The former issue presents challenges in the design of the transverse epitaxial structure: as the mode profile moves away from the p-side, the grating becomes weaker in coupling with the mode profile, leading to a lower coupling coefficient. To address this issue, we improve this situation by reasonably thinning the thickness of the p-side waveguide and introducing the mode expansion layer structure with certain internal losses. This strategy also yields additional benefits, for example, reducing the vertical divergence angle, raising catastrophic optical mirror damage (COMD) threshold, and boosting the output power and enhancing the refractive index difference to boost the coupling coefficient^[8]. Near-infrared range (NIR) lasers suffer from low conversion efficiency due to the large bandgap energy of quantum wells, which results in easy electron leakage and reduces the internal quantum efficiency. To improve the injection efficiency of the electron and reduce the carrier escape phenomenon, this manuscript introduces an electron energy release layer in the n-side of the epitaxial layer. This layer enables high-energy electrons to recombine in the active region and release some of their energy in advance, increasing their likelihood of being captured by the quantum well. To mitigate the adverse effects of the escaped electrons, which usually accumulate and recombine on the p-side waveguide, causing the power drop, the concept of dual waveguide structure is proposed to counteract this issue. In addition, the lateral mode limitation is also an essential task. As the epitaxial layer structure changes, the width of the ridge varies with the change in the effective refractive index due to the mode cutoff condition. When designing the epitaxial structure, it is crucial to maintain an adequate lateral refractive index difference. Finally, the choice of the longitudinal mode is determined by the Bragg grating, and it is known that there is a correlation between the grating order and the emission width (FWHM); that is, the lower the grating order, the broader the FWHM^[9-10]. To ensure a sufficient coupling effect, we choose to use low-order DBR grating for mode-locking. To achieve sufficient output power, a long cavity length laser design is employed, which not only increases the optical amplification gain but also enhances heat dissipation. This results in a lower thermal resistance for the device.

Previous reports on the epitaxial structures of 785 nm semiconductor lasers have predominantly employed symmetric waveguide (cladding) designs, necessitating deeper grating etching to achieve the desired reflectivity. This approach, however, frequently introduces heightened internal losses and poses numerous challenges during fabrication due to the larger etch depth-to-width ratio. Furthermore, excessively deep etching tends to create V-shaped grooves, which adversely impact the grating coupling coefficient. To address these issues, this paper proposes an innovative epitaxial structure that significantly reduces the grating etching depth while maintaining high-level output performance.

The epitaxial layer structure is grown on a GaAs substrate through metal organic chemical vapor deposition (MOCVD). The thickness and doping concentration of each layer are elaborated in Section 3. Following epitaxial growth, the ridge waveguide of the distributed Bragg reflector (DBR) laser with a shallow etched grating structure is obtained by means of different lithography processes. The front and rear surfaces are not coated after laser cleavage, resulting in an expected reflectivity of approximately 30%. The conventional laser structure consists of a substrate, buffer layer, upper and lower cladding layers, upper and lower waveguide layers, active region, and ohmic contact layer, which constitutes a simple structure with low beam quality. Building upon this foundation, a series of rational auxiliary layers are established to reduce resistance and loss and further enhance the output performance of the device. The details of these layers will be discussed in the subsequent section.

The maximum output power of a semiconductor laser is positively related to the COMD power density P_COMP of the product with the following relationship^[11]:

$ P_{\max}=\frac{d}{\mathit{\Gamma}_{\mathrm{QW}}}W\frac{1-R}{1+R}P_{\mathrm{COMD}}\quad, $ (1)

where $d$ is the quantum well thickness, $ \mathit{\Gamma}_{\mathrm{QW}} $ is the active region confinement factor, $R$ is the reflectivity of the front and rear cavity surfaces, and $W$ is the device strip width. When the device quantum well width, front and rear cavity reflectivity, and device strip width are certain, the maximum output power of the device is inversely proportional to the optical confinement factor of the active region. The confinement factor is inversely correlated with the threshold current, and the maximum output power of the device is increased by appropriately lowering the confinement factor in the active region by reasonably setting the epitaxial structure.

The mode expansion layer is essential if we want to achieve a certain confinement factor to be maintained on the p-side. The confinement factor is expressed as the ratio of the light field intensity of a layer to the total light intensity and is defined by the equation:

$ {{\mathit{\Gamma}} _i} = \frac{{\displaystyle\int_{{y_{i - 1}}}^{{y_i}} {{H^2}(y){\mathrm{d}}y} }}{{\displaystyle\int_{ - \infty }^{ + \infty } {{H^2}(y){\mathrm{d}}y} }} \quad,$ (2)

where ${y_{i - 1}}$, ${y_i}$ represents the transverse position (the growth direction) of the layer, $H(y)$ is expressed as the distribution of the mode profile in the ${i_{th}}$ layer. It can be known that the asymmetric waveguide is able to shift the mode profile to the n-side while the presence of the p-side extension layer keeps part of the mode profile on the p-side. However, the presence of too much mode profile can be a great waste of energy, and since the p-side holes have a stronger effect on light absorption, the relationship of internal losses has to be considered. The expression is^[12]:

$ \alpha=\alpha\mathrm{_i}+\alpha_{\mathrm{m}}\quad, $ (3)

$ \alpha_{\mathrm{m}}=\frac{1}{2L}In\frac{1}{r_1r_2}\quad, $ (4)

$ \alpha_{\mathrm{i}}=\frac{1}{p}\cdot\int_{ }^{ }\alpha(x)\left|E(x)\right|^2\mathrm{d}x\quad, $ (5)

where $ \alpha $, $ \alpha_{\mathrm{i}} $, $ \alpha_{\mathrm{m}} $ are total optical loss, internal loss, and mirror loss, respectively. $ L $ is the cavity length, $r$ is the reflectance of the front and rear cavity surfaces, $ P=\displaystyle\int_{ }^{ }\left|E(x)^2\right|\mathrm{d}x $, $E(x)$ is the distribution of the mode in the epitaxy direction. $ \alpha(x)=\sigma_{\mathrm{n}}n+\sigma_{\mathrm{p}}p $, $n$ and $p$ are the densities of electrons and holes respectively, $ \sigma_{\mathrm{n}} $ and $ \sigma_{\mathrm{p}} $ are the absorption cross sections of the electrons and holes respectively.

Based on the above equations, it is evident that since the mirror reflectivity and cavity length are the same for each laser, the corresponding mirror losses are also equal. The distinguishing factor is that different epitaxial structures result in varying mode profile distributions within the devices, resulting in the mode profile overlapping with the waveguide and cladding layers to varying degrees, and then producing different internal losses. Among these, the p-side loss is particularly significant. Therefore, during the design of the mode expansion layer, considerations should be given to the p-side confinement factor and loss weighting analysis.

The software employed for the simulation of semiconductor lasers is Crosslight from Canada - PICS3D^[13]. This software enables the simulation of the energy band structure, gain profile, and output characteristics of dedicated software for semiconductor lasers. The initial ridge width of the semiconductor laser is 5 μm, with a stripe width of 500 μm. The initial cavity length is assumed to be 1 mm and background loss to be 500 m⁻¹. The initial wavelength is 0.77 µm. Mirror reflectivity value is of approximately 0.32.

The growth material of the NIR laser typically consists of either GaAsP or AlGaAs system, the latter often contains Al component that is susceptible to oxidation, making the cavity surface susceptible to non-radiative recombination and burning. Nonetheless, AlGaAs exhibits higher electrical and thermal conductivity compared to GaAsP. Therefore, our research focuses on a GaAsP/AlGaAs system, where GaAsP serves as the well layer and AlGaAs forms the remaining layers for the 785 nm epitaxial layer of the laser. It is widely recognized that increasing the number of wells can boost optical output power. However, an excessive number of wells can lead to different numbers of confined carriers among the wells, resulting in disparate gain. Furthermore, surpassing the critical limit for a number of quantum wells can cause stress release and generate numerous defects, significantly reducing the device's lifetime. Therefore, a single quantum well laser is adopted in this paper.

The lattice constant of GaAsP is smaller than that of GaAs substrate, leading to tensile stress in the active region, resulting in the dominance of the TM mode^[14]. Taking into account the operation of the device due to thermal effects and the requirement to achieve a specific wavelength, the design of the epitaxial wafer should aim for a peak wavelength of a photoluminescence (PL) spectrum with luminescence is around 770 nm, with a single quantum well being accepted in the study. The reference and new epitaxial structure are shown in Fig. 1(a) and 1(b) (color online). The structural diagram of the DBR laser is shown in Fig. 1(c) (color online). The ridge waveguide width is denoted as W, the grating period is Λ, the grating height is H_g, and the green arrow indicates the propagation path of the DBR mode within the cavity. The resonant cavity of the laser is composed of the DBR reflector and the front cavity surface, which selectively feedbacks specific modes. Fig. 1(d) (color online) shows the gain spectrum of the active material. The internal mode profile is mostly primarily transmitted along the waveguide layer, making the design of the waveguide layer essential. Enhancing the mode profile within the device can be achieved by employing various waveguide structures, such as symmetric waveguide, asymmetric waveguide, and extremely asymmetric structure (ETAS), which involve designing different epitaxial layers and optimizing composition^[15-16]. Notably, the Al component has a linear relationship with the refractive index of Al_xGa_1-xAs. Therefore, when designing the epitaxial wafer, it is crucial to ensure a gradual decrease in the refractive index from the active region towards both sides to limit the mode profile.

There is a relationship between the thickness of the waveguide layer D and the cutoff condition of the mode:

$ D=\frac{2\text{π}}{\lambda}t_{\mathrm{w}}\sqrt{n_{\mathrm{w}}^2-n_{\mathrm{cl}}^2}\quad, $ (6)

where $ n_{\mathrm{w}} $, $ n\mathrm{_{cl}} $ are the refractive index of the waveguide layer and the cladding layer, respectively, $ t_{\mathrm{w}} $ is the total thickness of the waveguide layer and D is normalized thickness of the waveguide layer.

As can be seen in Fig. 2, the shaded area indicates the overlap of the active region with the mode field. In the symmetric waveguide case, the active region overlaps with the optical field the most, making its confinement factor higher, and as the p-side waveguide is gradually thinned, the confinement factor of the active region decreases. The maximum output power of the asymmetric waveguide can be improved due to the fact that the optical confinement factor is inversely proportional to the power. The waveguide thickness and the divergence angle have the following relationship equation:

$ w_0=t_{\mathrm{c}}(0.31+2.2/D^{3/2}+30/D^6)\quad, $ (7)

$ \theta _{1/2} = 1.18{\rm{arctan}}(\lambda/{{\text{π}} {w_0}})\quad, $ (8)

where ${w_0}$ is equivalent to a near-field Gaussian beam waist, $ {\theta _{{1}/{2}}} $ is fast-axis divergence angle. The advantage of the asymmetric waveguide lies in the fact that the thinning of the p-waveguide not only biases the mode profile to the n-side, leading to lower internal optical loss but also reduces the series resistance.

The total thickness of the waveguide layer is determined by the cutoff condition, and after the thickness of the p-side waveguide is determined, which in turn determine the refractive index difference $\Delta n$ between the waveguide and the cladding layer. As illustrated by Equation (6), it is known that when the refractive index of the waveguide layer is certain, a smaller difference of refractive index between the cladding and waveguide layers results in a larger critical thickness. When the refractive index of the cladding layer is certain, a smaller refractive index of the waveguide layer corresponds to a larger critical thickness. Smaller waveguide thickness, however, is insufficient to fully confine the mode profile within the waveguide layer, resulting in most optical modes leaking into the cladding layer. To facilitate fiber coupling in the subsequent stage, the vertical divergence angle should be reduced commonly. Therefore, the difference in aluminum component between the cladding layer and the waveguide layer should not be excessive in the selection of epitaxial materials.

Specially, we discuss the relationship between light confinement factor on the p-side and refractive index difference as well as the interrelation among different refractive index, different waveguide widths, and the divergence angle (FWHM). Fig. 3 (color online) shows the mode field distribution under asymmetric waveguide obtained by FDE. It can be clearly seen that most of the mode field is biased towards the n side of the device. And as the refractive index difference ($ \Delta n $) between the waveguide layer and the cladding layer gradually increases, the optical field is more compressed in the waveguide layer, the optical confinement factor on the p side gradually weakens, the near-field becomes more concentrated, and the far-field divergence angle increases. If the difference is too small, it cannot form an optical waveguide to restrict the optical field. In order to reduce the etching depth of the grating, we need to keep the $ \Delta n $ on the p side within a certain range. Meanwhile, it should be noted that if the thickness of the cladding layer is too thick, it will seriously affect the resistance of the device, and if it is too thin, it will lead to leakage of optical modes. Finally, the thickness of the cladding layer is chosen to be 400 nm, and a suitable $ \mathit{\bigtriangleup n} $ of 0.175 is determined.

The total thickness of the waveguide layer is chosen to be within the range of the second-order mode cutoff rather than the first-order mode based on the fact that a reasonable widening of the waveguide layer thickness effectively mitigates the overlap of the mode profile with the cladding layer and prevents excessive losses. Despite the fact that the thicker the waveguide layer, the easier it is to produce higher-order modes, the confinement factor of the fundamental mode is much greater than that of the other modes, thereby it should be placed in a favorable position in the mode competition. Beyond that, increasing the total thickness of the waveguide layer within a specific range can reduce the fast-axis divergence angle. The total waveguide thickness of 1000 nm within the second-order mode cutoff width is preferential.

Subsequently, it is crucial to settle on the thickness of the p-side waveguide D. As illustrated in Fig. 4(a) (color online), on the premise that the total waveguide thickness remains unchanged, an increase in the thickness of p-side waveguide leads to an elevation in the output power and divergence angle^[17]. Figure 4(b) (color online) displays the current density at the interface (m-m cross section) between the upper barrier layer and the waveguide layer provided that the width of the ridge remains constant. On the one hand, the thinner p-side waveguide the results in lower divergence angle, less internal loss, and reduced series resistance, leading to produce slight Joule heat. On the other hand, the confinement effect of the ridge waveguide restrains the lateral diffusion of carriers (x-direction), thus enriching the current in the ridge waveguide region. A thinner p-waveguide corresponds to a smaller effective gain area (described in WXR) for the same cavity length, resulting in a lower output power. Ultimately, a p-waveguide thickness of 100 nm is recommended to achieve a lower divergence angle.

To effectively enhance the output performance of the device, the gradient waveguide is employed to effectively reduce the voltage drop at the heterojunction interface, preventing the voltage loss generated by the abrupt heterojunction. Additionally, it inhibits the diffusion of some Al components into the active region.

Regrettably, there are still a few electrons escaping from the quantum well to the p-waveguide layer during the operation of the device, diminishing the efficiency of carrier recombination in the active region and generating parasitic recombination with the holes of the waveguide on the p-side. This results in a nonlinear output power, further restricting the application of the device^[18]. Consequently, it is necessary to incorporate an inner waveguide as an electron barrier layer (EBL) between the last barrier and the waveguide, while maintaining the thickness of the p-side waveguide layer constant to mitigate the aforementioned damage. Simultaneously, as an EBL, it forms a stepped potential barrier in conjunction with the barrier layer. The following comparison examines the output power of lasers with internal waveguide structures with varying aluminum components.

As illustrated in Fig. 5 (color online), the additional EBL fails to achieve the purpose of increasing power. Instead, the slope efficiency as well as output power decline as the aluminum component is incrementally (Al:0.35-0.65) increased under a 300 mA working current. According to the formula:

$ \frac{1}{SE}=\frac{q\lambda}{hc\eta_{\mathrm{inj}}}\left(1+\alpha_{\mathrm{i}}\frac{1}{\alpha_{\mathrm{m}}}\right)\quad, $ (9)

where $SE$ is the slope efficiency, $q$ is the electron charge, $\lambda $ is the excitation wavelength, $h$ is the Planck constant, $c$ is the speed of light, and $ \eta_{\mathrm{inj}} $ is the injection efficiency. Based on the above equation, it can be seen that the slope efficiency is primarily associated to ${\eta _{\rm{inj}}}$, ${\alpha _{\rm{i}}}$, ${\alpha _{\rm{m}}}$, because the reflectivity of the front and rear cavity surfaces of LD are the same, so the mirror losses ${\alpha _{\rm{m}}}$ are equal. Changes in slope efficiency are related to the internal absorption loss (${\alpha _{\rm{i}}}$), and current injection efficiency (${\eta _{\rm{inj}}}$). When the aluminum composition is around 0.45, the output power of the device is relatively sizable, and the effect of EBL is more obvious. In order to better analyze the reasons for the decrease in output power, we calculate the optical field distribution and band structure when the aluminum composition is between 0.41−0.44, and the epitaxial structure without EBL is used as a reference group. The mode field of the composite waveguide will be biased towards the p side, compared to the structure without waveguide. This is due to the lower refractive index of the added p-side internal waveguide, which makes the overall equivalent refractive index of the p-side waveguide lower while the refractive index difference with the cladding also decreases. Therefore, the optical field will be slightly shifted towards the p-side. However, the gradual increase of the aluminum component, the refractive index of the internal waveguide decreases, leading to an increase in the overall equivalent refractive index on the p side. This, in turn, increases the difference in refractive index between the waveguide and the cladding layer. As the refractive index difference increases, the mode profile shifts towards the n side shown in Fig. 6(a) (color online), and the shift of the mode profile changes the active region confinement factor as well as the internal loss. However, Modification of the light field should lead to an increase in the slope efficiency of the device, thus the decrease in the device efficiency is due to the reduced injection efficiency of electrons.

Electron injection efficiency is inversely correlated with electron leakage, which is influenced by the magnitude of the leakage current and the bandgap of the p-side waveguide. A higher barrier makes it more challenging for electrons to enter the p-waveguide. However, paradoxically, the power decreases as the waveguide barrier increases. The energy band diagram presented in Fig. 6(b) (color online) may provide a reasonable explanation for the above phenomenon.

From Fig. 6(b), it can be seen that an increase in the Al component of the p-side inner waveguide results in a decrease in the refractive index and an increase in the effective bandgap for electronic transitions within the p-side waveguide. With further increase in the bandgap, additional "pseudo wells" are created, resulting in the recombination of carriers overflowing from the wells into the pseudo wells, as demonstrated in the enlarged image. The waste of carriers contributes to a reduction in luminescence efficiency, explaining why the output power does not increase but decreases instead^[19]. In summary, the energy of the injected electrons may be excessive, combined with internal losses and the presence of pseudowells, which hinder the effective utilization of the electrons. Consequently, this leads to a decline in luminescence efficiency.

To fundamentally enhance the recombination efficiency in the active region, it is necessary to confine the carriers supplied by the n-side cladding layer to the well as much as possible. Previous reports have focused on the structural design of the well or the barrier layer^[20], which requires a robust confinement capacity of the well or wider bandgap of the barrier, thereby making it challenging for the carriers to migrate outward. Another alternative option is to reduce the energy of the injected carriers, as reported in [21]. In this section, we will separately discuss the effects of a stepped waveguide, a high refractive index constant waveguide, and low refractive index constant waveguide as the energy release layer (ERL) on the output performance, energy band structure, and electron carrier concentration distribution of the devices^[22-23]. The electron composite efficiency is defined as the ratio of the difference of electrons flowing into and out of a quantum well to the electrons flowing out at the final barrier layer. The total thickness of the n-side waveguide is 900 nm for the subsequent discussions.

As seen in Fig. 7 (color online): (Ⅰ): n-side inner waveguide with Al compositions of 0.35 and thickness of 0.4 μm; (Ⅱ): n-side inner waveguide with an Al compositions of 0.3 and thickness of 0.4 μm; (Ⅲ): stepped waveguide with Al compositions of 0.35,0.37,0.4-0.45 and a thickness of 0.3 μm are discussed respectively. As shown in Fig. 7 (color online), the ERL structure with an aluminum composition of 0.35 exhibits a slope efficiency (SE) of 1.041 W/A, which is 3.39% lower than that of the ERL structure with an aluminum composition of 0.3 (1.0764 W/A), and 1.13% lower than that of the stepped ERL structure (1.0529 W/A). The device with a higher Al composition demonstrates lower maximum power and lower threshold current. This phenomenon can be attributed to the decreased energy of the waveguide layer; the electrons supplied by the cladding layer release some energy in the waveguide layer, enabling most electrons to recombine in the well. This process is accompanied by the EBL on the p side, resulting in a greater number of carriers recombining to generate photons, thereby enhancing efficiency. The bandgap of the high refractive index waveguide is narrower compared to the barrier layer, and the electrons must also traverse the barrier layer to participate in the recombination, which reduces the overall recombination efficiency. However, at higher current, more electrons recombine in the well, leading to increased output power. The step waveguide takes last place.

Previously, it was speculated that the high energy of the injected electrons causes many of them to reside in the pseudo well, resulting in a reduced efficiency. This part is believed to play a role of electron absorption rather than electron blocking. To verify the hypothesis, a comparison of the output power and electron concentration distributions is conducted.

It can be seen from Fig. 8 (color online) that the chip incorporating EBL and ERL structures achieved an output power of 296.043 mW and SE of 1.7066 W/A at an injection current of 300 mA. In comparison to a chip without these auxiliary layers, the output power and SE are enhanced by 2.32% and 2.34%, respectively. To further widen this performance gap, a strategy of moderately increasing the cavity length could be implemented. There is a difference in power with and without the EBL, while the EBL-only structure exhibits a lower threshold current, the output power is also low at high current. The inset figure displaying only the EBL reveals that the mode profile is biased towards the p-side, leading to higher losses and a seemingly higher threshold current, but the actual outcome is that the high-energy injected carriers flow back into the quantum well at low currents due to the EBL, but the output optical power at high injection current is generally lower than that with an ERL, due to the excess electrons do not participating in the recombining in the well. In contrast, the epitaxial layers with EBL and ERL structures exhibit a higher threshold current because of the lower light confinement factor in the active region. The Fig. 8(b) illustrates that under high current conditions, the presence of an ERL on the n-side allows for the recombination in the well. In the absence of an ERL, the concentration of injected electrons is lower, while the number of leaked electrons remains relatively constant. Consequently, the structure with an ERL demonstrates higher recombination efficiency and improved performance. Although the EBL presents some obstacles, it does not completely obstruct the recombination of electrons on the p-side, which becomes more pronounced under high current situations.

In an effort to achieve increased output power, simulations are conducted on ERL with varying components and thicknesses. As shown in Fig. 9 (color online), a higher light confinement factor in the active region correlates with increased output power when the Al composition is set at 0.3. Additionally, when the thickness of the ERL is 0.1 μm, the output power reaches a high level that is not shown in this paper. Therefore, the component and thickness are 0.3 and 0.1 μm, respectively.

The mode extension layer (MEL) is situated on the p-side, although it can cause a certain degree of optical loss. Nonetheless, the primary objective of this article is to reduce the etching depth of the grating. On the one hand, the MEL needs to maintain a certain optical confinement factor on the p-side, allowing for shallow grating etching. On the other hand, it should not introduce excessive internal loss, which could exacerbate performance degradation. Furthermore，the refractive index of the MEL needs to be higher than that of the cladding layer.

When the thickness of the MEL is set at 0.1 μm and the distance from the waveguide layer is 0.2 μm. The following simulations are conducted separatly. The effects of the size of different aluminum components of the MEL on mode distribution, the fundamental mode confinement factor on the p-side, and the divergence angle in fast axis are shown in Fig. 10 (color online). In addition, the grey area represents the location of the active area. It can be seen from Fig. 10, the increase in the refractive index of the MEL (in the direction of component reduction), and the confinement factors on the p-side, while significant rise of the internal loss. The grey area denotes the location of the active area. When the aluminum component of the MEL is approximately 0.35, among divergence angle, the internal loss and the p-side confinement factor remain at moderate levels. Therefore, the optimal choice for the Al component of the MEL is 0.35. Furthermore, the effect of the distance between the MEL and the waveguide layer, as well as the thickness of the MEL, on these characteristics are discussed again. Ultimately, the thickness of the MEL and distance between the MEL and the waveguide layer are determined to be 0.1 μm.

The doping concentration of the cladding layer also has a significant impact on the output performance of the laser.

$ {\rho _i} =1/{\sigma _i} = 1/{{n_i}q{\mu _i}} \quad,$ (10)

where ${n_i}$, ${\mu _i}$ is the concentration and the mobility of the electrons (holes), $q$ is electron charge. From the formula (10), it can be seen that the higher the doping concentration, the lower the series resistance. To ensure sufficient output performance of the device, considering the influence of material properties, we chose a cladding layer with high doping concentration. The parameters of the optimized asymmetric waveguide structure are summarized in Tab. 1.

As shown in Fig. 11 (color online), the gray area marks the position of the quantum well. And the fundamental mode exhibits a greater overlap with the active region, whereas the higher-order modes demonstrate a lesser overlap. As a result, there are significant differences in the confinement factors among the three modes, which enhances the gain difference and maintains the device in single transverse mode (fundamental mode) excitation, while suppressing the remaining modes in competition^[24]. It is worth noting that the refractive index of the waveguide layer is higher than that of the active region, but its bandgap is remain larger than that of the quancum well. This is due to the fact that the two belong to the different material systems, thus preventing any alteration in the lasing (photoluminescence) wavelength.

It has been analyzed that the output power of a traditional laser could reach 303.442 mW with an injected current at 300 mA due to its larger gain area. In contrast, the output power of optimized laser can be elevated to the same level as that of the symmetrical and wide waveguide, which is 306.03 mW. However, compared with the asymmetric waveguide without an EBL and an ERL, the output power of new structure has been increased by approximately 20 mW, thanks to its higher internal recombination efficiency. Therefore, the new structure exhibits lower internal losses and higher output power by rational optimization of the epitaxial structure.

According to the coupling mode theory equations (11)、(12)、(13), the coupling coefficient is proportional on the reflectivity R. The length $L$ of the grating has a great impact on the reflectivity, with the larger $L$ is, the larger $R$ is^[25-26].

$ \Lambda=\frac{m\lambda_0}{2n_{\mathrm{eff}}}\quad, $ (11)

$ \kappa = \frac{2(n_{\mathrm{m}}^2 - n_{\mathrm{s}}^2)n_{\text{eff}} \sin(m\text{π}\gamma)}{m((1-\gamma)n_{\mathrm{m}}^2 + \gamma n_{\mathrm{s}}^2)\lambda} \Gamma \quad, $ (12)

$ R = {\tanh ^2}(\kappa L)\quad, $ (13)

where $\Lambda $ is the period of the grating, $m$ is the number of the order, $ n_{\mathrm{eff}} $ is the effective refractive index, $\kappa $ is the coupling coefficient. $\Gamma $ is confinement factor, $R$ is reflectivity, $\Delta n$ is the refractive index difference between the etched zone and the unetched zone. From the above equation, it's evident that increasing the p-side confinement factor can lead to a higher coupling coefficient. Since the refractive index of the MEL is higher than that of the cladding layer, the refractive index difference increases with greater etch depth through the extension layer. Additionally, the relationship between reflectivity intensity and the etching depth should be considered.

The grating structure is simulated using the Eigenmode Expansion (EME) method, and its refractive index and reflectance distributions are shown in Fig. 12 (color online). The grating is designed to be etched on the P side of the epitaxial layer. The relationship between different etching depths and reflectance with mode extension layers are compared for the same number of grating pairs, period, and duty cycle. It can be seen that the reflection peaks of the device are gradually blue-shifted and increased as the etch depth increases. In addition, as the etched grating extends to the mode expansion layer (with etching depth exceeding 0.2 μm), its reflectance is significantly enhanced. Given that the Full Width at Half Maximum (FWHM) of the reflection spectrum being less than 0.2 nm, the spectral line-width of the laser will be even narrower. The inset shows the reflection spectrum at an etching depth of 0.3 μm. To further narrow the line-width, increasing the order or the number of gratings can be effective strategies. When the depth of the grating in the symmetric waveguide structure is 0.4 μm, the optimized structure requires less than 0.3 μm depth to achieve the same reflectivity. In other words, the optimized device can be etched with shallower grating depths and still maintaining resonance. The improved p-side epitaxial structure and grating etching depth are much smaller than the previously reported cladding layer thickness (1 μm) and grating etching depth^{[1-2, 24]}.

In conclusion, the critical factor that affects the efficiency of the device is the electron injection efficiency. It is found that the design of the electron blocking layer on the p-side does not effectively improve the output power of the laser. The reason is that the introduction of the electron-blocking layer brings a pseudo-well where the high-energy injected electrons recombine. Consequently, the energy of the electrons needs to be released in advance on the n-side, and it is observed that the injection efficiency can be improved through the combined effect of the constant waveguide and the electron blocking layer. Furthermore. The thinner epitaxial cladding and the mode expansion layer structure enormously reduce the grating etching depth. The laser with a mode extension layer exhibits greater reflectivity under shallow etching conditions. The internal loss of the optimized structure is considerably reduced, leading to improved output performance compared to symmetric waveguide structure.