Introduction

Due to minimal optical-fiber dispersion and loss, semiconductor diode lasers operating at 1.3 μm and 1.55 μm with low divergence are of great importance to optical interconnections and optical fiber communications. However conventional edge-emitting quantum well lasers have small active area and tight optical confinement which have caused a large beam divergence in the direction perpendicular to the junction plane. The far field is typically about 10° ~ 30° in the horizontal direction and 40° ~ 60° in the vertical direction for InP-based lasers. And this strongly elliptical beam reduces the coupling efficiency and coupling tolerance between lasers and coupling optics.

Many works have been done to reduce vertical beam divergence. GaAs-based lasers emitting at a wavelength between 800 ~ 1060 nm with small beam divergence have been achieved by many ways, such as using large optical cavity (LOC) or super-large optical cavity (SLOC) ^[1,2], engineering the cladding layers with passive waveguides inserted^[3,4] or low refractive index layers inserted^[5,6]，adopting low index quantum barriers^[7,8]. Most of them make a tradeoff between optical confinement and mode size, and suffer from high threshold current, big side lobes or multimode output risks. While approaches with surface plasmonic nanostructures^[9] or longitudinal photonic band crystal (PBC) designs^{[10,11,12,13]} require thick and complex epitaxial structures, approaches monolithically integrated with spot size converters^[14] require precision etch and regrowth process.

Nevertheless, there are few researches about laser emitting at 1.55 μm with small beam divergence^[15,16]. The confinement factor in InP-based lasers is higher than that in GaAs-based lasers, which makes it harder to decrease vertical beam divergence.

Compared to InGaAsP/InP material ( ∆Ec=0.4∆Eg ), AlGaInAs/InP material ( ∆Ec=0.72∆Eg ) has a lager conduction band offset and reduces carrier leakage from the quantum-well region^[17]. As the AlGaInAs quaternary material has higher refractive index than an InGaAsP quaternary material of the same bandgap^[18], which also makes it difficult to decrease vertical beam divergence, the AlGaInAs waveguide provides not only excellent carrier confinement but also good optical confinement,

In this paper, we propose a simple effective way to reduce beam divergence by using a asymmetric mode expansion layer (MEL) without obvious performance deterioration and we present a comprehensive discussion on the design and optimization of AlGaInAs /InP λ~1.55 μm lasers with small beam divergence, which shows a great agreement with experiment results. Through asymmetric mode expansion layer, more parameters can be utilized. The optical field is pulled away from p-cladding and extends into lower layers which reduces the internal loss^[19] and decreases beam divergence without large side lobes or obvious confinement deterioration. In addition, it doesn’t need an overgrowth process and can be fabricated as conveniently as conventional ridge lasers.

1 Epitaxial structure design and simulation

Figure 1(a) illustrates a typical refractive index profile and near-filed distribution of 1.55 μm laser with graded-index separated confinement heterostructure (GRINSCH). After detailed simulation, the strain-compensated multiple quantum wells (SC-MQW) structure has been used. The epitaxial structure contains an active region with three compressively strained (+1.2%), 6 nm thick, Al_0.08Ga_0.22In_0.7As quantum wells (QW) and four tensile strained (-0.5%), 9 nm thick barriers, which is sandwiched by two 0.1 μm-thick GRINSCH layers. The Al composition of GRINSCH layers changes from 0.178 near active region to 0.474 near AlInAs carrier blocking layers. The carrier blocking layers utilize asymmetric structure with 140 nm thick in n-side and 50 nm thick in p-side to expand optical field into n-cladding, which reduces the internal loss since p-cladding absorption is the main contributor to it^[20].

Fig. 1 Refractive index profiles (left axes) and near-filed intensity distribution（right axes）of conventional (a) and special asymmetric MEL (b) lasers

图 1 传统结构（a）和特殊非对称MEL结构（b）激光器折射率（左轴）和近场光场（右轴）分布示意图

We get the band parameters and refractive indices of the materials referring to Ref. [21,22,23,24]. The near optical field is calculated by solving one dimensional Helmholtz equation with MATLAB software. And the far field pattern can be obtained by taking the Fourier transformation of the near optical field. The field intensity versus angle θ is written as^[25]:

where Ey(x,0) is the electric field distribution at the laser facet. The terms r , θ are the distance from the output facet and the angle relative to the waveguide axis, respectively. The term λ0 is the emission wavelength in free space. For the fundamental mode, the beam divergence is defined as the full width at half maximum (FWHM) of the far field pattern. The far field distribution corresponding to widen near optical field exhibits smaller beam divergence.

The threshold current density Jth for conventional quantum-well lasers can be well approximated as the exponential expression^[26]:

where J0 is the transparent current density, ηi is the internal quantum efficiency, αt is the total loss including the internal material loss and mirror loss, Γ is the optical confinement factor, and β0 is the gain coefficient.

From the expression (1) and (2), we can see a tight trade-off between the optical confinement factor (threshold current density) and the beam divergence. The calculated optical confinement factor of the typical laser is 2.93% with 45.72° vertical beam divergence. And this tightness can be solved by the insertion of a mode expansion layer in the n-cladding layer, which provides an additional degree of freedom in the device design. The MEL is a passive waveguide that has a refractive index lower than that of the core waveguide but higher than that of the claddings, and it can expand the optical field slightly into lower cladding and suppress higher mode lasing. For the fundamental mode, the optical confinement Γ' of laser with MEL can be written as^[27]:

where

where neff1 and neff2 are the effective refractive indices for the passive waveguide and uncoupled core waveguide, respectively. κ is the coupling coefficient between core waveguide and the passive waveguide. Since all the parameters except Γ and αt of expression (2) are independent （ J0 and β0 dependent only on the active region） of whether the MEL is inserted, and the existence of passive waveguide causes only a very small amount of increase in material loss which can be ignored, the threshold current density for lasers with mode expansion layer can be written as^[27]:

Clearly, the threshold current density for the mode expansion structure is always larger than that for the conventional structure, because the exponent is always positive. But the threshold current density Jth' can remain insensitive to MEL by designing suitable c to make the argument of the exponential function small^[27]. Since neff2 is greater than neff1 to guarantee a fundamental mode emission, the value of κ and neff1 should be small to obtain a suitable c and further to get a small argument of the exponential function. The parameters used for optimization are: the separation distance (D) between the GRINSCH and MEL，the thickness (T) of the MEL, and the composition (Q) of the MEL, as showed in Fig. 1(b). To avoid a large index of MEL and big band offset in n-cladding, we choose 1.06Q (InP lattice-matched InGaAsP with a bandgap wavelength of 1.06 μm) and 1.1Q to be the composition of the MEL.

Figure 2 shows the calculated optical confinement factor Γ' and vertical FWHM θ as functions of the separation distance D (a) and the thickness T of the MEL (b) when the composition is 1.06 Q. As showed in Fig. 2(a), when T is fixed at 200 nm, with the increase of D, the vertical beam divergence decrease from 39.15° to 35.1° and then increase to 40.45° while the confinement factor has a little increase, but is still lower than that of conventional laser without MEL. This is due to the inserted MEL which expands the near filed distribution and a larger D will decrease the vertical beam divergence but a too large D will weak the influence of EBL to active region and can’t expand near optical filed efficiently. As D increasing, the coupling coefficient κ between core waveguide and MEL decreases, leading to larger c and Γ' . When D is fixed at 1000 nm showed in Fig. 2(b), the increasing T causes lower Γ' and smaller vertical beam divergence. As T increases, the refractive index of EBL increases, and more light has been expanded into lower cladding result in lower Γ' and smaller vertical divergence. But from Fig. 3 we can see the effect of EBL to active region is still small even when the T is increased to 500 nm. This is because the refractive index of 1.06 Q EBL (n _{1.06 Q} = 3.25) is too small compared to that of the active region (n _ac = 3.5) and the EBL can only confine a small amount of optical field. And then we fixed the composition to be 1.1Q (n _{1.1 Q} = 3.28), D to be 750 nm and 1000 nm.

Fig. 2 Calculated optical confinement factor Γ' and vertical FWHM θ versus the separation distance D (a) and the thickness T of the MEL (b) when the composition is 1.06Q. T is fixed at 200 nm in (a) and D is fixed at 1000 nm in (b)

图 2 在组份为1.06 Q时，模拟的限制因子Γ'和垂直远场发散角θ随分隔距离D（a）和MEL的厚度T（b）之间的关系。（a）中T为200 nm，（b）中D为1000 nm

Fig. 3 Near field intensity distributions under different T with D = 1000 nm and 1.06 Q

图 3 组份为1.06 Q和D = 1000 nm时，在不同T值下近场光场的分布

Figure 4 shows the calculated optical confinement factor Γ' and vertical FWHM θ versus the thickness T of the MEL when the composition is 1.1Q under different D. Figure 5 shows some of the near field intensity distributions. It has a much better effect of MEL to active region and shows the similar tendency when the composition of MEL is 1.1 Q compared to 1.06 Q. And the structure with 1000 nm MEL has a smaller vertical beam divergence and a larger optical confinement factor under the same thickness of MEL in comparison with the structure with 750 nm MEL. Side lobes may appear when the thickness of MEL is large to 500 nm, as showed in Fig. 5 (b) and (d). And side lobes can lower the coupling efficiency and coupling tolerance between lasers and coupling optics which should be avoid. Moreover，when T is 500 nm, no matter the D is 750 nm or 1000 nm, the optical confinement factors suffer a significant decrease and it will lead to a large threshold current density.

Fig. 4 Calculated optical confinement factor Γ' and vertical FWHM θ versus the thickness T of the MEL when the composition is 1.1Q. Solid line is D = 1000 nm and dashed line is D = 750 nm

图 4 当组份为1.1Q时，模拟的限制因子Γ'和垂直远场发散角θ随MEL的厚度T之间的关系。实线为D = 1000 nm，虚线为D = 750 nm

Fig. 5 Near field intensity distributions under different D and T with 1.1Q MEL

图 5 当MEL组份为1.1Q时，在不同D值和T值下近场光场的分布

Finally, we choose the value of the separation distance (D) between the GRINSCH and MEL as 1000 nm，the thickness (T) of the MEL as 400 nm, and the composition (Q) of the MEL as 1.1Q. The calculated optical confinement factor of this special laser with EBL is 2.45% with 27.99° vertical beam divergence. The optical confinement factor only decrease by 0.45% (16.3%) while the vertical beam divergence reduces by 17.73° (38.8%) compared with that of the typical structure. We investigated the light–current–voltage (L-I-V) characteristics of both typical and special structures by using commercial available LASTIP (LASer Technology Integrated Program) simulation software, as showed in Fig. 6. The threshold current of the special structure with MEL is slightly higher than that of typical structure because of a smaller optical confinement factor. But the slope efficiencies as well as the series resistance of both structures are almost equal, indicating that the inserted MEL barely has negative effect on laser performance.

Fig. 6 The simulated L-I-V characteristics of typical structure (dashed-line) and special structure with MEL (solid-line)

图 6 模拟的传统结构（虚线）和特殊MEL结构（实线）激光器的L-I-V特性

The variation of threshold current with temperature can be written as:

where Ith(T) and Ith(Tr) are threshold currents at temperature T and room temperature Tr , respectively. T0 is the characteristic temperature. The characteristic temperature can be calculated by linear fitting between temperature and threshold current, as showed in Fig. 7. The characteristic temperature of typical structure and special structure with MEL are 105.8 K and 102.1 K respectively between 296 K and 326 K, which are both much higher than that (65 K) of InGaAsP/InP material. It indicates that the inserted MEL will not affect the temperature characteristic of laser negatively.

Fig. 7 The simulated relationship between threshold current and temperature of typical structure (black line) and special structure with MEL (red line)

图 7 模拟的传统结构（黑线）和特殊MEL结构（红线）激光器的阈值电流和温度之间的关系

2 Device fabrication and test results

Figure 8 shows the measured and simulated L-I-V characteristics of special designed laser with MEL at room temperature. The measured threshold current is 56 mA, a little higher than the value of simulation because of processing step. Over-etching might lead to higher internal loss as well as the threshold current because of the increase of non-radiative recombination near the active region. Annealing for ohmic metallization with a comparatively high temperature made ohmic contact imperfect and caused a higher series resistance (15 Ω) than usual (4 Ω). The simulated value of series resistance (2.25 Ω) is close to normal condition. However, the output power achieves 17.38 mW@120 mA and the slope efficiency is 0.272 W/A, similar to the value 0.278 W/A of simulation and much higher than that reported in Ref. [15]. The divergence angles for the horizontal and vertical direction are 15.5° and 29.6°, respectively. And the vertical divergence shows highly consistent with the simulation value 27.99°, also as the far field intensity distribution. It has decreased about 35.3% compared to that of typical laser as showed in Fig. 9, which indicates that the inserted MEL can expand near field distribution and lower vertical beam divergence effectively.

Fig. 8 Measured and simulated (inset) L-I-V characteristics of special designed laser with MEL at 296 K

图 8 在296 K温度下，特殊MEL结构激光器的L-I-V特性测试和模拟（小图）

Fig. 9 Far field intensity distributions of typical laser (blue-line, θ_⊥ = 45.72 °)，simulated special laser (red-line, θ _⊥ = 27.99 °) and tested special laser (black-solid-line, θ_⊥ = 29.6 °, black-dashed-line, θ _∥ = 15.5 °) with MEL at 160 mA

图 1 在160 mA注入电流下，传统结构激光器（蓝线，θ⊥ = 45.72°），模拟的特殊MEL结构激光器（红线，θ⊥ = 27.99 °）和测试的特殊MEL结构激光器（黑实线，θ⊥ = 29.6 °，黑虚线，θ∥ = 15.5 °）的远场强度分布

Figure 10 shows the stability of the far field beam divergence at different injection currents. The laser works under fundamental mode at all level injection currents. The vertical FWHM barely varies with the injection current while the horizontal FWHM increases slightly with the increase of the injection current, which result from the ridge waveguide index changes caused by thermal and carrier injection effects. The aspect ratio ranges from 2.06 to 1.84 vary with the change of injection current and consistently demonstrates better performance as the typical aspect ratio of conventional lasers is about 3.

Fig. 10 Measured far field beam divergence under different injection currents

图 10 测试的远场垂直发散角随注入电流的变化

3 Conclusions

In summary, a special designed 1.55 μm laser based on AlGaInAs/InP material with small beam divergence has been reported by simulation and experiment. An asymmetrical mode expand layer (MEL) has been inserted in lower cladding to expand near field intensity distribution and decrease vertical beam divergence. As showed by simulation, the inserted MEL barely have negative influence on laser performance, and the whole structure doesn’t need a regrowth process. For 4 μm-wide and 1000 μm-long ridge waveguide lasers, the threshold current is 56 mA, and the output power is 17.38 mw@120 mA. The slope efficiency of 0.272 W/A has been achieved. The horizontal and vertical beam divergence of the laser is 15.5° and 29.6°, respectively, which shows a high agreement with the simulation results. The vertical beam divergence has decreased about 35.3% compared to that of typical lasers. And the far field intensity distribution also shows a high stability for injection current.

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References