1. Introduction

The 980-nm high-power lasers are often designed to have a larger near field width to prevent thermal problems and they have elliptical mode fields at their laser endfaces. The aspect ratios of the elliptical fields of 980-nm lasers typically range from three to five [1]. To improve the mode match between the high-power laser and single-mode fiber (SMF), one common approach is that the laser couples directly to the SMF, where the tip of the SMF is an asymmetric microlens. Several structures of asymmetric fiber microlenses for coupling the higher aspect ratio of 980-nm lasers to SMFs have been employed, such as an up-tapered wedge-shaped fiber endface [2], an asymmetric hyperbolic fiber microlens [3, 4], an anamorphic lens [5], a wedge-shaped fiber endface [6–8], a quadrangular-pyramid-shaped fiber endface (QPSFE) [9, 10], and a conical-wedge-shaped fiber endface (CWSFE) [11, 12]. However, the fabrication methods of these asymmetric fiber microlenses required multi-step grinding processes [2, 5–12] or complicated laser micromachining [3, 4], resulting in a complicated process and a low-yield fabrication.

Recently, the QPSFE [9, 10] and CWSFE [11, 12] for coupling between high-power 980-nm lasers and the SMFs have demonstrated up to 83–84% coupling efficiency. The QPSFE and CWSFE structures could be controlled over two axial curvatures through grinding and polishing processes to form good asymmetric fiber microlenses. However, the fabrications of the QPSFE and CWSFE required four-step and three-step grinding processes, respectively.The more grinding and polishing processes were performed, the more difficult it was for the QPSFE and CWSFE to control a small fiber offset to form a reproducible elliptical microlens endface, thus resulting in a low-yield fabrication process. The offset of fiber microlens is specified by the eccentricity between the center of the fiber and the microlens. The offset of fiber microlens may give rise to additional coupling loss in laser modules. For the design and optimization of the pump laser modules used in lightwave communication systems, essential knowledge of the microlens imperfections and the resulting coupling loss is important.

In this study, a new scheme of an asymmetric elliptic-cone-shaped microlens (AECSM) using a single-step grinding technique for efficient coupling 980-nm laser diodes to SMFs is proposed. In the single-step grinding technique, a periodically variable torque is applied on the fiber holder of the grinder to change the pressure between the fiber tip and the grinding film. The material removal rate of the fiber tip is changed periodically to form different aspect ratios of asymmetric elliptic-cone-shaped fiber endface to match the far field of the high-power lasers. Due to the continuous single-step grinding process in the fabrication, the grinding offset of the AECSM is very small, resulting in a high-yield fabrication. In comparison with the previous works on asymmetric fiber microlenses fabricated by the multistep processes [2–12] with complicated fabrication, the advantages of the AECSM structure for achieving high coupling are a single-step fabrication, a reproducible process, and a highyield output. The results of this study have led to the development of a simple and reproducible fabrication process for achieving a high-yield and high-coupling AECSM structure that is suitable for use in commercial high-power pump laser modules.

2. Theory

A theoretical approach for calculating the coupling efficiency between the 980-nm laser diodes and the SMFs was similar to the previous work [9–12]. The 980-nm laser-to-fiber coupling model was based on the diffraction theory [5, 13]. From the laser diode to the AECSM, the Fresnel diffraction theory was used for beam propagation through free space. At the lens tip a phase delay caused by the AECSM was added to the laser mode field. An overlap integral between the transformed laser mode field and the fiber mode field was then calculated to obtain the coupling efficiency [14].

For a fixed one of the curvatures, the coupling efficiency between the laser diode and the fiber was calculated. Figures 1 and 2 show the simulated coupling efficiencies as the function of radii curvatures in horizontal R_lx (horizontal) and vertical (R_ly) directions respectively. The calculated coupling efficiency includes the 3.5% reflections from both the lens tip and the far end of the fiber. Table I lists the simulated and measured values for the AECSM with the radii of curvatures of R_lx and R_ly, and the optimum working distance of Z. The parameters of the laser far-field angles θ_ox and θ_oy were 5.3 degrees and 30.2 degrees, respectively. The farfield divergence angle was specified as a full angle at the half maximum of the far-field intensity distribution. Figure 1 shows that the coupling efficiency is insensitive to R_lx as the R_lx > 25 μm. Based on Figs. 1 and 2, in order to achieve a higher coupling efficiency for AECSMs, the optimum values of the horizontal and vertical radii of curvatures were found to be greater than 25 μm and about 3 μm, respectively.

 

Fig. 1. Simulated coupling efficiency as a function of R_lx (horizontal) for the single mode fiber with a mode-field diameter of 4.0 μm.

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Fig. 2. Measured and calculated coupling efficiency as a function of R_ly (vertical).

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Table I. Measured and Simulated Values for AECSM.

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3. Fabrication and measurement

3.1. Fabrication of asymmetric elliptic-cone-shaped fiber endface using single-step grinding technique

According to Preston’s Equation [15], the material removal rate of optical fiber is proportioned to the grinding pressure and the relative velocity between a fiber and a grinding film. The equation of the material removal rate, dT/dt (T: material thickness, t: time), is expressed as,

where the K, N/A (N: normal force, A: contact area), and dS/dt (S: relative motion distance)are the Preston coefficient, the grinding pressure, and the relative velocity between the two materials, respectively. Based on Eq. (1), the material removed from the fiber increases as the applied grinding pressure on the fiber increases while the other parameters are kept constant.Two minimum and two maximum grinding pressures formed the major axis and the minor axis of the cross section of an elliptical cone. Figure 3(a) shows a schematic diagram of an AECSFE.

The fiber used in this study was Prime [16] 980-nm step-index SMF with a mode-field diameter of 4.0 μm and a core–cladding concentricity of 0.5 μm, while the refractive index of the core was 1.459 and the refractive-index difference of the fiber was 0.85%. An angle polishing machine of Ultratec fiber polisher [17] was used in this work. A modified equipment setup of Ultratec fiber polisher is shown in Fig. 4. The elliptic-cone-shaped fiber endface (AECSFE) was fabricated by a single-step grinding and polishing a cleaved fiber by applying a periodically variable torque on the fiber ferrule to change the grinding pressure.The periodically variable torque was made by an eccentric mass with a constant rotation speed double that of the fiber. A scanning electron microscope (SEM) photo of a fabricated AECSFE is shown in Fig. 3(b).

 

Fig. 3. (a). Schematic diagram of an AECSFE, and (b) an SEM of a fabricated AECSFE.

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Fig. 4. An angle polishing machine with periodically variable torque.

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3.2. Design of different aspect ratios of the asymmetric elliptical-cone-shaped fiber endface

Different aspect ratios of the AECSFE can be obtained by applying different amplitudes of variable torques. The aspect ratios of the asymmetric elliptical-cone-shaped fiber endface is given by

In Eq. (2), the P₁, P₂, h, and θ are the maximum grinding pressure, the minimum grinding pressure, the distance from cone apex, and the fiber inclined angle, respectively. The aspect ratio of the elliptical cone as a function of the ratio of grinding pressure is shown in Fig. 5. In this work, the h and θ were designed to be 3-5 μm and 45°, respectively. The AECSFE can be formed any different aspect ratio by changing the ratio of grinding pressures.

 

Fig. 5. The aspect ratio as a function of the ratio of grinding pressure

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3.3. Comparison with different structures of the asymmetric fiber endfaces

Table II lists the schematic diagram, the grinding step, and the grinding offset for different structures of the asymmetric fiber endfaces. The range/average of the fiber offset were about 2.3/1.5, 1.2/0.9, and 0.8/0.4 μm for the QPSFE [9, 10], CWSFE [11, 12], and AECSFE structures, respectively. Table II shows that the fiber grinding offset of the AECSFE structure is very small when compared to the QPSFE and CWSFE structures. The fabrication of the QPSFE and CWSFE structures required four-step and three-step grinding processes, respectively; whereas the fabrication of the AECSFE structure was only a single-step grinding process. The more grinding and polishing processes were performed, the more difficult it was for the QPSFE and CWSFE to control a small fiber offset to form a reproducible elliptical microlens endface, thus resulting in a low-yield fabrication. The offset of fiber microlens is specified by the eccentricity between the center of the fiber and the microlens. The offset of fiber microlens may give rise to additional coupling loss in laser modules.

Table II. Different Structures of Asymmetric Fiber Endface.

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3.4. Fabrication of asymmetric elliptic-cone-shaped microlens

After AECSFE was formed, an asymmetric elliptic-cone-shaped microlens (AECSM) was obtained by heating the fiber tip in a fusing splicer, as shown in Fig. 6. The AECSM had an elliptical endface microlens with two radii of curvatures. Figure 6(a) shows a schematic diagram of the AECSM with the radii of curvatures of R_lx (x-axis, horizontal) and R_ly (y-axis, vertical). An SEM photo of a fabricated AECSM is shown in Fig. 6(b). In this work, the horizontal and vertical curvatures were controlled by the arc current and arc time of the splicing machine, and the distance between the fiber tip and the electrodes.

 

Fig. 6. (a). A schematic diagram of an AECSM with radii of curvatures of R_lx and R_ly, and (b) an SEM of a fabricated AECSM.

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3.5. Measurement techniques

The quality of the elliptical radii of curvatures and the aspect ratios of AECSM can be identified by a fiber far-field profile measurement. A fiber far-field profile setup consisted of a 980-nm laser source, an infrared charge-coupled device, and a computer. The far-field profiling of the lensed fiber can be used as an important technique for characterizing the effects of the aspect ratio and imperfection on the coupling performance of AECSMs.

A 980-nm pump laser diode from Axcel Photonics [18] was used for the coupling evaluation. The laser diode was coated at the rear facet with a high reflectivity (HR) of 95% for reducing the cavity loss, and coated at the front facet with an antireflection (AR) of 2.5% for a higher output. The 980-nm high-power diode lasers had typical far-field divergence angles of 5.3 degrees (horizontal) × 30.2 degrees (vertical) with the relative beam waist radii of 4μm and 0.7μm, respectively.

4. Measurememt results

4.1. Coupling efficiency

For each AECSM, the maximum coupling efficiency between the laser diode and the fiber was measured. Figure 2 also shows the measured coupling efficiency as a function of R_ly (vertical) for the single mode fiber with a mode field diameter of 4.0 μm. A maximum coupling efficiency of 85 % was obtained. The measured and simulated values for the AECSM with the radii of curvatures of R_lx and R_ly, and the optimum working distance of Z were listed on Table I. There were no AR coatings on both the fiber lens tip and the far end of the fiber. An AR coating on the lens tip is usually used for laser module production. When the fiber pigtail of a pump module is fused with an Erbium-doped fiber, the reflection from the far end of the fiber was reduced to near zero. Therefore, an additional 7.4 % more power could be recovered for practical applications.

In this work, the trends of the experimental relationship between the coupling efficiency and the vertical radius of curvature are consistent with the simulation results. The deviation of several data points, as shown in Fig. 2, can be explained by the different offset values of the individual microlens from the fiber core center or from the asymmetrical elliptical far-field pattern.

4.2. Tolerance analysis

The simulated results of the 3-dB coupling tolerances with x, y, and z translational displacements and θ_x, θ_y angular deviations between the AECSM and the laser diode were ± 2.3 μm, ± 0.6 μm, 14.5 μm, ± 31.7 degree, and ± 27.4 degree, respectively. It showed that the optical misalignment of the vertical direction was less tolerable than that of the other directions. This was due to the smaller curvature of R_ly in the vertical direction for the measured values of AECSM. Both experimental and numerical results indicate that the critical fabrication process for the AECSM is to control the smaller elliptical curvature of R_ly in the vertical direction. In this study, the optimum value of the vertical radius of curvature was found to be about 3 μm.

4.3. Fiber far-field profile

The quality of the elliptical curvatures and the aspect ratios of AECSMs can be investigated by a fiber far-field profile measurement. Figure 7 shows the far-field profiles of the AECSM with two values of aspect ratios. If the AECSM is symmetric, the far-field profile is well approximated by a Gaussian profile, as shown in Fig. 7(b). However, if it is asymmetric, the far-field profile deviates significantly from a Gaussian profile, as shown in Fig. 7(a). In addition to the symmetric profile of the AECSM, the aspect ratio of the AECSM needs to be matched to that of the laser for a highly efficient coupling. In this work, a higher coupling efficiency of 85% with an aspect ratio of 5 [Fig. 7(b)] versus for a lower coupling efficiency of 50% with an aspect ratio of 1.3 [Fig. 7(a)] was demonstrated.

Based on the far-field profile measurements of Fig. 7, the higher coupling efficiency of the AECSM lensed fiber is attributed to a better matching of both the Gaussian field distribution and the aspect ratio between the laser source and the fiber. Therefore, the far-field profile of the fiber microlens can be used as an important technique for characterizing the coupling performance between the laser diodes and the fibers.

 

Fig. 7. Far-field profiles of the AECSM with two aspect ratios of (a) 1.3 and (b) 5.

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4.4. Yield analyses

To demonstrate the reproducibility of the fabricated AECSMs, coupling efficiencies were measured from batch-produced samples. A histogram of measured coupling efficiencies for the 980-nm laser diodes to the SMFs is shown in Fig. 8. The best value for the measured coupling efficiency was 85%, and the average coupling efficiency for 30 measurements was 71%. In Fig. 8, the horizontal and vertical radii of curvatures of AECSMs were measured from 30 to 50 μm and 2.5 to 4.0 μm, respectively and the fiber offset was within 0.8 μm. In this work, the surface cleanliness, both before and after lens formation, and the surface imperfection of the fiber affected the coupling efficiency measurements have been observed. Figure 8 indicates that the 980-nm laser to fiber coupling using the AECSMs has a good reproducibility and a high average value of coupling efficiency of 71%.

 

Fig. 8. Histogram of measured coupling efficiencies between 980-nm laser diode and SMF.

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5. Discussion and conclusion

In comparison with other fabrication methods using multi-step grinding techniques to form asymmetric fiber miceolenses, such as an anamorphic microlens of coupling 78% [5] for a laser with an aspect ratio of 3.6, a wedge-shaped graded-index fiber microlenses of coupling 56% [7] for a laser with an aspect ratio of 42, a wedge-shaped fiber endface with an antireflection coating of coupling 95% [8] for a laser with an aspect ratio of 3.5, a quadrangular-pyramid-shaped fiber endface of coupling 83% for a laser with an aspect ratio of 5 [9, 10], and a conical-wedge-shaped of coupling 84% for a laser with an aspect ratio of 4.3 [11, 12], the proposed AECSM exhibited a high coupling efficiency of 85% and a high average coupling efficiency of 71% for a laser with an aspect ratio of 5. The average grinding offset of this AECSM structure was smaller by about 0.4 μm when compared to the previous structures of the multi-step grinding processes for the CWSFE [11, 12] and QPSFE [9, 10], which were about 0.9 and 1.5 μm, respectively. Due to more grinding and polishing processes, the fabrication methods of the fiber microlenses using the multi-step grinding techniques proved difficult to control the small offset of fiber to form a reproducible microlens, thus resulting in a low-yield fabrication. In this study, the fabricated AECSMs require only a single-step grinding technique and therefore, the advantages of the fabrication method for achieving high-coupling AECSM structure are a simple process, a reproducible fabrication,and a high-yield output when compared to the currently available asymmetric fiber microlenses using multi-step grinding or process techniques [5, 7, 8, 10, 12] with complicated processes.

In conclusion, a new scheme of an asymmetric elliptic-cone-shaped microlens (AECSM) employing a single-step fabrication technique for efficient coupling between the high-power 980-nm laser diodes and the single-mode fibers was demonstrated. By controlling the parameters of a vertical radius of curvature about 3 μm; a horizontal radius of curvature greater than 25 μm; and an offset within 0.8 μm, a maximum coupling efficiency of 85% and a high-average coupling efficiency of 71% were achieved for a 980-nm laser diode with an aspect ratio of 5. The results of this study have led to the development of a simple and reproducible fabrication process for achieving a high-yield and high-coupling AECSM structure that is suitable for use in commercial high-power pump laser modules.