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Abstract
We present the design and fabrication of a 3 × 1 signal combiner with high beam quality based on supermode theory. For improving beam quality, the fiber with core diameter of 34 µm and numerical aperture of 0.11 is first chosen as the output fiber. An 8.89 kW output laser with a power transmission efficiency of 97.2% and a low temperature rise coefficient of 3.5 °C/ kW at >8 kW is obtained when the combiner launched by three Yb-doped fiber lasers. In addition, the energy density distribution of the output beam is Gaussian-like and M2 factor is 2.32, which is the best beam quality compared with the presented signal combiners for high power laser to the best of our knowledge.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber lasers have shown significant progress as evidenced by the commercial availability of kW-class fiber lasers, which are used in industrial processing such as welding, marking, and cutting. The output power limit of single fiber laser has increased significantly year by year, and recently reached the level of 20 kW [1,2]. However, it is a challenge to further improve the output power of single fiber lasers due to mode instability, thermal damage, and nonlinear effects [3,4]. Beam combining technology with the advantages of compact structure, high reliability, low cost, good stability has been gradually considered as an effective way to further improving the output power, showing great potential in the high-power all-fiber laser system [5]. Recently, fiber combiners by using tapered fiber bundles (TFB) technology have been widely used to combine several middle power laser beams to form a higher power laser beam [6–8]. In early 2011 [9], a 7 × 1 signal combiner with a 70 µm output fiber core was fabricated to provide a total power of >4 kW, and beam quality of M2 = 7.3. In 2018 [10], a 14 kW output laser with beam quality of M2 = 5.37 was combined by a 7 × 1 signal combiner with an output fiber of 50/70/360 µm (the numerical aperture (NA) = 0.22) when the M2 of laser sources were 1.2-1.4, indicating the stability and potential of >10 kW high beam quality laser combining based on an all-fiber signal combiner. In 2021 [11], a 4 × 1 fiber signal combiner with output fiber diameter of 50 µm (NA = 0.12) was fabricated, and the total output power was 12.03 kW with a M2 of 4.03 when the M2 of laser sources were 1.27, which further improved the beam quality for high-power signal combiners. In the same year [12], the 6015 W output laser with M2 of 3.6 and transmission efficiency of 98% was obtained by a 3 × 1 signal combiner with the output fiber diameter of 50 µm (NA = 0.22), which is the best beam quality reported so far in the field of high-power signal combiners. However, In early 2010 [13], Yariv Shamir et al. have fabricated several 3 × 1 signal TFBs with M2 of 2.3-2.7, indicating the potential to further improving the beam quality of the signal combiners for high-power laser.
There are two factors that affect the beam quality of the combiners, one is the structural design of the TFB, which determines the mode composition in the end of the TFB. And the other is regarding the output fiber, whose core diameter and NA determine the mode fields of the output fiber. When the mode fields of the output fiber are not perfect matching with the fields of the TFB at the splice, high-order modes will be stimulated in the output fiber, thus deteriorating the output beam quality of the combiner [14]. Therefore, proper design of TFB and reasonable selection of output fiber can greatly improve the beam quality of the combiner. In above works for high-power and high beam quality laser [10–12], the output fibers with 50 µm core diameters are selected to design the structure of TFB based on the beam propagation method. In 2012 [14,15], a parabolic-index fibers with core diameter of 100 µm was used as the output fiber of a 3 × 1 signal combiner to significantly reduce degradation of the injected beam quality compared with step-index fibers. However, the output fiber with smaller core diameter has not been tried because the output fiber with smaller core diameter needs the TFB with smaller diameter, increasing the difficulty of the fabrication process.
In this paper, we compared the difference between 34/250 µm (NA = 0.11) and 50/250 µm (NA = 0.12) as output fibers based on the supermode theory. For a well match between the mode fields of TFB and the output fiber, the fiber signal combiner composed of TFB with taper ratio of 0.116 and output fiber of 34/250 µm was fabricated. In addition, other two 3 × 1 signal combiners with output fiber of 50/250 µm were fabricated for comparison. Three 3 kW-level Yb-doped fiber lasers (YDFLs) at the wavelength of 1080 nm were used as the laser sources to test the fabricated 3 × 1 combiners. When the 34/250 µm fiber functioned as the output fiber, the combiner yielded a high beam quality with a M2 factor of 2.32, which is much better than that of the other two combiners.
2. Theoretical analysis and simulations
The signal combiner is built by splicing the output fiber and the TFB, which is formed by placing multiple input fibers into a low refractive index capillary tube and then adiabatically tapering. The structure of the 3 × 1 signal combiner and the cross-sections of the TFB before tapering and after tapering are shown in Fig. 1. In this paper, the fibers of 25/250 µm (NA = 0.065) are used for the input fiber. In order to ensure transmission efficiency, the selection of the output fiber needs to meet the brightness conservation. According to brightness conservation theory, the brightness ratio (BR) defined as
where N is the total number of input fibers; and ${\textrm{D}_{\textrm{in}}}$ and ${\textrm{D}_{\textrm{out}}}$ are the core diameters of the input and output fibers, and $\textrm{N}{\textrm{A}_{in}}$ and $\textrm{N}{\textrm{A}_{\textrm{out}}}$ are the NA of the input and output fibers of the combiner respectively [16,17]. Generally, in the design of a combiner, BR should be greater than 1 to ensure high power transmission efficiency, and closer to 1 to achieve low brightness loss [17]. Therefore, the output optical fibers need to meet: ${\textrm{D}_{\textrm{out}}}\mathrm{\ \times N}{\textrm{A}_{\textrm{out}}}\textrm{} \ge \textrm{2}\textrm{.815}$.
Fig. 1. The structure of the 3 × 1signal combiner and the cross-sections of the TFB before tapering and after tapering.
In the process of tapering the whole composite structure, the core diameters of the input fibers gradually decrease with the decrease of the taper ratio (here defined as the ratio of the outer diameter of the capillary after tapering to it before tapering). At the same time, the air gaps gradually disappear and the claddings of each port are also fused with each other after tapering as shown in Fig. 1. When the taper ratio is small enough, the TFB will become a new waveguide structure, where the core of the input fibers are too small to function, the claddings of each adjacent port form a new guide core, and the tapered capillary tube forms the new cladding [18]. The two-dimensional cross-sectional structure of the TFB is similar to multi-core optical fiber [19], and the whole combiner structure is similar to a photonic lantern [20,21].
Reasonable structural design provides an adiabatic beam propagation in the 3 × 1 TFB. Under adiabatic propagation of the pure LP01 mode input in the TFB, there is no coupling between the fundamental mode and higher-order modes in the TFB, and only the mode field distribution is changed [22–24]. Therefore, the process of pure LP01 mode transmission in TFB is equivalent to the evolution of eigenmodes supported in the waveguide structure. In the waveguide structure of 3 × 1 TFB, the eigenmodes supported and the mode fields distributions on the two-dimensional cross sections is different at different taper ratio [19,20]. In Fig. 2, we use a commercial finite element mode solver (COMSOL) to simulate mode evolution process of the 3 × 1 TFB waveguide structure at the discrete cross-sections with different taper ratio. The NA of the low refractive index capillary tube is 0.11. Input fiber are 3 × 25 µm cores diameter with a core NA of 0.065. The cladding diameters of input fibers are etched from 250 µm to 130 µm for a TFB with reasonable length.
Fig. 2. (a) Mode effective refractive indexes neff, and (b) evolution process of modes filed distributions on the discrete cross-section at different taper ratio of the 3 × 1 TFB under the independent LP01 modes input.
In Fig. 2(a), the mode effective refractive indexes (neff) of fundamental modes (LP01 modes) and the first high-order modes (LP11 modes) are plotted against the taper ratio starting at 1 to 0.1. At the initial stage of taper, the modes corresponding to each core are well confined, and the LP01 modes or the LP11 modes in each port transmit independently, which degenerates the neff curves (the overlapping red and blue curves). As the taper ratio decreases, the diameter and V value of each core decrease. The modes originally confined in the core diffuse in the cladding, and the overlapping integral of the fields between different cores increases, thus they are coupling with each other to form supermodes. LP11 modes in the three cores are coupled to form different higher-order supermodes, breaking the degeneracy at the taper ratio of ∼0.7. At the taper ratio lower than 0.4, the degeneracy of fundamental modes breaks (the red curves separate to the pink curve and the red one), and the first two supermodes of LP01 mode (pink line) and LP11 modes (red line) are formed. Figure 2(b) shows the evolution process of fundamental mode filed distributions on the discrete cross-section under different taper ratio. Here, the different polarization states are simplified, presenting the first supermode of LP01 mode and the second supermodes of LP11 modes orthogonal in two spatial position directions (LP11a and LP11b). The input independent LP01 modes are set as ${\textrm{v}^\textrm{i}}$, and ${\textrm{u}^\textrm{1}}$, ${\textrm{u}^\textrm{2}}$, and ${\textrm{u}^\textrm{3}}\textrm{}$ are represent the supermodes of LP01, LP11a, and LP11b modes respectively.
A transfer matrix A has been derived to describe the relation between the input and output, which is expressed by $\textrm{A}{\textrm{v}^\textrm{i}} = {\textrm{u}^\textrm{i}}$ [25–27]. This relationship describes that a pure supermode ${\textrm{u}^\textrm{i}}$ can be obtained under a proper combination of inputs. Through the inverse matrix of A, the superposition output when an independent LP01 mode is launch into the TFB can be expressed as ${\textrm{v}^\textrm{i}} = {\textrm{A}^{ - 1}}{\textrm{u}^\textrm{i}}$, which is compactly expressed as:
According to this ideal transfer matrix, when a single fundamental mode was launched into no matter which individual port with an adiabatic propagation, the output of the TFB emerges as a superposition of LP01, LP11a and LP11b modes, and the energy of LP11 modes is larger than LP01 mode. Here, only the power ratio between the supermodes is considered, and the phase difference between them is not considered. The first supermode of LP01 mode will be formed at the end of the TFB when three coherent fundamental modes with the same amplitudes and conjugate phases are launched into the TFB. However, the three laser sources are incoherent in the application scenario of 3 × 1 signal combiner. In this case, each isolated single-mode of each port evolves into supermodes during transmission, and the total output of the 3 × 1 TFB is an incoherent addition of their respective supermodes.
At the end of the TFB, The M2 factor limit of the ultimate output beam under incoherent single-mode inputs was numerical calculated as $\textrm{1}\textrm{.15} \cdot {\textrm{N}^{\textrm{1/2}}}$,which is equal to 2 in the 3 × 1 TFB [25]. However, it is difficult for the laser sources to be pure single-mode in practical applications, where the beam quality $\textrm{M}_{out}^\textrm{2}$ of output laser can be estimated by [22]:
Where the $\textrm{M}_i^\textrm{2}$ is the beam quality of each laser source launched into the TFB. In the following experiment, the M2 factors of the three YDFLs are 1.24, 1.22 and 1.25 respectively, leading an output beam at the end of the TFB with a theoretical $\textrm{M}_{out}^\textrm{2}\; $ of 2.14.The final output beam quality of the 3 × 1 signal combiner is determined by the mode composition in the output fiber. The mode fields mismatch between the TFB and the output fiber at the splice point causes higher-order modes stimulated in the output fiber, which leads the deterioration of the output beam quality. Therefore, an appropriate taper ratio of the TFB and output fiber should be selected to minimize the mode mismatch. The coupling efficiencies η of the mode fields between TFB and the output fiber at the splice can be calculated as [28]:
Fig. 3. Coupling efficiencies of the LP01, LP11a and LP11b mode between the TFB and output fibers at the splice changing with the taper ratio of the TFB, the solid lines and dotted lines represent the output fiber of 34/250 µm and 50/250 µm respectively.
3. Fabrication
The TFB was fabricated by tapering after forming a bundle of three etched input fibers. In the preparation process of TFB, the glass capillary was pre-tapered first. The glass capillary used here was low refractive index F-doped SiO2 material with NA = 0.11. The inner/outer diameters of the capillary were 390/780 µm. The low-refractive index capillary can constrain light in the fiber core without radiating into the capillary glass. Its numerical aperture matches to the output fiber of NA = 0.11, which can reduce the splicing loss between TFB and the output fiber. In addition, from the perspective of preparation technology, the capillary with a thick wall can ensure the mechanical stability of TFB with a very small diameter.
The inner diameter of the glass tube after pre-tapered was designed to be 285µm. Then, the three input fibers whose cladding have been etched to 130 µm were inserted into the glass tube. Since the inner diameter of the glass tube was just enough to meet the insertion of the three input fibers, the fibers were pressed against each other to form an equilateral triangle arrangement. Then, the glass tube after inserting three optical fibers would be tapered again. To ensure the condition of adiabatic propagation, we set the tapering length to 2 cm. After the tapering process completed, the TFB was cleaved smoothly in the middle of the tapered waist. The image of the whole tapered TFB profile is shown in Fig. 4 (top panel). The microscope images of cross-sections at different point along the length of the TFB are shown in the bottom panel of Fig. 4. It shows that the air gaps gradually collapse during tapering until the air gaps completely disappear and the claddings of the three input fibers are fully fused to form a new core. The inner core diameter at the end of the TFB was approximately equal to 32 µm with a taper ratio of 0.116 within the range of appropriate value calculated theoretically above.
Fig. 4. The micrograph of the whole tapered TFB (top panel), and microscope images of cross-sections at different point along the length of the TFB (bottom panel).
Then, the TFB was spliced with the etched output fiber at the 3SAE Large Diameter Splicing System LDS 2.5. The side images of the splice between the output fiber and the TFB are shown in Fig. 5(a, b). The left one is the output fiber, whose cladding has been etched to 130 µm for a good mechanical stability of splice. In addition, a rough area approximate 1.5 cm in length was obtained by etching the cladding, and the length of cladding area between the rough area and the etched area was about 1.5 cm as shown in Fig. 5(c). In rough area, the stray light in cladding was stripped before reaching the coating, avoiding the thermal damage. Then, the prepared fiber combiner was packaged in a structural and fixed with UV-glue to protective the key part of the combiner. Finally, as the same with the output fiber, a rough area approximate 2 cm in length was obtained by etching the cladding on each input fiber before the TFB, which were called Cladding Light Strippers (CLS). The CLSs of input fibers can reduce the thermal damage of the combiner and improve the beam quality. After above steps, the fabrication of the all-fiber 3 × 1 signal combiner was completed, which numbered Sample #1. By comparison, the other two 3 × 1 signal combiners with output fibers of 50/250 µm (sample #2 and Sample #3) were fabricated with the same fabrication process. Details of the three samples are shown in Table 1.
Fig. 5. (a) The side image of alignment TFB and etched output fiber, (b) The side image of splicing point, (c) The micrograph of the etched output fiber.
Table 1. Structural parameters of the three fabricated signal combiners
4. Experiment and discussion
The main performance parameters of the signal combiner include: transmission efficiency, power-carrying capability and beam quality. We used three 3 kW-level YDFLs at the wavelength of 1080 nm as the laser sources to test the fabricated 3 × 1 combiners. The M2 factors of the three YDFLs were 1.24, 1.22 and 1.25 respectively. The experimental setup was displayed in Fig. 6. The output fibers of the fiber lasers were 25/250 µm (NA = 0.065), which were completely matching with the input fibers of the signal combiners. The output fiber of the combiner was connected to the quartz block head (QBH) for transmitting the light to the power meter. At the same time, the infrared thermal imager was used for thermal monitoring of the entire test system.
Under the condition that no cooling water was supplied to the signal combiners, the output power and the temperature regions of several important positions of the combiners were shown in Table 2. For combiner Sample #1, the efficiency of each port was higher than 97%, and the rise of temperature was very small when 3050 W continuous laser was launched into each port of the combiner. When the three ports worked together, the total output power of 8.89 kW with transmission efficiency of 97.2% and a maximum temperature of 56 °C was obtained as shown in Fig. 7. The rise coefficient of the temperature was about 3.5 °C/kW. The transmission efficiency and temperature distribution of Sample #1 were similar to Sample #2 and Sample #3, proving the excellent power-carrying capability of the output fiber with a core diameter of 34 µm. For the three combiners, the highest temperature of the combiners was in the rough area of output fibers because light in the cladding leaking from the rough area was absorbed by metal structure. The thermal damage will be smaller if the combiners packaged in a structural with water cooling to take away the heat, indicating that the 3 × 1 signal combiner is potential for 10 kW-level high-power laser.
Fig. 7. (a) The infrared thermal image of the 3 × 1 combiner Sample #1 during the test, (b) the testing QBH with water cooling and testing power meter with water cooling in a light blocking black box. (c) the packaged 3 × 1 signal combiner.
Table 2. Experimental results for the transmission efficiency and thermal effect
Beam quality of the combiners was test by Primes Focus Monitor FM + . The M2 factors of output lasers when each YDFL conducts separately was tested first. As shown in Fig. 8, when each port of the signal combiner Sample #1 worked independently, the energy distributions of the light output in the spot at beam waist position were mainly divided into two opposing parts. According to simulation, the output of the TFB was a superposition of LP01 and LP11 modes, which will appear as 2-lobes distribution under certain mixture. This indicated that the supermdoes of the TFB had good fields match with the output fiber, leading few higher-order modes excited in the output fiber. Therefore, the output laser of the combiner presented a 2-lobes distribution as well.
Next, the output laser had a small M2 factor of 2.32 when the three ports of the signal combiner worked together as shown in Fig. 9(a). The intensity contour lines in x-axis and y-axis of the laser spot at Fig. 9(b) were Gaussian-like distribution, which was an incoherent intensity addition of three superposition fields excited by three laser sources. In addition, the experimental M2 factor of 2.32 was very close to the theoretical M2 value of 2.14.
Fig. 9. Beam quality of Sample #1. (a)The beam quality of output laser when the three ports worked together, (b) the intensity contour line of laser spot at beam waist position.
Finally, the beam quality of Sample #2 and Sample #3 were tested as shown in Fig. 10. The taper ratio of Sample #2 was 0.116, the same as that of Sample #1. So, the guided modes at the end of the TFB of Sample #2 was similar as Sample #1. Combined with the theoretical analysis in Fig. 3, the mode fields match (especially the LP11 modes) at the splice of Sample# 2 were poor compared with Sample #1. Therefore, more high-order modes in the output fiber of 50/250 µm were stimulated, resulting in a larger M2 of 3.44 in Fig. 10(a). The taper ratio of Sample #3 was 0.16 and the inner diameter of TFB was 45µm. The field match of LP01 mode at splice was similar as Sample #2, while fields match of LP11 modes were worse. The ultimate output laser had a M2 of 3.62 as shown in Fig. 10(b).
In general, Due to the difference in the shape of the mode fields between the TFBs and the output fibers, as well as the non-pure single-mode laser sources, the final output lasers of all three combiners are complex mixture of the LP01 mode, LP11 modes and other higher-order modes. When the fiber of 34/250 µm functioned as the output fiber of the combiner, it has the best mode fields match of the first two modes between the TFB and the output fiber at the splice, leading fewer higher-order modes stimulated in the output fiber. Besides, because the V value of the fiber with a core diameter of 34 µm (NA = 0.11) is smaller than that of the fiber with a core diameter of 50 µm (NA = 0.12), the output fiber of 34/250 µm has a lower high-order mode capacity. Due to the above reasons, the beam quality of Sample #1 has made a breakthrough compared with Sample #2 and Sample #3. Although the beam quality of the 3 × 1 signal combiner obtained in this experiment is close to the theoretical value, reasonable structural optimization, improvement of light source quality and well controlling of tapering process can further improve the beam quality of the signal combiners.
5. Summary
We present a 3 × 1signal combiner design based on supermode theory, and firstly adopted a small core diameter as the output fiber of the high-power signal combiner. The combiner yielded an 8.89 kW output laser with a high transmission efficiency of 97.2% and a low temperature rise ratio of 3.5 °C/ kw, indicating a potential for 10kW-level fiber laser transmission. In addition, the energy density distribution of the output beam is Gaussian-like and M2 factor is 2.32. According to the supermodes theory, the beam quality of the 3 × 1 combiner has potential to be further improved through reasonable structural optimization, improvement of light source quality and well controlling of tapering process.
Funding
National Natural Science Foundation of China (61905080, 11875139).
Acknowledgments
The authors would like to thank Yongjun Xu, Xiuxiu Hu for the sincere help and support on the fabrication and test.
Disclosures
The authors declare no conflicts and interest.
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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