Abstract

In addition to the pump coupling efficiency and power handling capability of a signal/pump coupler, it is of great importance for high power fiber lasers and amplifiers to maintain the optical properties of the signal light propagating through the component. We report on the comprehensive theoretical and experimental investigations on the beam quality degradation of the signal light in a side pumping coupler with large-mode-area (LMA) signal fiber, fabricated by tapered-fused technique. For the purpose of further understanding the mechanism of beam quality degradation of a side pumping coupler, the impact of micro deformation and thermal dopant diffusion in the signal core is analyzed and discussed theoretically through Beam Propagation Method (BPM). The beam quality and signal insertion loss of several home-made couplers with different fabrication parameters are measured experimentally. We show theoretically and experimentally (using a hydrogen/oxygen flame) that the beam quality degradation and the signal insertion loss are dependent on the temperature and duration of heating process, as well as on the size of the heating region. Accordingly, several solutions and suggestions about the component design and fabrication with the consideration of beam quality are proposed.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

For high power fiber laser sources, an all-fiber structure makes the system more robust, more compact and less sensitive to the external impact such as contamination and vibrations. Thus, all-fiber components have captured more and more attention of researchers in recent years and become more and more challenging because of the growing power level of fiber lasers and amplifiers [1,2]. One of the key fiber-based-components in a high power all-fiber construction is a signal/pump coupler, which can couple pump and signal light into the inner cladding and the active core, respectively. The side pumping coupler, which means the pump light is coupled into the double-clad fiber through the outer cladding surface, has many attractive characteristics, such as low insertion loss with uninterrupted signal fiber core [3–5] as well as unlimited pump points [6,7] which an end pumping coupler (such as TFB, i.e., tapered-fused bundle [8]) cannot achieve, thus facilitating their potential and unique applications in fiber laser and amplifiers.

Typically, a high power all-fiber side pumping coupler is fabricated by fused tapered method [4], which is based on direct heating fusion of tapered pump fibers to the outermost surface of a signal fiber. This type of power coupler seems to be more promising than other techniques, because of its high pump coupling efficiency (up to 98%) and the potentiality of handling high pump power up to kW-class [9]. In addition to pump coupling efficiency and high pump power handling, it is also of great importance for fiber lasers and amplifiers to maintain the optical properties of the signal light when propagating through the coupler. For a side pumping coupler based on tapered-fused technique, the signal fiber core is, theoretically, not interrupted and non-tapered during the fusion splicing process, which can lead to a smaller signal insertion loss (less than 3%) than that of TFB end pumping coupler (up to 10%). Nevertheless, during the fabrication of the coupler, the signal insertion loss and the unwanted degradation of the signal beam quality, resulted from externally-induced mechanical stress and thermal diffusion of the core dopants [10–12] cannot be ignored at high signal power level, especially for large-mode-area (LMA) double-clad fiber. Beam quality degradations of the signal light in a side pumping coupler was measured in [3], where a power in higher-order modes of 2% was found for the signal feedthrough of the component. In 2013, a side pumping fiber coupler achieved via tapered-fused technique, with the functions of not only highly efficient coupling the pump light but also suppressing the high-order-mode through the coupler, was investigated theoretically and experimentally [13]. The double-clad main fiber with micro-deformation resulted in much power leak of high-order mode than low-order mode in the main fiber, thus leading to a better beam quality. However, as for the signal fibers with large mode area or high core dopants, the introduced signal transferring loss may become evident. This may result in a signal power leaking into the cladding, leading to the instability of the component in high power level case especially embedded in a backward pumping scheme. So far, though the beam quality degradations as well as the signal insertion loss has been pointed out and measured, the causes and physical mechanisms were rarely analyzed comprehensively. Thus, it is worth to focus carefully on all three features: the maintenance of high beam quality of the signal, equally critical with pump coupling efficiency and also power handling capability, especially when the LMA fiber is embedded as the signal fiber.

In this paper, we characterize the mechanism of beam quality degradation of signal light in a side pumping coupler theoretically and experimentally. First, we calculate the signal propagation characteristics in a side pumping coupler with the consideration of two types of micro deformation in the signal fiber, i.e. the unsymmetrical and symmetrical deformation. Then, we provide the discussion regarding the influence of thermal dopant diffusion in the signal fiber core theoretically. Next, the experimental investigations on the beam quality degradation is demonstrated and discussed via measuring the beam quality of couplers samples fabricated in different heating environments. At last, the conclusion is given.

2. Numerical analysis

During the fabrication of the components, especially involving the fusion splicing of pump fibers with signal fiber at high temperature heating source, some specific difficulties may occur. On the one hand, the signal fiber core may suffer from micro deformation at the coupling region between the signal fiber and the tapered pump fiber, due to the mechanical stress. On the other hand, heating the signal fiber will lead to the enlargement of the fiber mode field diameter (MFD) by diffusion of the core dopant into the cladding [10]. Either the variation of the waveguide shape or the MFD could cause the beam quality degradation and insertion loss of the signal light. In this work, the influence of micro deformation and dopant diffusion is theoretically calculated and analyzed. The numerical simulation is performed by beam propagation method (BPM). The spatial properties of the propagation beam as well as the mode field distribution along the fiber length can be obtained by solving Helmholtz equation.

2.1 Micro deformation

Figure. 1 shows the structure of the coupler with consideration of the micro deformation. As shown in Fig. 1(a), on the coupling region, the tapered pump fiber and signal fiber are contact with each other. The micro deformation of the signal fiber core usually locates at this coupling region. In general, there are two typical types of the micro deformation. One is the unsymmetrical deformation, as can be seen in Fig. 1(b), which is attributed to the misalignment (either vertically or horizontally) between two fiber holders or mechanical stages at both ends during the fabrication. This type is the most common one in our previous investigation on the side pumping coupler based on tapered fused method. The longitudinal length of this micro deformation region is L and R is the width. Figure. 1(b) also shows the microscope image of a home-made coupler with observable unsymmetrical deformation. Another type is symmetrical deformation also with the length and width of L and R respectively as shown in Fig. 1(c), which can result from the stress between the tapered pump fiber and the signal fiber during the heating splicing process with high temperature, especially when the pump fibers not stretch well on the signal fiber surface before heating, or there is only one pump fiber. The microscope image in Fig. 1(c) shows the symmetrical deformation of a coupler which is caused by the first case.

 figure: Fig. 1

Fig. 1 Structure of side pumping coupler with consideration of the micro deformation: (a) the structure of side pumping coupler (b) the unsymmetrical deformation (c) the symmetrical deformation.

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Note that in the simulation model, R in both types of deformation only appears on y-axis but not on x-axis, as shown in Fig. 1(b) and 1(c). For Unsymmetrical deformation, the waveguide has two acr waveguides with opposite curvature. For symmetrical deformation, the waveguide has two acr waveguides with the same curvature. Curvature radius of two arcs is decided depending on the value of L and R. The propagation properties of a fundamental mode in the signal fiber with this deformation considered can be calculated. The total input power is set to 1. The signal wavelength is 1060 nm. The core NA of the double clad signal fiber is 0.06.

2.1.1 Unsymmetrical deformation

First, we demonstrate the impact of the unsymmetrical micro deformation on the signal beam quality. Figure. 2(a)-(c) illustrate the monitored total output power and the output power of different modes, as a percentage of the total input power (Pout/Pin), versus the increase of R. Figure 2(d)-(e) show the far field intensity distribution for different structure parameters. For the 30 μm core diameter of the signal fiber and 1cm L, the normalized total output power, and the normalized output power of LP01, LP11, LP21 and LP02 mode versus the increase of R, are presented in Fig. 2(a). The total output power decreases slightly, while it can be observed that the decrease of the LP01 mode power is combined with the increase of the higher-order mode powers (i.e. LP11, LP21 and LP02), with the growth of R from 0 to 200 μm. This is chiefly because some portion of LP01 transfers to higher-order modes, and the higher the R is, the more power will transfer, as it can be seen in Fig. 2(d), which shows the corresponding far fields distribution at different R. However, when the deformation length is 0.5 cm, as shown in Fig. 2(b), the monotonic variation of the powers of fundamental mode and LP11 mode are not observed as R increase from 0 to 100 μm. Instead, the power of LP11 mode increase to the maximum at R = 60 μm and then decrease, while in the case of the fundamental mode power, the opposite trend was observed. This can be explained by the fact that the micro deformation could be served as a mode selecting component for some specific structure parameters, as discussed in [13]. Along the propagation in the micro deformed waveguide, fractional portion of LP11 that have transferred from LP01 before, could then transfer back to LP01 [13] leading to the reduction of LP11 and rise of LP01 at higher deformation width (R), compared with the case with lower R. Similar phenomenon can be observed in the case when the core diameter of signal fiber and the deformation length is 50 μm and 1 cm respectively, as shown in Fig. 2(c) and 2(e). The difference is that, the power proportions of LP01 and LP11 seem more sensitive to the increase of R, meanwhile more faction of launched LP01 converts to LP21 and LP02 due to the larger core diameter of the signal fiber.

 figure: Fig. 2

Fig. 2 The normalized total output power and the output power of different modes depend on the increase of R for the unsymmetrical deformation when the core diameter of the signal fiber and the deformation length L is: (a) 30 μm and 1cm (b) 30 μm and 0.5 cm (c) 50 μm and 1cm. The far field intensity distribution at different R when the core diameter of the signal fiber and the deformation length L is: (d) 30 μm and 1cm (e) 50 μm and 1cm.

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Beam quality parameter Mx2 and My2 can be calculated from the output field intensity profile obtained by BPM. M2 can be written as

Mx2=wθw0θ0=πλwxθxMy2=wθw0θ0=πλwyθy

Where θxand θy is the beam divergence angle, wx and wyis the beam width, which can be calculated by using the second moment of the beam intensity profile I(x, y, z) and the center of gravity of the beam [14]. I(x, y, z) can be calculated by the output profile E(x,y) which is obtained by BPM simulation. According to Huygens-Fresnel principle, the calculation method is as shown in Eq. (2)-(4):

E(x,y,z)=E(x,y)*h(x,y,z)
h(x,y,z)=eikziλzexp[ik2z(x2+y2)]
I(x,y,z)=|E(x,y,z)|2

Figure. 3(a) and 3(b) presents Mx2 and My2 parameter versus the deformation width R when the core diameter and L are 30 μm and 1 cm, 50 μm and 1 cm, 30 μm and 0.5 cm. Figure. 3(a) and 3(b) shows that the influence of R on parameter Mx2 is not evident (cp. My2), which can be explained by the fact that the micro deformation width R only appears on one axis, as illustrated in Fig. 1. Generally, the change of My2 corresponds to the trend of the power of LP11 along with the growth of R. For example, when the core diameter and L is 50 μm and 1 cm, the value of My2 increases to 1.732 when the deformation width is 60 μm, then decreases to 1.407 when the deformation width is 100 μm. Though it can be seen a decrease for the power portion of LP11 and an improvement of the output beam quality with the further increase of R, the decrease of the total output power is observed, which means the insertion signal loss become more and more non-ignorable and introduce uncertainty to the component especially under high power operation. Thus, an extremely larger R is not desirable.

 figure: Fig. 3

Fig. 3 The calculated Mx2 and My2 versus the deformation width R for unsymmetrical deformation: (a) Mx2 (b) My2.

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The simulation results about the unsymmetrical deformation imply that: firstly, a longer tapering length of the pump fiber or a longer heating region of pump fibers and the signal fiber, leading to a longer length of coupling region, is greatly useful to obtain a good signal beam quality and low insertion loss, especially for those fibers which have larger fiber core diameter; Secondly, since the deformation width R results from the misalignment between two fiber holders or mechanical stages, two stages or holders should be well aligned horizontally and vertically before the fusion splicing of the pump fiber and signal fiber, which ensure the deformation width to be as small as possible.

2.1.2 Symmetrical deformation

Then, the symmetrical deformation is investigated. When the core diameter of the signal fiber and L are 30 μm /1cm and 50 μm /1cm, the normalized output power, and the normalized total output power of the LP01, LP11, LP21 and LP02 mode depend on the increase of R and are shown in Fig. 4(a) and 4(b). Figure. 4(c) and 4(d) present the far field intensity distribution for 30 μm and 50 μm core diameter respectively. Figure. 4(a) and 4(b) illustrates that the power proportion of LP01 decreases greatly whereas the powers of high-order modes increase with the rise of R, even when R is lower than 100 μm (cf. Figure 4(a)) or 50 μm (cf. Figure 4(b)), compared with the situation of unsymmetrical deformation presented in Fig. 2. Moreover, the power ratio of LP21 become more and more evident with the growth of R, especially in the case of 50 μm core diameter. Therefore, it can be seen in Fig. 4(d) that LP21 is clearly recognizable when R increases to 100 μm.

 figure: Fig. 4

Fig. 4 The simulation results of the symmetrical deformation: the normalized total output power and the output power of different modes depend on the increase of R when the core diameter of the signal fiber and the deformation length L is: (a) 30 μm and 1cm (b) 30 μm and 0.5 cm; The far field intensity distribution at different R when the core diameter of the signal fiber and the deformation length L is: (d) 30 μm and 1cm (e) 50 μm and 1cm.

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Figure. 5(a) and 5(b) depict the calculation results of Mx2 and My2 parameter for symmetrical deformation. It can also be concluded that the beam quality degrades evidently with the increase of R, which is more serious than that for unsymmetrical deformation under the same R. Meanwhile, not only My2 but also Mx2 increases with R in the case of 50 μm as the core diameter. This is mainly because the power portion of LP21 greatly grows with the rise of R from 0 to 100 μm, leading to the increase of both My2 and Mx2. As illustrated before, this type of micro deformation is generally caused by the stress between the tapered pump fiber and the signal fiber during the fusion splicing with high flame temperature, which means the temperature of the heating source and the heating time should be well-selected to weaken this deformation as much as possible. Meanwhile, preserving proper tension on the coupling region - before and during the fusion process is also very important. For example, too high tension may increase the risk of micro deformation whereas too low tension will cause tapered pump fibers falling down in the heated region (simply due to the gravity).

 figure: Fig. 5

Fig. 5 The calculated Mx2 and My2 versus the deformation width R for unsymmetrical deformation. (a) Mx2 (b) My2.

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2.2 Thermally dopant diffusion

During the fabrication of the tapered-fused side pumping coupler, the last but the most important step is fusion splicing of the pump fiber(s) and the signal fiber by using a heating source, such as hydrogen-oxygen flame, which has a temperature far higher than 1300 °C. As a result, the Germanium dopants in the fiber core of the signal fiber will diffuse to the clad, thus leading to an enlarged MFD [11]. The main parameters that impact on the dopant diffusion are Germanium concentration doped in the core, the heating temperature and heating time, etc. Hence, the impact of temperature and heating time of the heating source on the signal light beam quality degradation can be analyzed through introducing the diffused refractive index profile at the heating region in the simulation based on BPM.

Figure. 6(a) illustrates the schematic of the signal fiber with considered dopant diffusion. After heating the coupling region, the refractive index at the center of the fiber core will decrease and the effective core radius increase in the heating region. This refractive index profile is highly similar with a thermally diffused expanded core (TEC) fibers, which is commonly used for the alignment and matching of the modal fields between the fibers and optical devices and can be achieved via heating a single mode fiber locally at a high temperature (1200–1400 °C) for several hours and diffusing the germanium dopant from the core into the cladding [16]. Unlike TEC fibers, in a side pumping coupler, the signal fiber and the tapered pump fiber are heated at a much higher temperature (1600°C-2000°C) for just dozens of seconds [4].

 figure: Fig. 6

Fig. 6 (a) Schematic of the signal fiber with dopant diffusion considered. (b) The simulated refractive index profiles for different heating conditions.

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The refractive index profile of the TEC fiber along center of the cross section can be given as [15,16]

n2(r)=n12+(n02n12)a2A2exp(r2A2)
Where n0 and n1 are the original refractive index of the core and cladding, a is the core radius, r is the polar coordinate and A=2Dt is defined as the effective core radius of TEC fibers . Here, t is the heating duration (s) and D is the diffusion coefficient, which is known as Arrhenius equation and expressed as
D=D0exp(QRT)
Where D0 is frequency factor constant [12], Q is the heat of activation, T is the absolute temperature, and R is the gas constant (8.31 J/K/mol). Different fibers have different values of D0 and Q [12]. For the purpose of analyzing and predicting the negative impact of dopant thermal diffusion on the beam propagation characteristics of the signal light, several simulated index profiles have been given by using Eq. (1)-(2). The core/cladding diameter of the double-clad signal fiber is 30 μm and 250 μm, respectively, with a core numerical aperture (NA) of 0.06. D0 and Q is 5.6 × 10−6 m2/s and 2.4 × 105 J respectively in this simulation. The core refractive index profiles for the heating condition (flame temperature / heating time) of 1600°C/ 60 seconds, 1650°C/ 60 seconds and 1600°C/ 80 seconds are depicted in Fig. 6(b).

The numerical model with the consideration of dopants thermal diffusion is presented in Fig. 7. This waveguide includes 0.5 mm original signal fiber core at the beginning, 10 mm heated region and 5 mm original signal fiber core at the end. The radius of this monitored waveguide is 30 μm. The launching field is LP01 mode. The section of the original signal fiber core has a step-index profile, which is shown in the dotted black line in Fig. 6(b), where the core refractive index is 1.4512 and the background index (the cladding refractive index) is 1.45. The section of heated region has a Gaussian index profile (cf. solid lines in Fig. 6(b)), which means the background refractive index nearby the waveguide is no longer 1.45 but appears to be Gaussian distribution. For simplification, we assume that the coupling region of the coupler is heated under the same temperature and neglect the transition region at the boundary of the heated region and non-heated region [17,18], which means the refractive index profile is uniform along the longitudinal length in the heated region.

 figure: Fig. 7

Fig. 7 The monitored waveguide power, as well as the power portion of LP01 and LP02 along the longitudinal length.

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As shown in Fig. 7, the total waveguide power (with a radius of 30 μm), as well as the power portion of LP01 and LP02 in the waveguide are monitored along the longitudinal length. When the signal fiber is heated at 1600°C for 60 seconds, the beam is no longer pure fundamental mode but a combination of LP01 and LP02 modes during its propagation in the heated region. Meanwhile, the total waveguide power decreases after propagating through the heated region and a power portion of 2.5% expand into the cladding. This can be explained by the fact that MFD of the fundamental mode expands due to the dopant diffusion into the cladding. However, when the relative refractive index difference between the core and the cladding is further reduced because of the increased heating temperature or heating time (cf. Figure 6(b)), the total power loss of the signal core after the propagation of heating region is more serious, which is approximately 4.2% for 1650°C/60 seconds and 5.2% for 1600°C/80 seconds at an average level. Apart from the total power loss, the power portion of LP01 mode and LP02 mode oscillates more evidently along the heating region (cp. the heating condition of 1600°C/60 seconds), which might lead to the increased risk of the beam quality deterioration at the final fiber output. Figure. 8(b)-(d) shows the output far field distributions with different heating conditions and Fig. 8(a) shows the launching field distribution which is a pure fundamental mode with a M2 of 1. It can be observed in Fig. 8(a) and 8(b) that the field distribution with heating at 1600°C/60 seconds is highly similar with the launching field, while beam quality parameter Mx2 and My2 has increased to 1.324 and 1.325 respectively, which means the beam quality has become poor and high-order modes has emerged. Moreover, as the heating temperature or heating duration time increases, the far field distribution has been affected distinctly and the beam quality become worse, with the Mx2 /My2 parameter to be 1.835/1.723 at 1600°C/80 seconds and 1.954/1.875 at 1650°C/60 seconds.

 figure: Fig. 8

Fig. 8 The far field intensity distributions at the output for different heating conditions. (a) the launching field-fundamental mode (b) at 1600°C/60 seconds: Mx2- 1.324, My2-1.325 (c) at 1600°C/80 seconds: Mx2-1.835, My2-1.723 (d) at 1650°C/60 seconds: Mx2-1.954, My2-1.875.

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Since D0 and Q in Eq. (6) is determined so as to get the best fitting between a measured dopant distribution and a simulated one [12], the characteristics of thermally-diffused fiber core may vary depending on the types of fiber and the heating condition, which means the index profiles used in this simulation cannot radically represent the realistic situation. It should be stressed that the purpose of this simulation is to concretely understand how the signal light propagates in the side pumping coupler whose signal fiber core is partially thermally-diffused during the fabrication and what consequences it may have on the signal performance of the components. The simulation results presented above imply that dopant thermal diffusion of the signal fiber core will impact the propagation of signal light and cause undesirable signal insertion loss as well as the deterioration of the beam quality. The higher heating temperature or longer heating time, the poorer the beam quality and the larger signal insertion loss. In our previous work [4,7], it was proved that the increased fused depth between the signal fiber and pump fiber, which can be achieved through increasing the heating time or heating temperature, could contribute to not only the rise of pump coupling efficiency but also the reduced pump power loss into the fiber coating. Nevertheless, with consideration of thermal dopant diffusion, the heated duration and temperature for fusion-splicing the pump fibers and the signal fiber requires careful design in the coupler fabrication, aiming at achieving not only the high pump coupling efficiency but also the maintenance of the signal beam quality and low signal insertion loss.

3. Experimental results and discussion

3.1 Component fabrication and experimental setup

The fabrication system and the fabrication process of the coupler was described in our previous work in detail [4,9]. The heat source for tapering and fusion splicing is a hydrogen–oxygen flame. We have fabricated six (2 + 1) × 1 side pumping coupler samples by using tapered-fused method. The core/cladding diameter of the pump fiber is 200/220 μm with a NA of 0.22. All the tapered pump fibers have the same tapered structure, with a waist diameter of 22 μm and the tapering length of 10 mm (9 mm down taper and 1 mm taper waist). The core/cladding diameter of the signal fiber and the heating condition for fusion splicing, including hydrogen/oxygen flow, heating duration and scanning length of the flame, for different coupler samples are shown in Table 1. The temperature of the flame can be controlled by the flow of hydrogen and oxygen. Empirically, we have found that every 10 cm3/min rise of the hydrogen flow lead to 25-30°C temperature increase and 20 °C for every 10 cm3/min rise of the oxygen flow. Increasing the scanning length of the flame will lengthen the coupling region of the coupler.

Tables Icon

Table 1. Parameters for Side Pumping Coupler Samples.

Figure.9 illustrates the experimental setup for measuring the optical properties of the signal light propagating through the couplers. Since the output fiber of the 1060 nm seed laser is a single-mode fiber with a core/cladding diameter of 10/125 μm, a home-made mode field adaptor (MFA) is spliced with the output fiber to match the mode area between the 10 μm-core of the output fiber and the 30 μm-core of the signal fiber of the coupler. The beam quality maintains well in the MFA, with the M2 value of 1.05. A cladding light stripper is used to strip the cladding light arising from the signal insertion loss of the coupler.

 figure: Fig. 9

Fig. 9 Experimental setup of the measurement system. MFA: mode field adaptor; CLS: cladding light stripper.

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3.2 Experimental results and discussion

First, the signal insertion loss for coupler 1-5 versus different signal input powers has been measured, which is shown in Fig. 10. As shown in Fig. 10(a), the average insertion loss for Coupler 1-5 is 1.0%, 2.1%, 3.5%, 5.6% and 3.0%. According to the hydrogen/oxygen flow for Coupler 1-3 (cf. Table 1), the temperature of fusion splicing for the coupler samples, from low to high, is Coupler 1, Coupler 2, Coupler 3, which means the rise of heating temperature results in more signal insertion loss. This can be explained by the fact that the higher flame temperature can lead to not only the more serious micro deformation of the signal fiber core but also the more expanded MFD of the signal due to the thermal dopant diffusion (cf. Section 2.2). Varying the scanning length of the flame is the most straightforward way to change the length coupling region or heating region. Coupler 4 and Coupler 2 has the same heating temperature and duration but different scanning lengths of the flame, in other words, the length of coupling region or heating region is different. The average insertion loss of Sample 4 (5.65%) is much higher than Sample 2 (2.1%). It indicates that a longer coupling region or heating region of the signal fiber and pump fibers will contribute to reducing the signal insertion loss, which is consistent with the simulation results in Section 2.1.1. The insertion loss of Coupler 5 is higher than that of Coupler 2 due to the longer heating duration. A longer heating duration leads to a more serious dopant diffusion of the signal core and more signal light propagating to the cladding (cf. Section 2.2).

 figure: Fig. 10

Fig. 10 The signal insertion loss for coupler sample 1-5 versus different signal input powers. (a) Coupler 1-3 (b) Coupler 4-5.

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As shown in Fig. 9, the beam quality of each coupler is measured by PRIMES LQM system. The output beam is collimated by a collimating lens (F = 75 mm). A beam splitter with a reflectivity of 4% is used to split the collimating beam. The reflected beam is used for beam quality measurement. Figure. 11 shows the measured results of Coupler 2-5. The beam quality is evaluated by M2 factor. Unsurprisingly, the beam quality of Coupler 3 (M2 = 1.18), Coupler 4 (M2 = 1.42) and Coupler 5 (M2 = 1.27) is poorer than Coupler 2 (M2 = 1.05), due to the higher heating temperature, shorter scanning length of the flame and longer heating duration, respectively. Besides, the difference between Mx2 and My2 of Coupler 3-5 illustrates that the micro deformation of the signal core dominates the beam quality degradation of the signal light. This can be also verified by the field distribution of Coupler 3-5, which is highly similar with the simulation results shown in Section 2.1. The signal fiber of Coupler 2-5 has the large core diameter of 30 μm yet just moderate cladding diameter of 250 μm, which means, compared with the thermal dopant diffusion in the signal core, the micro deformation of the signal fiber, either arising from the stress between the signal fiber and the pump fibers (cf. Section 2.1.2) or the misalignment of two fiber holders (cf. Section 2.1.1), is more sensitive to the variation of heating condition. It is worth noting that the beam quality degradation of Coupler 4, whose heating region is shorter than Coupler 2 while under the same heating temperature and duration, is extremely serious than other couplers, which corresponds to the conclusion in Section 2.1 that a longer heating region is critical to obtain a good signal beam quality, especially for those fibers which have larger fiber core diameter.

 figure: Fig. 11

Fig. 11 Field images and beam quality results of different couplers evaluated by M2 factor. (a) Coupler 2: Mx2- 1.04, My2- 1.05, M2- 1.05 (b) Coupler 3: Mx2- 1.19, My2- 1.05, M2- 1.18 (c) Coupler 4: Mx2- 1.15, My2- 1.62, M2- 1.42 (d) Coupler 5: Mx2- 1.02, My2- 1.45, M2- 1.27. The left image in each subgraph is 3D isometry distribution of the output field and the right image is the plane at the beam waist.

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In order to figure out whether the thermal dopant diffusion has a non-negligible impact on the beam quality of a side pumping coupler, the effect of micro deformation should be excluded or at least weakened. Therefore, we choose a double-clad fiber with core/cladding diameter of 20/400 μm and core NA of 0.06 as the signal fiber (cf. Coupler 6 in Table 1), which has a smaller mode area and larger cladding diameter than Coupler 2-5. This fiber has better bending resistance under high temperature heating and lower sensitivity of the generation of higher-order mode to the enhancement of micro deformation. The MFA for connecting the seed laser and Coupler 6 is able to match the mode area between the 10 μm-core and the 20 μm-core. The average signal insertion loss of Coupler 6 is 2.9%. The beam quality measurements results of the signal before and after Coupler 6 are shown in Fig. 12. It can be seen that the output beam from Coupler 6 has an M2 factor of 1.165, with Mx2 and My2 of 1.195 and 1.131, which is more radially symmetric than Coupler 2-5 with larger core/cladding diameter ratio. It can be predicted that this variation of the beam quality when the signal light propagates through Coupler 6 results from the dopant diffusion at high temperature environment. Consequently, we find that the considerations of this effect on the beam quality degradation of the side pumping coupler is required when designing the components. Since the concentration of germanium is very low due to the low core NA of the signal fiber, the effect of dopant diffusion on the beam quality degradation is not distinct compared with the micro deformation. Therefore, further theoretical and experimental investigations are necessary for figuring out how the signal light will propagate in the thermally dopant diffused region of the signal fiber core with high NA or high concentration of dopants.

 figure: Fig. 12

Fig. 12 Field images and beam quality results before and after Coupler 6 evaluated by M2 factor. (a) Before Coupler 6: Mx2- 1.062, My2- 1.033, M2- 1.051 (b) After Coupler 6: Mx2- 1.195, My2- 1.131, M2- 1.165.

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In conclusion, in order to maintain the optical properties of the signal light when propagating through a side pumping coupler fabricated by tapered-fused technique, it is viable to reduce the heating temperature and the duration of fusion-splicing as much as possible, on condition that a high pump coupling efficiency of the component can be guaranteed. Meanwhile, increasing the fused length is another effective and straightforward approach to weaken the impact of micro deformation on the signal light. Moreover, compared with micro deformation, the effect of dopant thermal diffusion on the mode field distribution is radially symmetric and the beam quality degradation of it is less obvious especially for the signal fiber with low NA.

4. Conclusion

In summary, we have clarified the characteristics of signal light propagating through a side pumping coupler with the consideration of micro deformation and thermal dopant diffusion theoretically and experimentally. The results indicate that LMA signal fibers are very sensitive to heating condition and mechanical stress. We reveal that during the side pumping coupler fabrication, increasing the coupling region length is effective in terms of reducing the signal insertion loss and beam quality degradation arising from the micro deformation of the signal core. Moreover, the fiber holders at both sides should be perfectly aligned to prevent unsymmetrical deformation and the heating parameters should be well-designed to minimize the possibilities of symmetrical deformation. We have also figured out, both theoretically and experimentally, that the effect of thermal dopant diffusion, which leads to an expanded mode field diameter and the reduction of signal intensity in the fiber core, needs to be paid more attention, especially when the coupler is heated at a high temperature or longer duration. An extremely high heating temperature or long heating duration for merely pursuing a high pump coupling efficiency in the fabrication is inadvisable.

Funding

National Key R&D Program of China (2016YFB0402204).

References

1. D. Stachowiak, “High-Power Passive Fiber Components for All-Fiber Lasers and Amplifiers Application—Design and Fabrication,” Photonics 5(4), 38 (2018). [CrossRef]  

2. H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, and S. Desmoulins, “Fibers and fiber-optic components for high-power fiber lasers,” in Fiber Lasers VIII: Technology, Systems, and Applications(International Society for Optics and Photonics, 2011), p. 791414.

3. T. Theeg, H. Sayinc, J. Neumann, L. Overmeyer, and D. Kracht, “Pump and signal combiner for bi-directional pumping of all-fiber lasers and amplifiers,” Opt. Express 20(27), 28125–28141 (2012). [CrossRef]   [PubMed]  

4. C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017). [CrossRef]  

5. X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013). [CrossRef]  

6. T. Qirui and G. Tingwu, “Cascaded combiners for a high power CW fiber laser,” Laser Phys. 26(2), 025102 (2016). [CrossRef]  

7. C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018). [CrossRef]  

8. D. J. DiGiovanni and A. J. Stentz, “Tapered fiber bundles for coupling light into and out of cladding-pumped fiber devices,” (US Patent 5864644, 1999).

9. Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017). [CrossRef]  

10. M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996). [CrossRef]  

11. K. Shiraishi, T. Yanagi, and S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11(10), 1584–1591 (1993). [CrossRef]  

12. K. Shiraishi, Y. Aizawa, and S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8(8), 1151–1161 (1990). [CrossRef]  

13. Q. Xiao, X. Chen, H. Ren, P. Yan, and M. Gong, “Fiber coupler for mode selection and high-efficiency pump coupling,” Opt. Lett. 38(7), 1170–1172 (2013). [CrossRef]   [PubMed]  

14. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: applications and Issues(Optical Society of America, 1998), p. Q1.

15. G. S. Kliros and N. Tsironikos, “Variational analysis of propagation characteristics in thermally diffused expanded core fibers,” Optik (Stuttg.) 116(8), 365–374 (2005). [CrossRef]  

16. X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013). [CrossRef]  

17. Y. C. Lin and S. C. Lin, “Thermally expanded core fiber with high numerical aperture for laser-diode coupling,” Microw. Opt. Technol. Lett. 48(5), 979–981 (2006). [CrossRef]  

18. H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012). [CrossRef]  

References

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  1. D. Stachowiak, “High-Power Passive Fiber Components for All-Fiber Lasers and Amplifiers Application—Design and Fabrication,” Photonics 5(4), 38 (2018).
    [Crossref]
  2. H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, and S. Desmoulins, “Fibers and fiber-optic components for high-power fiber lasers,” in Fiber Lasers VIII: Technology, Systems, and Applications(International Society for Optics and Photonics, 2011), p. 791414.
  3. T. Theeg, H. Sayinc, J. Neumann, L. Overmeyer, and D. Kracht, “Pump and signal combiner for bi-directional pumping of all-fiber lasers and amplifiers,” Opt. Express 20(27), 28125–28141 (2012).
    [Crossref] [PubMed]
  4. C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017).
    [Crossref]
  5. X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
    [Crossref]
  6. T. Qirui and G. Tingwu, “Cascaded combiners for a high power CW fiber laser,” Laser Phys. 26(2), 025102 (2016).
    [Crossref]
  7. C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
    [Crossref]
  8. D. J. DiGiovanni and A. J. Stentz, “Tapered fiber bundles for coupling light into and out of cladding-pumped fiber devices,” (US Patent 5864644, 1999).
  9. Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
    [Crossref]
  10. M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
    [Crossref]
  11. K. Shiraishi, T. Yanagi, and S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11(10), 1584–1591 (1993).
    [Crossref]
  12. K. Shiraishi, Y. Aizawa, and S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8(8), 1151–1161 (1990).
    [Crossref]
  13. Q. Xiao, X. Chen, H. Ren, P. Yan, and M. Gong, “Fiber coupler for mode selection and high-efficiency pump coupling,” Opt. Lett. 38(7), 1170–1172 (2013).
    [Crossref] [PubMed]
  14. A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: applications and Issues(Optical Society of America, 1998), p. Q1.
  15. G. S. Kliros and N. Tsironikos, “Variational analysis of propagation characteristics in thermally diffused expanded core fibers,” Optik (Stuttg.) 116(8), 365–374 (2005).
    [Crossref]
  16. X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
    [Crossref]
  17. Y. C. Lin and S. C. Lin, “Thermally expanded core fiber with high numerical aperture for laser-diode coupling,” Microw. Opt. Technol. Lett. 48(5), 979–981 (2006).
    [Crossref]
  18. H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
    [Crossref]

2018 (2)

D. Stachowiak, “High-Power Passive Fiber Components for All-Fiber Lasers and Amplifiers Application—Design and Fabrication,” Photonics 5(4), 38 (2018).
[Crossref]

C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
[Crossref]

2017 (2)

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017).
[Crossref]

2016 (1)

T. Qirui and G. Tingwu, “Cascaded combiners for a high power CW fiber laser,” Laser Phys. 26(2), 025102 (2016).
[Crossref]

2013 (3)

Q. Xiao, X. Chen, H. Ren, P. Yan, and M. Gong, “Fiber coupler for mode selection and high-efficiency pump coupling,” Opt. Lett. 38(7), 1170–1172 (2013).
[Crossref] [PubMed]

X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
[Crossref]

X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
[Crossref]

2012 (2)

T. Theeg, H. Sayinc, J. Neumann, L. Overmeyer, and D. Kracht, “Pump and signal combiner for bi-directional pumping of all-fiber lasers and amplifiers,” Opt. Express 20(27), 28125–28141 (2012).
[Crossref] [PubMed]

H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
[Crossref]

2006 (1)

Y. C. Lin and S. C. Lin, “Thermally expanded core fiber with high numerical aperture for laser-diode coupling,” Microw. Opt. Technol. Lett. 48(5), 979–981 (2006).
[Crossref]

2005 (1)

G. S. Kliros and N. Tsironikos, “Variational analysis of propagation characteristics in thermally diffused expanded core fibers,” Optik (Stuttg.) 116(8), 365–374 (2005).
[Crossref]

1996 (1)

M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
[Crossref]

1993 (1)

K. Shiraishi, T. Yanagi, and S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11(10), 1584–1591 (1993).
[Crossref]

1990 (1)

K. Shiraishi, Y. Aizawa, and S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8(8), 1151–1161 (1990).
[Crossref]

Aizawa, Y.

K. Shiraishi, Y. Aizawa, and S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8(8), 1151–1161 (1990).
[Crossref]

Chen, H.

X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
[Crossref]

H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
[Crossref]

Chen, Q.

H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
[Crossref]

Chen, X.

Chen, Z.

C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
[Crossref]

C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017).
[Crossref]

X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
[Crossref]

Gong, M.

Gu, Y.

C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
[Crossref]

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017).
[Crossref]

Haibara, T.

M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
[Crossref]

Haichui, R.

X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
[Crossref]

Hou, J.

C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
[Crossref]

C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017).
[Crossref]

X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
[Crossref]

Kawakami, S.

K. Shiraishi, T. Yanagi, and S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11(10), 1584–1591 (1993).
[Crossref]

K. Shiraishi, Y. Aizawa, and S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8(8), 1151–1161 (1990).
[Crossref]

Kihara, M.

M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
[Crossref]

Kliros, G. S.

G. S. Kliros and N. Tsironikos, “Variational analysis of propagation characteristics in thermally diffused expanded core fibers,” Optik (Stuttg.) 116(8), 365–374 (2005).
[Crossref]

Kracht, D.

Lei, C.

C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
[Crossref]

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017).
[Crossref]

Leng, J.

Li, G.

H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
[Crossref]

Li, J.

X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
[Crossref]

Li, R.

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

Lin, S. C.

Y. C. Lin and S. C. Lin, “Thermally expanded core fiber with high numerical aperture for laser-diode coupling,” Microw. Opt. Technol. Lett. 48(5), 979–981 (2006).
[Crossref]

Lin, Y. C.

Y. C. Lin and S. C. Lin, “Thermally expanded core fiber with high numerical aperture for laser-diode coupling,” Microw. Opt. Technol. Lett. 48(5), 979–981 (2006).
[Crossref]

Liu, J.

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

Liu, L.

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

Mali, G.

X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
[Crossref]

Matsumoto, M.

M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
[Crossref]

Neumann, J.

Overmeyer, L.

Ping, Y.

X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
[Crossref]

Qirong, X.

X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
[Crossref]

Qirui, T.

T. Qirui and G. Tingwu, “Cascaded combiners for a high power CW fiber laser,” Laser Phys. 26(2), 025102 (2016).
[Crossref]

Qiu, Y.

H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
[Crossref]

Ren, H.

Sayinc, H.

Shiraishi, K.

K. Shiraishi, T. Yanagi, and S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11(10), 1584–1591 (1993).
[Crossref]

K. Shiraishi, Y. Aizawa, and S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8(8), 1151–1161 (1990).
[Crossref]

Stachowiak, D.

D. Stachowiak, “High-Power Passive Fiber Components for All-Fiber Lasers and Amplifiers Application—Design and Fabrication,” Photonics 5(4), 38 (2018).
[Crossref]

Theeg, T.

Tingwu, G.

T. Qirui and G. Tingwu, “Cascaded combiners for a high power CW fiber laser,” Laser Phys. 26(2), 025102 (2016).
[Crossref]

Tomita, S.

M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
[Crossref]

Tsironikos, N.

G. S. Kliros and N. Tsironikos, “Variational analysis of propagation characteristics in thermally diffused expanded core fibers,” Optik (Stuttg.) 116(8), 365–374 (2005).
[Crossref]

Xiao, C.

X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
[Crossref]

Xiao, H.

C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
[Crossref]

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

Xiao, Q.

Yan, P.

Yanagi, T.

K. Shiraishi, T. Yanagi, and S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11(10), 1584–1591 (1993).
[Crossref]

Zhang, H.

H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
[Crossref]

Zhou, X.

X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
[Crossref]

High Power Laser Sci. Eng. (1)

C. Lei, Z. Chen, Y. Gu, H. Xiao, and J. Hou, “Loss mechanism of all-fiber cascaded side pumping combiner,” High Power Laser Sci. Eng. 6, e56 (2018).
[Crossref]

J Lightwave Techno (1)

X. Qirong, Y. Ping, R. Haichui, C. Xiao, and G. Mali, “A Side-Pump Coupler With Refractive Index Valley Configuration for Fiber Lasers and Amplifiers,” J Lightwave Techno 31(16), 2715–2722 (2013).
[Crossref]

J. Lightwave Technol. (4)

C. Lei, Z. Chen, J. Leng, Y. Gu, and J. Hou, “The influence of fused depth on the side-pumping combiner for all-fiber lasers and amplifiers,” J. Lightwave Technol. 35(10), 1922–1928 (2017).
[Crossref]

M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
[Crossref]

K. Shiraishi, T. Yanagi, and S. Kawakami, “Light-propagation characteristics in thermally diffused expanded core fibers,” J. Lightwave Technol. 11(10), 1584–1591 (1993).
[Crossref]

K. Shiraishi, Y. Aizawa, and S. Kawakami, “Beam expanding fiber using thermal diffusion of the dopant,” J. Lightwave Technol. 8(8), 1151–1161 (1990).
[Crossref]

Laser Phys. (1)

T. Qirui and G. Tingwu, “Cascaded combiners for a high power CW fiber laser,” Laser Phys. 26(2), 025102 (2016).
[Crossref]

Microw. Opt. Technol. Lett. (1)

Y. C. Lin and S. C. Lin, “Thermally expanded core fiber with high numerical aperture for laser-diode coupling,” Microw. Opt. Technol. Lett. 48(5), 979–981 (2006).
[Crossref]

Opt. Eng. (1)

Y. Gu, C. Lei, J. Liu, R. Li, L. Liu, and H. Xiao, “Side-pumping combiner for high-power fiber laser based on tandem pumping,” Opt. Eng. 56(11), 116109 (2017).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (2)

H. Chen, Y. Qiu, G. Li, H. Zhang, and Q. Chen, “Improving fiber to waveguide coupling efficiency by use of a highly germanium-doped thermally expanded core fiber,” Opt. Laser Technol. 44(3), 679–682 (2012).
[Crossref]

X. Zhou, Z. Chen, H. Chen, J. Li, and J. Hou, “Mode field adaptation between single-mode fiber and large mode area fiber by thermally expanded core technique,” Opt. Laser Technol. 47, 72–75 (2013).
[Crossref]

Opt. Lett. (1)

Optik (Stuttg.) (1)

G. S. Kliros and N. Tsironikos, “Variational analysis of propagation characteristics in thermally diffused expanded core fibers,” Optik (Stuttg.) 116(8), 365–374 (2005).
[Crossref]

Photonics (1)

D. Stachowiak, “High-Power Passive Fiber Components for All-Fiber Lasers and Amplifiers Application—Design and Fabrication,” Photonics 5(4), 38 (2018).
[Crossref]

Other (3)

H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, and S. Desmoulins, “Fibers and fiber-optic components for high-power fiber lasers,” in Fiber Lasers VIII: Technology, Systems, and Applications(International Society for Optics and Photonics, 2011), p. 791414.

D. J. DiGiovanni and A. J. Stentz, “Tapered fiber bundles for coupling light into and out of cladding-pumped fiber devices,” (US Patent 5864644, 1999).

A. E. Siegman, “How to (maybe) measure laser beam quality,” in Diode Pumped Solid State Lasers: applications and Issues(Optical Society of America, 1998), p. Q1.

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Figures (12)

Fig. 1
Fig. 1 Structure of side pumping coupler with consideration of the micro deformation: (a) the structure of side pumping coupler (b) the unsymmetrical deformation (c) the symmetrical deformation.
Fig. 2
Fig. 2 The normalized total output power and the output power of different modes depend on the increase of R for the unsymmetrical deformation when the core diameter of the signal fiber and the deformation length L is: (a) 30 μm and 1cm (b) 30 μm and 0.5 cm (c) 50 μm and 1cm. The far field intensity distribution at different R when the core diameter of the signal fiber and the deformation length L is: (d) 30 μm and 1cm (e) 50 μm and 1cm.
Fig. 3
Fig. 3 The calculated Mx2 and My2 versus the deformation width R for unsymmetrical deformation: (a) Mx2 (b) My2.
Fig. 4
Fig. 4 The simulation results of the symmetrical deformation: the normalized total output power and the output power of different modes depend on the increase of R when the core diameter of the signal fiber and the deformation length L is: (a) 30 μm and 1cm (b) 30 μm and 0.5 cm; The far field intensity distribution at different R when the core diameter of the signal fiber and the deformation length L is: (d) 30 μm and 1cm (e) 50 μm and 1cm.
Fig. 5
Fig. 5 The calculated Mx2 and My2 versus the deformation width R for unsymmetrical deformation. (a) Mx2 (b) My2.
Fig. 6
Fig. 6 (a) Schematic of the signal fiber with dopant diffusion considered. (b) The simulated refractive index profiles for different heating conditions.
Fig. 7
Fig. 7 The monitored waveguide power, as well as the power portion of LP01 and LP02 along the longitudinal length.
Fig. 8
Fig. 8 The far field intensity distributions at the output for different heating conditions. (a) the launching field-fundamental mode (b) at 1600°C/60 seconds: Mx2- 1.324, My2-1.325 (c) at 1600°C/80 seconds: Mx2-1.835, My2-1.723 (d) at 1650°C/60 seconds: Mx2-1.954, My2-1.875.
Fig. 9
Fig. 9 Experimental setup of the measurement system. MFA: mode field adaptor; CLS: cladding light stripper.
Fig. 10
Fig. 10 The signal insertion loss for coupler sample 1-5 versus different signal input powers. (a) Coupler 1-3 (b) Coupler 4-5.
Fig. 11
Fig. 11 Field images and beam quality results of different couplers evaluated by M2 factor. (a) Coupler 2: Mx2- 1.04, My2- 1.05, M2- 1.05 (b) Coupler 3: Mx2- 1.19, My2- 1.05, M2- 1.18 (c) Coupler 4: Mx2- 1.15, My2- 1.62, M2- 1.42 (d) Coupler 5: Mx2- 1.02, My2- 1.45, M2- 1.27. The left image in each subgraph is 3D isometry distribution of the output field and the right image is the plane at the beam waist.
Fig. 12
Fig. 12 Field images and beam quality results before and after Coupler 6 evaluated by M2 factor. (a) Before Coupler 6: Mx2- 1.062, My2- 1.033, M2- 1.051 (b) After Coupler 6: Mx2- 1.195, My2- 1.131, M2- 1.165.

Tables (1)

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Table 1 Parameters for Side Pumping Coupler Samples.

Equations (6)

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M x 2 = w θ w 0 θ 0 = π λ w x θ x M y 2 = w θ w 0 θ 0 = π λ w y θ y
E ( x , y , z ) = E ( x , y ) * h ( x , y , z )
h ( x , y , z ) = e i k z i λ z exp [ i k 2 z ( x 2 + y 2 ) ]
I ( x , y , z ) = | E ( x , y , z ) | 2
n 2 ( r ) = n 1 2 + ( n 0 2 n 1 2 ) a 2 A 2 exp ( r 2 A 2 )
D = D 0 exp ( Q R T )

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