1. Introduction

Silica ytterbium-doped fibers (YDFs) have been widely used in space optical communications, medicine, industrial processing, national defense, etc. as the gain medium for high-power fiber lasers and amplifiers due to their simple energy level systems, broad gain-bandwidths, high light-to-light conversion coefficients, and good beam quality [1–4]. Additionally, because of the absence of excited state absorption and concentration quenching, compact high-power ytterbium-doped fiber lasers (YDFLs) and amplifiers (YDFAs) are enabled by using short fiber lengths [3]. To avoid nonlinear effects and long-time-scale degradation of the fiber properties, high-power (in the range of 100 W–1 kW) YDFs need large-mode-areas (LMAs) in order to decrease the power density. To obtain optimal beam quality, LMA YDFs must operate in the single-mode (SM) regime, which requires low numerical apertures (NAs) and small normalized index differences. Thus, LMA-SM-YDFs are sensitive to unintended refractive index (RI) perturbations such as the relaxation of residual stress (RS) and frozen-in viscoelasticity, dopant diffusion, etc. [5–11].

Many researchers have characterized the RS and RI distributions in optical fibers using various techniques [12–16]. Recently, Feng et al. used a state-of-the-art three-dimensional concurrent stress-index (3D-CSI) measurement method [17] to provide a detailed characterization of RS and RI perturbations in LMA erbium-doped fibers (EDFs) resulting from manufacturing, cleaving, and arc fusion splicing [18]. Results indicate that LMA EDFs are sensitive to the aforementioned perturbations, especially in the case of arc fusion splicing. During fusion splicing, high temperatures from the arc discharge can result in the relaxation of RS and frozen-in viscoelasticity and induce dopant diffusion, which will perturb the RI distribution significantly. Due to higher power requirements for YDFLs and YDFAs, LMA-SM-YDFs have lower NAs than LMA-EDFs and are therefore more sensitive to RS and RI perturbations. For example, LMA-SM-YDFs with NAs as low as $\sim 0.08$ are already commercially available [19].

Arc fusion splicing is a preferred process for the interconnection of optical systems and the fabrication of fiber-based devices. Generally, there are several fusion splicing points in high-power all-fiber YDFLs and YDFAs. Fusion splice quality can directly affect many properties in YDFLs and YDFAs, such as pump threshold, output power level, and beam quality. Researchers have recently investigated the effects of splice and return loss on power distribution in YDFL systems [20] as well as splice shift and tilt on beam quality in YDFLs [21]. None of these investigations have considered the effects of the aforementioned perturbations on YDFL performance, even though there is considerable evidence suggesting that they may have a significant impact [18]. Therefore, it is important to understand the characteristics of RS and RI perturbations in fusion spliced LMA-SM-YDFs. Investigating such physical properties allows researchers to predict their effect on YDFL and YDFA system performance as well as improve LMA-SM-YDF design and fabrication.

In this paper we employed the same measurement technique as in [18] to study the characteristics of RS and RI in fusion spliced LMA-SM-YDFs for the first time. The measurements are based on a commercial LMA-SM-YDF (LIEKKI Yb1200-10/125-DC), generally used in medium to high-power YDFLs and YDFAs, spliced to a Corning SMF-28 fiber. Using the experimental data, a finite-difference beam-propagation method (FD-BPM) [22] is employed to describe the propagation of the fundamental mode from the LMA-SM-YDF to the SMF-28. The splice coupling coefficient and the mode transformation effect are predicted based on the simulated results.

2. Experimental Method

The experiments performed in this paper are based on the state-of-the-art 3D-CSI measurement method presented in [17]. In the RS measurement, the NA of the microscope condenser was 0.15. In the RI measurement, the condenser NA and defocus distance were 0.1 and 8 μm, respectively. The fiber sample was surrounded by index-matching oil (Cargille Labs, $n=1.460$, temperature coefficient of $-0.389\times {10}^{-3}/+°\mathrm{C}$). In this technique, the associated RS and RI accuracies are 0.35 MPa and $2.34\times {10}^{-5}$ RI units, respectively [17]. In this paper, ${\sigma }_z$ and $\mathrm{\Delta }n$ denote the axial component of RS and the RI relative to the index-matching oil as in [18].

In this measurement, the SMF-SMF P.01 program of an Ericsson FSU 975 arc fusion splicer was used. The LIEKKI Yb1200-10/125-DC has a core diameter of $\sim 10\mathrm{\mu m}$ and a cladding diameter of $\sim 125\mathrm{\mu m}$. The nominal cladding RI, core NA, and mode-field-diameter (MFD) are 1.4573, 0.08, and 11.1 μm, respectively. The ytterbium concentration is $\sim 9\times {10}^{19}\mathrm{ions}/{\mathrm{cm}}^3$. The fiber is designed to have a step-index profile, and the core/cladding RI difference, $\mathrm{\Delta }{n}_{\mathrm{cc}}$, is $\sim 2.3\times {10}^{-3}$. The outer edge of the cladding is octagonal as shown in Fig. 1.

 

Fig. 1. Cross section of LIEKKI Yb1200-10/125-DC as observed in a bright-field microscope.

Download Full Size | PDF

For the results presented in Figs. 2 and 5, and later simulated in Fig. 7, RS/RI cross sections were reconstructed under an assumption of axial symmetry, in which one projection angle was assumed to be representative of all projection angles. This assumption was made due to the impracticality of gathering full tomographic data over an axial length of $\sim 3\mathrm{mm}$ (due to a limited camera field-of-view) and also because the primary focus of our investigation is on the effects associated with the fundamental mode, which is located in the vicinity of the core region where the assumption is most valid. In addition, Figs. 3 and 6 were reconstructed using all projection angles and their lack of axial asymmetry indicates that this assumption is reasonable.

 

Fig. 2. (a) Measured RS distribution along the LIEKKI Yb1200-10/125-DC (left) and the SMF-28 (right) after arc fusion splicing. The inserted figure (top) shows the mean axial stress near the splicing point. (b) RI profiles at indicated positions along the transition region from the splicing point.

Download Full Size | PDF

 

Fig. 3. Cross-sectional RS distribution (reconstructed using all projection angles) in LIEKKI Yb1200-10/125-DC 20 μm from the splicing point.

Download Full Size | PDF

 

Fig. 4. Calculated change of radial RI $\mathrm{\Delta }{n}_r$ induced by the RS change along the fusion splice between the LIEKKI Yb1200-10/125-DC (left) and the SMF-28 (right).

Download Full Size | PDF

 

Fig. 5. (a) Measured RI distribution along the LIEKKI Yb1200-10/125-DC (left) and the SMF-28 (right) after arc fusion splicing. (b) RI profiles at indicated positions along the transition region from the splicing point.

Download Full Size | PDF

 

Fig. 6. Cross-sectional RI distribution (reconstructed using all projection angles) in LIEKKI Yb1200-10/125-DC 20 μm from the splicing point.

Download Full Size | PDF

 

Fig. 7. FD-BPM simulation of a fusion splice between a LIEKKI Yb1200-10/125-DC (left) and a SMF-28 (right). (a) Using the measured RI data and (b) using the ideal RI data without any perturbations. The splicing point is at $z=0\mathrm{mm}$. A fundamental guided mode of the LIEKKI Yb1200-10/125-DC core is used as the input at $z=-1.5\mathrm{mm}$. (c) Electric field amplitudes from (a) at the indicated positions.

Download Full Size | PDF

3. Experimental Results and Discussion

Figure 2(a) shows the RS profiles within 1.5 mm on the LIEKKI Yb1200-10/125-DC side and within 0.3 mm on the SMF-28 side, where the splicing point is located at $z=0\mathrm{mm}$. The fiber axial resolution is 0.49 μm and there are 3674 profiles utilized in the figure. The RS contains both mechanical and thermal components [15]. During the splicing process, the arc discharge heats the LIEKKI Yb1200-10/125-DC beyond its fictive temperature, relaxing both thermal and mechanical stress. Because the fiber is not held under tension, mechanical stress does not form upon cooling and only thermal stress remains. In Fig. 2(a), a stress transition region is observed in the LIEKKI Yb1200-10/125-DC over an axial length of $\sim 1.3\mathrm{mm}$, where the RS gradually changes from having thermal and mechanical components to thermal only. In this region, from left to right, the tensile stress in the outer cladding has become slightly compressive while the compressive stress in the core has become tensile. At approximately $z=-0.8\mathrm{mm}$ the tensile stress in the core has reached a maximum, after which it gradually decreases to the splicing point. This is due to the diffusion of ytterbium ions, which reduces the thermal expansion in the core. To visualize this effect more clearly, Fig. 2(b) displays RS profiles at indicated positions along the transition region.

Figure 3 shows the cross-sectional RS distribution (reconstructed using all projection angles) in the LIEKKI Yb1200-10/125-DC 20 μm from the splicing point, and is consistent with the profiles given in Fig. 2. Also, after splicing, the outer edge of the cladding has become round instead of octagonal due to the effects of surface tension as the fiber cools down from its liquid state. In general, this rounding phenomenon may have some effect on the pump modes in the cladding. However, this is beyond the scope of the present work.

The inserted figure on top of Fig. 2(a) shows the cross-sectional mean axial stress, ${\sigma }_{zm}$, along the LIEKKI Yb1200-10/125-DC from the far-zone, $z<-1.3\mathrm{mm}$, to the splicing point. ${\sigma }_{zm}$ is calculated using Eq. (1) [7]:

Employing the same method presented in [18], using the RS data from Fig. 2(a), the radial RI change $\mathrm{\Delta }{n}_r$ is calculated and shown in Fig. 4. From this figure, it is seen that the core RI is decreased by as much as $4\times {10}^{-4}$, which represents a 17.4% change compared to the unperturbed index difference, $\mathrm{\Delta }{n}_{\mathrm{cc}}\approx 2.3\times {10}^{-3}$. Furthermore, the affected fiber length is on the order of millimeters, or many hundreds of wavelengths within the core. Changes of this magnitude cannot be ignored when considering fusion splice characteristics for current LMA-SM-YDFs and their effect on YDFL and YDFA system performance will be appreciable. Still further, in future LMA-SM-YDFs, with even lower NAs, this effect will become more pronounced. Lastly, because these RI changes are mainly induced via relaxation of draw-induced stress, they will be exacerbated as draw speeds increase for high volume production.

Figure 5(a) shows the RI profiles within 1.5 mm on the LIEKKI Yb1200-10/125-DC side and within 0.3 mm on the SMF-28 side, where the splicing point is located at $z=0\mathrm{mm}$. The fiber axial resolution is the same as Fig. 2(a). In Fig. 5(a), a transition region with a length of $\sim 0.8\mathrm{mm}$ is observed in the LIEKKI Yb1200-10/125-DC. In the transition region, there are RI changes in both core and cladding regions. The cladding RI is uniformly increased due primarily to the relaxation of the isotropic component of frozen-in viscoelasticity formed via fiber manufacturing; however, the outer cladding RI is also increased due to the relaxation of tensile mechanical stress as shown in Fig. 4. The core RI is decreased due primarily to the diffusion of ytterbium ions, which results in a spreading out of RI; however, the core RI is also decreased due to the relaxation of compressive mechanical stress as shown in Fig. 4. Figure 6 shows the cross-sectional RI distribution (reconstructed using all projection angles) in the LIEKKI Yb1200-10/125-DC 20 μm from the splicing point, and is consistent with the profiles given in Fig. 5(a).

To visualize these effects more clearly, Fig. 5(b) displays RI profiles at indicated positions along the transition region. From this figure, we obtain the mean increase in cladding RI as $0.21\times {10}^{-3}$ and the maximum decrease in core RI as $1.53\times {10}^{-3}$. The core shape has become graded near the splicing point. Compared to the unperturbed value of $\sim 2.3\times {10}^{-3}$, $\mathrm{\Delta }{n}_{\mathrm{cc}}$ is decreased by as much as $1.74\times {10}^{-3}$, representing a 75.8% change. Once again, such RI changes over axial distances on the order of hundreds of wavelengths should not be ignored when analyzing the optical characteristics of fusion splices involving fibers of this type. In order to emphasize this point, the effects of the measured RI data will be investigated in the following simulation.

Using the measured RI data within 1.5 mm on the LIEKKI Yb1200-10/125-DC side and within 1.4 mm on the SMF-28 side and employing a FD-BPM [22], the propagation of the LIEKKI Yb1200-10/125-DC fundamental mode across the fusion splice is simulated at an operating wavelength of 1060 nm. The resulting electric field amplitude $|E(r,z)|$ is shown in Fig. 7(a). For comparison, we performed an identical simulation using ideal RI data taken from unperturbed measurements of the LIEKKI Yb1200-10/125-DC and the SMF-28 and the result is presented in Fig. 7(b). In both simulations, the radial node spacing $\mathrm{\Delta }r$ is 0.2 μm and the axial node spacing $\mathrm{\Delta }z$ is 1 μm. It is apparent that a larger percentage of fundamental mode energy is lost to radiation modes in Fig. 7(a) compared to 7(b). Also, in Fig. 7(a), significant mode transformation is observed in the RI transition region as marked in Fig. 5(a). Based on these results, the splice loss for cases (a) and (b) are calculated to be 1.37 dB (72.9% transmission, 27.1% loss) and 0.28 dB (93.7% transmission, 6.3% loss), respectively, using an overlap integral technique [23]. This indicates that an extra 20.8% of incident power is lost when RS/RI effects are considered for this example. Figure 7(c) illustrates the mode transformation associated with the RS/RI transition regions created by the splice process. From this figure, and assuming that both fields are reasonably described by a Gaussian function, the MFDs can be obtained by locating the radial positions where the field is 1/e times its maximum value. The MFD before the transition region is $\sim 10.6\mathrm{\mu m}$, which matches well with the nominal value supplied by the manufacturer of 11.1 μm, and $\sim 14.8\mathrm{\mu m}$ after the transition region. Therefore the RS/RI transition region results in a 39.6% change in MFD which in most cases cannot be ignored, especially for applications involving high-power all-fiber YDFLs and YDFAs. Regardless of which fiber the LIEKKI Yb1200-10/125-DC is spliced to, this RS/RI induced mode transformation effect will be present.

4. Conclusions

Recently, a state-of-the-art 3D-CSI measurement method was used to investigate RS and RI perturbations in LMA EDFs resulting from manufacturing, cleaving, and arc fusion splicing [18]. The method was found to be especially well-suited to investigations of this type, and the results indicated that the effects of fusion splicing are significant for LMA EDFs [18]. The results of the current investigation indicate, for the first time, that the effects of fusion splicing are even more prominent in LMA-SM-YDFs. The experiments are based on a commercial LMA-SM-YDF (LIEKKI Yb1200-10/125-DC) spliced to Corning SMF-28. Arc fusion splicing can relax both the anisotropic and isotropic components of frozen-in viscoelasticity as well as the mechanical component of RS. High splicing temperatures also result in heavy diffusion of core dopants. Together, these perturbations decrease the core/cladding RI difference by as much as $1.74\times {10}^{-3}$, representing a 75.8% change from the unperturbed fiber, over an axial distance of many hundreds of wavelengths.

Using an FD-BPM as a numerical tool, the optical effects of the aforementioned perturbations were simulated. For the measured sample, an extra 20.8% of incident power is lost when RS/RI effects are considered compared to the ideal situation without any perturbations. The transition region created by the RS/RI perturbations results in an expansion of the MFD by 39.6%. If not considered beforehand, this expansion will result in significant error in terms of expected splice loss. Because the performance of high-power all-fiber YDFLs and YDFAs depend heavily on this value, the results presented here are critically important for the design and optimization of such devices.