Abstract

We developed an all-fiber component with a signal feedthrough capable of combining up to 6 fiber-coupled multi-mode pump sources to a maximum pump power of 400 W at efficiencies in the range of 89 to 95%, providing the possibility of transmitting a high power signal in forward and in reverse direction. Hence, the fiber combiner can be implemented in almost any fiber laser or amplifier architecture. The complete optical design of the combiner was developed based on ray tracing simulations and confirmed by experimental results.

©2012 Optical Society of America

1. Introduction

For the realization of compact, reliable, rugged and efficient monolithic high power fiber laser systems, the efforts of integrating all-fiber components have been increased in recent years [1,2]. A key component of a highly integrated fiber laser or amplifier system is a high power all-fiber signal and pump combiner.

The most common type of fiber combiner, a fused tapered fiber bundle (TFB) [3,4], is based on the fiber end face pumping technique and is probably the most sophisticated pump combiner capable of handling several hundred watts of pump power [5]. A TFB with signal feedthrough consists of a central input signal fiber, guiding the signal light, surrounded by several multi-mode fibers, guiding the pump light, and an output pigtail double-clad (DC) fiber which combines the signal and pump light in a single pigtail fiber. In order to match the diameter of the fiber bundle to the diameter of the output pigtail fiber, the bundle is slowly melted and tapered. After the tapering process the fiber bundle is cleaved around the taper waist and fusion spliced to the output pigtail DC fiber. However, tapering of the fiber bundle inherently involves increasing the numerical aperture (NA) of the pump light and a change of the mode field diameter (MFD) of the signal light. Hence, the necessary optical matching and mechanical alignment requirements between the tapered fiber bundle and the output pigtail DC fiber can lead to several drawbacks of the TFB structure: (1) less flexibility in the choice of input fibers that match the output pigtail DC fiber after the tapering process, (2) a slight mismatch or misalignment between the signal mode field diameters (MFD) of the tapered input signal fiber and the output pigtail DC fiber leads to a degradation of the beam quality, primarily in conjunction with signal insertion loss, and (3) in the case of a backward propagating signal, e.g. for a counter-propagation pumped fiber amplifier, the signal insertion loss (up to 10%) can cause damage to the pump diodes due to their insufficient isolation against amplified signal light.

A more promising approach to overcome these problems is side-pumping technology, which involves coupling the pump light via the outermost cladding surface into the fiber. The key advantage of this technology is the uninterrupted signal core, eliminating the need for an additional fusion splice in conjunction with signal mode matching. In recent years several proposals for side-pumping of DC fibers have been reported, such as V-groove side pumping [6], a mirror embedded in the inner cladding of a DC fiber [7] or side-coupling by an angle polished pump fiber [8]. However, for most of these side-pumping configurations it is difficult to reach the mechanical accuracy required for a stable and efficient pump light coupling.

A more rugged approach is a monolithic all-fiber combiner like the GT-Wave coupler [9], the employment of a tapered capillary around a multi-clad fiber [10, 11] or direct fusion of one or more tapered multi-mode fibers to the outermost cladding of multi-clad fibers [1214]. In Ref [11] seven pump delivery fibers with a core diameter of 110 µm (NA 0.22) were combined and laterally coupled via a tapered capillary into a DC fiber with a core diameter of 400 µm (NA 0.46), which led to a combined pump power of 86 W with a coupling efficiency of ~80%. In Ref [13], direct lateral fusion of one tapered pump delivery fiber with a core diameter of 200 µm (NA 0.46) to a DC fiber of 250 µm (NA 0.46) led to a coupling efficiency of 90% at a pump input power of 120 W, furthermore, a pump delivery fiber with a diameter of 400 µm (NA 0.46) was used to couple a pump power of 300 W with an efficiency of 85% into a DC fiber with a diameter of 400 µm (NA 0.46). These impressive coupling efficiencies for one pump port were achieved by use of a straight and a tapered fiber section, allowing for highly efficient coupling of pump light rays with a high numerical aperture. Thus, in Ref [13] the impact of the straight fiber section on the side-pump coupling process was discussed. However, a review of the literature reveals that the impact of the fiber and taper parameters on the pump coupling behavior as well as the loss mechanism have not yet been investigated in detail for side-pumped combiners based on direct fusion of one or several tapered multi-mode fibers to the outermost cladding of a DC fiber.

We report detailed simulations and experiments for a component which combines up to 6 multi-mode fibers with a core diameter of 105 µm (NA 0.15 or 0.22) into a DC fiber with a cladding diameter of 250 µm (NA 0.46) via side-coupling. Firstly, we explain the principle of the optical design of the fiber combiner. For a fiber combiner with a single pump port, the achievable pump coupling efficiency and the corresponding loss mechanisms were investigated. For multiple pump ports, the simulations and experiments showed that with each additional pump port, the taper parameters need to be adjusted in comparison to a single pump port configuration. These simulation results can also be used as an estimation for fiber combiners, which combine one or several multi-mode fibers with a core diameter of 200 µm (NA 0.22) into a DC fiber with a cladding diameter of 400 µm (NA 0.46). Therefore, this work covers two important fiber combiner types, since active fibers with cladding diameters of 250 or 400 µm are typical sizes provided by fiber manufacturers and used for continuous wave and pulsed laser systems. In addition, we also investigated the signal feedthrough of the combiner. We demonstrated a low signal insertion loss, maintenance of an excellent signal beam quality and an efficient isolation of the pump diodes against signal light in the case of a reverse propagating signal. The preservation of the signal light properties by the fiber combiner was utilized in Ref [15] for the realization of a counter-propagation pumped single-frequency fiber amplifier with an amplified signal power of 300 W.

2. Optical design and relevant ray paths of the fiber combiner

A schematic side view of the side-pump combiner consisting of a pump feeding fiber (PFF), a coreless intermediate fiber (IF) and a target fiber (TF) is shown in Fig. 1 . The diameter of the PFF core and the cladding was 105 and 125 µm, respectively. The NA of the pure silica PFF core used in the simulations was 0.15, 0.22 or 0.3 and, therefore, the refractive index of the PFF cladding was depressed in comparison to the refractive index of the PFF core. The cladding of the PFF was surrounded by a polymer coating only for mechanical protection of the fiber. Therefore, the PFF preserved the same waveguide properties after removal of the polymer coating. In the case of side-pumping without an IF, the higher refractive index of the core of the PFF would suppress the pump power transfer into the TF as long as the PFF is untapered. An increase of the NA of the pump light due to tapering of the PFF would result in an increase of the pump power transfer, though only for rays that exceed the NA of the PFF core. Thus, it is especially difficult to couple pump light rays with a low NA into the TF. Unfortunately, this type of PFF is typically used as high power delivery fiber of pump diodes. To overcome this problem, without removing the glass cladding of the PFF, a coreless IF was inserted in the fiber combiner setup. At first the ~30 cm long IF with a cladding diameter of 125 µm was fusion spliced to the PFF. The IF had a NA of 0.46 due to the refractive index difference (Δn) between fused silica and the outermost polymer coating. After removing the polymer coating (e.g. with acetone) along a certain section of the IF (~15 mm), the IF was individually tapered, and afterwards the converging taper portion was laterally fused with the TF. The fusion level (FL) is defined as FL=(2z)/(dIF+dTF), where dIF and dTF are the cladding diameters of the IF and the TF at a certain taper position, respectively, and z represents the distance of the fused IF and TF, as depicted in Fig. 1. The FL was experimentally determined by measuring dIF, dTF and z at different positions along the converging taper portion with an optical microscope. With this measurement an averaged very low FL of 1.99 was determined, which was also used for the simulations. The overlap area between the TF and the IF is defined as the fusion zone. In contrast to the converging taper portion, the diverging taper portion of the IF was not fused to the TF, but placed under a small angle to the fiber axis of the TF, resulting in a small air gap between the IF and the TF. The employed TF was a DC fiber with a core diameter of 25 µm (NA 0.06) and a cladding diameter of 250 µm (NA 0.46). The cladding of the TF was also surrounded by a polymer coating, except along the coupling region of the combiner. The low index coating had to match the mechanical and additionally the optical properties of the DC fiber. An anchoring bond was used to fix the fiber bundle on each side on a copper substrate. Figure 1 shows the anchoring bond only on the right-hand side without the copper substrate. Additionally, the anchoring bond served as a pump light stripper for rays which do not satisfy the NA criterion of the TF.

 figure: Fig. 1

Fig. 1 Schematic side view of a side-pumped double-clad fiber including important ray paths.

Download Full Size | PPT Slide | PDF

Before proceeding with a more detailed investigation with the aid of simulations in the next section, we will qualitatively discuss some important ray paths of the fiber combiner. Pump light rays guided into the PFF and entering the tapered portion of the IF increase in NA as long as the rays propagate along the converging taper. As a rule of thumb, the pump light input NA increases by a factor of the taper ratio (TR), which is defined as the ratio of the original fiber diameter to the diameter of the taper waist. Pump light coupling into the TF occurs as soon the rays enter the fusion zone. The converging taper portion increases the probability for pump light transfer into the TF, since the number of ray-bounces along the lateral surface of the IF increases. Particularly, pump light rays with a low input NA couple more efficiently due to the converging taper.

Pump light rays remaining in the IF, and consequently not coupling into the TF, can occur as transmitted power (TP: transmitted power, Fig. 1) or power leakage into the ambient air (PAA: power leakage into the ambient air, Fig. 1). As long as the condition for internal total reflection is satisfied, the pump light rays are detected as TP, otherwise the rays escape into the ambient air as PAA. The angle of total internal reflection for the uncoated IF is 43.6°, since Δn between fused silica and air is 0.45 at a wavelength of 976 nm, which means the IF can guide light up to a theoretical NA of 1.05. Of course, the NA cannot exceed 1.0. Therefore, pump light rays with a theoretical NA in the range of more than 1.0 up to 1.05 would experience total reflection in the case of an existing fiber endface. Pump light rays which exceed the theoretical NA of 1.05 occur as PAA.

For almost loss-free pump light coupling into the TF it is necessary that the rays enter the TF before they exceed the cladding NA of the TF of 0.46. This desired coupling behavior can usually be achieved by adapting the taper parameters. However, pump light coupling for rays with an NA far above 0.46 cannot be completely suppressed. Unfortunately, this pump power leakage couple into the coating of the TF (PCT: power leakage into the coating of the target fiber) and can damage it.

In summary, the input pump power will be divided into the coupled pump power and the losses including PAA, PCT and TP (Fig. 1).

3. Fabrication

The IF was fusion spliced to the PFF with a filament splicing system (Vytran FFS-2000). A hydrogen-oxygen micro-flame was applied as heat source for tapering and lateral splicing of the IF. The working temperature for the tapering as well as the weak lateral splicing process of the IF was not measured but it can be assumed to be between the annealing and softening point of fused silica. The temperature adjusting was controlled by variation of the vertical distance between the fiber and the flame. Two precisely controlled motor stages were used to allow accurate alignment and tapering of the fiber(s). The heat source was placed at a fixed position in the center between the two motor stages. Each IF was individually tapered with a pulling speed of about 40 µm/s per motor stage and a fiber tension of about 10−2 N. After tapering, the IF was once twisted around the TF, which ensures that the converging taper portion remain in contact during lateral fusing. In case of a fiber combiner with several pump ports (see Section 5), the IFs were also individually tapered but simultaneously twisted around the TF. The final lateral fusion process along the converging taper portion was carried out at temperatures which allow sufficient softening of the tapered IF(s) and only slightly softening of the TF resulting in a weak fused component without any thermally induced damage of the core of the TF.

4. Simulations and experiments for a fiber combiner with a single pump port

The ray tracing simulations were carried out with the commercially available software Zemax (Radiant Zemax, LLC) in the non-sequential mode. Detailed information about ray tracing in tapered cylindrical fibers can be found in Ref [16] and [17]. The ray tracing method is applicable due to the large cross sections of the employed fibers compared to the applied wavelength of 976 nm. The 3-dimensional simulation model of the fiber combiner was based on the setup depicted in Fig. 1 with the approximation of a parallel fiber arrangement of the IF and TF. For the PFF a fully filled condition was always assumed, meaning that all possible pump light rays, independent of the NA and the transversal position in the fiber core, carry equal power. For the geometrical shape of the taper in the longitudinal direction, a simplified linear shape was assumed in the simulations, instead of the measured parabolic shape. As already mentioned, the FL was set to 1.99. Table 1 shows a summary of the fiber parameters used for simulations:

Tables Icon

Table 1. Overview of the fiber parameters.

4.1 Simulations of the pump coupling efficiency

The pump coupling efficiency in dependence of the converging taper length (TL) and the taper ratio (TR) of the IF for a PFF with an NA of 0.22 is depicted in Fig. 2(a) . The simulations show that an increasing TL leads to higher coupling efficiencies at a constant TR. For example at a constant TR of 6 a TL of 5 mm leads to a theoretical maximum pump coupling efficiency of 86%, whereas for a TL of 20 mm 96.4% were calculated. Furthermore, Fig. 2(a) shows that the TR can be reduced, if the TL is increased to maintain a certain coupling efficiency level. For instance, for a TL of 20 mm, a coupling efficiency of 85% can already be obtained at a TR of 2 instead of a TR of 5.5 at a TL of 5 mm. The improved coupling behavior at longer TLs can be explained by the increasing number of bounces of the pump light rays at the lateral surface of the converging taper portion. Hence, for shorter TLs it is necessary to taper more than for longer TLs in order to compensate for the shorter interaction length of the converging taper portion with the TF. The maximum theoretically obtainable pump coupling efficiency was limited to 97.3% due to different loss mechanisms, which will be discussed in Section 4.3.

 figure: Fig. 2

Fig. 2 (a) Pump coupling efficiency (CE) with respect to the taper ratio (TR) and the converging taper length (TL) and (b) a comparison of the pump coupling efficiencies without intermediate fiber (IF) and with IF for different fiber parameters, IF Ø: IF cladding diameter.

Download Full Size | PPT Slide | PDF

In the following section we discuss the impact of the intermediate fiber on the pump coupling efficiency and the taper parameters. Thus, for comparison the fiber combiner was also simulated without the IF, which means that the tapered PFF was directly connected to the TF, assuming the same FL and also a NA of 0.22. Figure 2(b) illustrates that the coupling efficiency can be increased and the TR reduced, if an IF is inserted between the PFF and the TF. For a TR of 2.5 at a TL of 20 mm the coupling efficiencies with and without IF are 61.2% and 90.1%, respectively. The moderate coupling efficiencies without the employment of an IF at low TR can be explained by the presence of a depressed refractive index of the cladding of the PFF, blocking the power transfer from the IF to the TF, as already discussed in Section 2. Thus, without IF, the pump light rays with a low NA cannot escape from the core of the PFF, and a considerable fraction of power will be transmitted via the diverging taper portion. A further increase of the pump light NA, due to the increase of the TR up to 10 at a TL of 20 mm for the PFF and the IF, results in a successive approximation of the pump coupling efficiencies. However, even at a TR of 10 and a TL of 20 mm (with IF) a 2.5% higher pump coupling efficiency can be obtained. That means for a hypothetical available input pump power of 1 kW, a reduction in power loss of 25 W can be essential to prevent thermal damage of the fiber combiner. Additionally, it must be taken into account that a TR of 10 corresponds to a considerable reduction of the mechanical stability due to the fiber diameter tapering from 125 µm to 25 µm. Furthermore, Fig. 2(b) clearly shows that the insertion of an IF with a TL of 10 mm already yields better pump coupling efficiencies than a PFF with a TL of 20 mm, especially for low TR.

A further increase of the pump coupling efficiency up to 97.8% can be realized by inserting an IF with a TL of 20 mm and diameter of 105 µm, which is perfectly adapted to the core diameter of the PFF, and thus, no pump brightness loss occurs. Note that for all of the following simulations and experiments, we only used the fiber component containing an inserted IF with a cladding diameter of 125 µm.

4.2 Simulations for the impact of the pump light input NA on the pump coupling efficiency

In the next simulation step we figure out, how the pump coupling efficiency changes with the pump light input NA depending on TR and TL. For these simulations three types of PFFs with a core NA of 0.15, 0.22 and 0.30 were investigated, assuming for each PFF a fully filled pump light condition. The TR was considered in the range from 1 to 10 at a TL of 5 mm (Fig. 3(a) ) and 20 mm (Fig. 3(b)). From both figures it can be seen that at lower TRs the coupling efficiency increases with NA, since the pump light rays with a higher NA have more bounces with the lateral surface of the converging taper portion. However, the pump coupling behavior changes with increasing TR, since a TR of much higher than 2 leads to pump light rays with a NA far above 0.46, which cannot couple into the TF, if the TL is too short. The occurring pump power losses will be discussed in Section 4.3. E.g., for a low TL of 5 mm and a TR of 7 the coupling efficiency for an input NA of 0.15 was simulated to be 10% higher than for an input NA of 0.30. In contrast, with a longer TL of 20 mm the coupling efficiency seems to be less sensitive to variations of the pump light input NA. Thus, it appears that for the combiner design, the pump coupling efficiency should not be significantly influenced by the pump light input NA in the range of 0.15 to 0.30, if a sufficient TL is considered.

 figure: Fig. 3

Fig. 3 Pump coupling efficiency with respect to the taper ratio at a converging taper length of (a) 5 mm and (b) 20 mm for a PFF with a pump light input NA of 0.15, 0.22 and 0.30.

Download Full Size | PPT Slide | PDF

If the pump light input NA gets closer to the NA of the TF of 0.46, it can be advantageous to use a straight IF portion in addition to the converging taper to obtain a highly efficient pump light transfer into the TF as described in Ref [13]. An alternative approach to the straight IF portion is an increased TL, i.e. for a pump light input NA of 0.46 a theoretical pump coupling efficiency of about 90% can be achieved, if the TL is at least 40 mm.

4.3 Simulations for the loss mechanism of the fiber combiner

As already discussed in Section 2, the total power loss is the sum of TP, PAA and PCT (Fig. 1). In this section we will quantitatively determine the power fraction of the different loss mechanisms to gain a better estimate of the resulting thermal load of the fiber combiner. To understand this approach, we first discuss the effect of the different loss mechanisms. The TP pump power loss is less critical, because this power fraction can be easily removed from the fiber component via the IF. The PAA is also less critical, since this power fraction can be handled by an air or water cooled combiner housing. The most critical pump power loss, PCT, is caused by NA-mismatched light, which couples into the coating of the TF and damages the fiber coating at a certain power level.

Figure 4(a) and 4(b) shows the three different pump power losses (TP, PAA, PCT) and the total pump power loss as a percentage of the input pump power for TL of 5 and 20 mm, depending on the TR. In the simulations the core NA of the PFF was 0.22 and fully filled pump light condition of the PFF core was assumed. It should be noted that for comparison, the axis of ordinates in Figs. 4(a) and 4(b) are scaled differently for a more comprehensive presentation of the results. In general, it can be seen that the total and individual losses are larger for a TL of 5 mm compared to a TL of 20 mm. For both TLs it turns out that the TP-fraction decreases and the PCT-fraction as well as the PAA-fraction increases with TR. As a result, the total power loss decreases with increasing TR. A closer analysis of the PCT-curve reveals that PCT loss does not exist below a TR of 2, since the pump light input NA of 0.22 will be approximately increased by the factor of the TR [18], and therefore cannot exceed the cladding NA of the TF of 0.46. Thus, the fraction of PCT can be reduced by choosing a low TR with a still acceptable total power loss. This means that the TR must be carefully adapted to satisfy the trade-off between a high pump coupling efficiency and a low power fraction of PCT to avoid optically induced damage of the fiber component during high power operation. This must always be accompanied by a sufficient converging taper length.

 figure: Fig. 4

Fig. 4 The loss mechanism and the total pump power loss of the fiber combiner for (a) a TL of 5 mm and (b) a TL of 20 mm at different taper ratios. The losses in percent were calculated with respect to the total input pump power. Please see Fig. 1 for TP, PCT and PAA.

Download Full Size | PPT Slide | PDF

For example, if the TR is set to 7 for a TL of 5 and 20 mm, respectively, the theoretical PCT is 7.7 and 1.2% of the input pump power. The PCT value of 1.2% at a TL of 20 mm can be further reduced to 0.6% by changing the TR from 7 to 4 in conjunction with an acceptable total power loss of just 5%. Hence, if 1 kW of input pump power is assumed, the resulting power handling for the coating of the TF and the pump light stripper can be reduced from 77 W (TL 5 mm, TR 6) to 6 W (TL 20 mm, TR 4) by adapting the TL and the TR.

The simulations indicate that the minimum total power loss cannot be reduced below 2.7% for a TL greater than 20 mm up to a TL of 50 mm and a FL of 1.99. One reason for the residual losses can be pump light rays with a high NA, which propagate along an unfavorable plane of the IF and do not enter the fusion zone. These rays leave the waveguide (PAA) structure after sufficient bounces along the lateral taper surface. In addition, rays with an extremely low NA, and consequently less bounces with the lateral surface of the converging taper portion, can occur in the form of TP. Furthermore, longer TLs lead to an increased probability that some rays will reverse couple from the TF into the IF.

Moreover, the simulations reveal that a lower FL-value, which means stronger fusing of the fibers, leads to a decrease of the total power loss. The exact reduction of the total power loss depends on the fiber and taper parameters. For a TL of 20 mm and a TR of 6, the simulated total power losses could be reduced from 4% to 2% when decreasing the FL from 1.99 to 1.93. The simulations indicate that for FLs below 1.93 the total power loss increase again.

4.3.1 Impact of pump light input NA on the power leakage into the coating of the TF (PCT)

The simulations in Section 4.2, Fig. 3(b) showed that a sufficient TL leads to pump coupling efficiencies of more than 90%, almost independent of the pump light input NA. Considering the losses, the simulation also shows that the PCT-fraction is strongly influenced by the pump light input NA. Figure 5 clearly reveals that for a TL of 20 mm and a TR of 6, the PCT-fraction increases by about 6 times for a NA of 0.3 compared to a NA of 0.15. Hence, it is possible to achieve almost the same coupling efficiency for a pump light input NA of 0.15 and 0.3 (see Fig. 3(b)), but with a significant difference in risk of optically induced damage to the fiber component. However, PCT can be further reduced by increasing the TL.

 figure: Fig. 5

Fig. 5 The ratio of power leakage into the cladding of the target fiber (PCT) to the total input pump power against the taper ratio for a TL of 20 mm.

Download Full Size | PPT Slide | PDF

4.4 Experimental results

In order to verify the simulations, two fiber combiners with a single pump port based on the setup described in Section 2 were developed. For the first combiner an IF with a low TR of 2.6 and a short TL of 9.5 mm was fabricated. In the case of the second combiner the TR and the TL were increased to 6.7 and 18 mm, respectively. For both combiners the geometrical dimensions of the obtained tapered IFs were measured with an optical microscope. After completion of the fabrication, both combiners were optically characterized. Therefore, each PFF (pump port) with a NA of 0.15 was connected to a pump diode (Oclaro BMU25) with a pigtail fiber delivering a maximum output power of ~25 W at a wavelength of 976 nm. The delivery fiber of the pump diode had parameters identical to the PFF.

The experimental results for the first fiber combiner are shown in Fig. 6(a) . Due to the low TR of 2.6, an experimental pump coupling efficiency of only 74% was achieved. The residual pump power was almost completely measured as TP, with a power fraction of 25.3%. The simulations for the coupled as well as the TP show good agreement with the experimental results, and confirm that in the case of a low TR of 2.6, the pump power is only divided into coupled power and TP. In Fig. 6(a) it can be seen that in the simulations the sum of the coupled and TP is 99.9%, corresponding to 0.1% of pump light rays not detected in the simulations. This can be treated as a simulation error. That the measured sum of coupled pump power and TP is only 99.3% can be explained by measurement uncertainties, marginal splice losses and additional power losses in the fiber component caused by dust particles. Since the thermal load of this fiber combiner design is negligible it would be feasible to couple several kW of pump power, but with the disadvantage of a moderate coupling efficiency of about 75% and consequently a undesirable overall efficiency for high power laser system.

 figure: Fig. 6

Fig. 6 Coupled and transmitted power measured for a fiber combiner with one pump port with (a) a TL of 9.5 mm (TR of 2.6) and (b) a TL of 18 mm (TR 6.7), * ratio of coupled or transmitted power to total diode power in percent.

Download Full Size | PPT Slide | PDF

For the second fiber combiner, depicted in Fig. 6(b), a higher pump coupling efficiency of 95.2% (96.0% in simulation) was measured as compared to the first combiner presented in Fig. 6(a) due to the increase in TR and TL. Following the simulations the residual pump power of 4% can be divided into TP, PCT and PAA with 2.4%, 0.6% and 0.9%, respectively. Again, the missing pump power of 0.1% was associated with an error owing to undetected power in the simulations. For the TP a fraction of 2.3% was measured and shows very good agreement with the simulation (2.4%), i.e. more than 50% of the total power loss was TP. This fraction of power represents no risk for damage to the fiber component. Due to the excellent agreement between simulation and experiment, the simulated PCT-fraction of only 0.6% is a good value for an estimate of the thermal load of the coating of the TF. Based on the simulations and experiments an error of less than 1% of the pump input power can be assumed for the PCT-fraction.

Unfortunately, the power fractions PAA and PCT are difficult to measure and therefore could not be experimentally determined. In future work an indirect measurement of PCT will be realized by measuring the coating temperature of the TF. In summary, the simulations describe the coupling efficiency as well as the fraction of TP very well, and thus, serve as a very good estimation for the fraction of PCT and PAA.

5. Simulations and results for a multi pump port configuration

So far, the modeling results consider a TF with only a single pump port. However, for monolithic high power fiber laser and amplifier systems, it is often required to provide multiple pump ports due to the limited output power of available fiber coupled pump diodes and the efforts to develop laser systems with redundancy. Thus, in this section, we investigate the impact of multiple pump ports on the coupling efficiency and the loss mechanism. The setup of each pump port of the combiner is identical to the description in Section 2 (see Fig. 1), but with several additional ports placed around the cladding of the TF, leading to a fiber bundle. A schematic of a fiber combiner with multiple pump ports is shown in Fig. 7 .

 figure: Fig. 7

Fig. 7 Fiber combiner with multiple pump ports, PFF: pump feeding fiber with a piece of coreless intermediate fiber (IF) as described in Fig. 1, TF: target fiber, TP: transmitted power.

Download Full Size | PPT Slide | PDF

5.1 Simulations of the pump coupling efficiency

The experiments and simulations in Section 4 showed that for a pump combiner with a single pump port, a TL of 20 mm and a TR of 6 yields an excellent coupling efficiency in the range of 95%. In comparison, for a fiber component with multiple pump ports, the simulations for a TL of 20 mm (Fig. 8(a) ) revealed that the pump coupling efficiency of the combined pump power depends on the number of pump ports and significantly on the choice of the TR. In the simulations the input pump light NA of the PFFs was 0.22. In general, it can be seen that the pump coupling efficiency decreases with each additional pump port. A lower TR yields a greater decrease of the pump coupling efficiency with each additional pump port than a higher TR. In the case of a TL of 20 mm and a TR of 2.5, the theoretically obtainable pump coupling efficiency of almost 90% decreases to 73%, if the number of pump ports increases from 1 to 6. However, as already mentioned, the increasing losses due to additional pump ports can be reduced with increasing TR. In Fig. 8(a) it can be clearly observed that for 6 pump ports and a TR of 6, a pump coupling efficiency of 90.2% can be achieved. For a TR higher than 6, it is not possible to achieve a significant improvement in pump coupling efficiency for multiple pump ports by increasing of the TR.

 figure: Fig. 8

Fig. 8 Simulated coupling efficiency for a pump combiner with up to 6 pump ports for (a) a TL of 20 mm and (b) a TL of 10 mm for a pump light input NA of 0.22.

Download Full Size | PPT Slide | PDF

For a single pump port configuration it is already known that the pump coupling efficiency decreases with shorter TLs at constant TRs (Fig. 2(a)). However, for multiple pump ports a reduction of the TL leads to the advantage that the pump coupling efficiency of the combined pump power decreases less with each additional pump port, especially at lower TRs. The simulation results for a TL of 10 mm instead of a TL of 20 mm are presented in Fig. 8(b). A comparison of Fig. 8(a) and 8(b) shows: If the number of pump ports is increased from 1 to 6 at a TR of 2.5, the pump coupling efficiency experiences a decrease of 16.9 and 11.2% for a TL of 20 and 10 mm, respectively. Although the total power losses for a TL of 10 mm are higher than for a TL of 20 mm, the example reveals, that the decrease of the pump coupling efficiency due to additional pump ports can be reduced by using shorter TLs.

Besides having less available combined pump power, the additional pump power losses generated in comparison to a fiber combiner with a single pump port, corresponds to an enhanced risk of damaging the component due to additional thermal load. Hence, the loss mechanism for a fiber combiner with multiple pump ports needs to be investigated in more detail.

5.2 Simulations of the loss mechanism caused by additional pump ports

As already discussed, the total power loss is comprised of TP, PAA and PCT. Since a TL of 20 mm and a TR of 6 seem to be promising parameters for a fiber combiner with multiple pump ports, Fig. 9 illustrates the behavior of the 3 different loss mechanisms and the total power loss against the number of pump ports. The input pump light NA of the PFFs was 0.22. The simulations clearly show that the TP-fraction as well as the PAA-fraction increase with the total power loss, and the PCT-fraction stays almost constant. The NA-mismatched pump light, which couples into the coating of the target fiber (PCT) can be kept below 1.7%, even up to 6 pump ports. Hence, an increasing number of pump ports and, therefore, scaling of the combined pump power results in additional power losses, but with an insignificant increase of thermal load to the coating of the TF. Of course, due to an increased PAA the combiner housing would be exposed to a higher thermal load, but this can be handled by an adequate thermalconcept. The increased PAA can be explained by pump light rays which couple back from the TF into one of the IFs, further propagate in the converging taper portion of the IF, increase in NA and undergo refraction into the ambient air. The increase of the TP-fraction with additional pump ports can be caused by pump light rays with a low NA which reverse couple into one of the IFs and further propagate there.

 figure: Fig. 9

Fig. 9 Simulated losses for a pump combiner with a TL of 20 mm and a TR of 6 providing up to 6 pump ports. Please see Fig. 1 for TP, PCT and PAA.

Download Full Size | PPT Slide | PDF

Finally, the simulations show that the total pump power loss increases with each additional pump port but the PCT, resulting in thermal load of the TF, does not increase significantly compared to a fiber combiner with a single pump port. In general, for the optical design of a side-pumped coupler with multiple pump ports, a TL as short as possible in conjunction with a TR as low as possible, but still satisfying the required pump coupling efficiency for the desired number of pump ports, ensures efficient pump light combining with low power losses. In contrast, for a single pump port, a longer TL in conjunction with a low TR is advantageous for increasing the pump coupling efficiency and reducing PCT-losses in particular.

5.3 Experimental characterization of pump combiners with multiple pump ports

Since the simulation results indicate that a TL of 20 mm and a TR of 6 are useful taper parameters, fiber combiners with two, four and six pump ports were developed. Each pump port consisted of an IF with a measured TL of 18 mm and a measured TR of 6.7. Each PFF had a NA of 0.15, and to characterize the combiner was connected to a pump diode (Oclaro BMU25) with a pigtail fiber delivering a maximum output power of about 25 W at a wavelength of 976 nm. The delivery fiber of the pump diode had parameters identical to the PFF.

Figure 10(a) shows the total diode power with respect to the combined pump power and TP for a fiber combiner with four pump ports. For the combined pump power a coupling efficiency of 92% (93.1% in the simulation) was measured, and the fraction of TP was 3.6% (3.9% in the simulation) compared to the total diode power. Thus, the measured TP of 3.6% was 45% of the total power loss of 8% (Fig. 10(a)). Based on the good agreement between simulation and experiments it can be assumed that the PCT-fraction and PAA-fraction were about 0.6% and 2.3% of the total diode power, respectively.

 figure: Fig. 10

Fig. 10 (a) Combined and transmitted power measured for a fiber combiner with 4 pump ports and (b) combined pump power measured for a fiber combiner with 6 pump ports, * ratio of coupled or transmitted power to total diode power in percent.

Download Full Size | PPT Slide | PDF

Microscope images of the top view and of the cross section view, close to the taper waist, of a fiber combiner with 4 pump ports are depicted in Fig. 11(a) and 11(b).

 figure: Fig. 11

Fig. 11 Microscope image of (a) the top view and (b) the cross section view of a fiber combiner with 4 pump ports.

Download Full Size | PPT Slide | PDF

The experimental results of a developed six pump port fiber combiner with a combined pump power of 141.5 W and an obtained coupling efficiency of 89.6% (91.1% in the simulations) is shown in Fig. 10(b). The fiber combiner with six pump ports was limited by the available pump power and not by thermal problems. For the combiner presented in Fig. 10(b), Fig. 12(a) shows the pump coupling efficiency of each individual pump port with a maximum and minimum pump coupling efficiency of 90.2 and 88.8%. The difference of only 1.4% indicates a very homogeneous fiber bundle structure, and supports the assumption of identical optical behavior of the individual pump ports.

 figure: Fig. 12

Fig. 12 (a) Pump coupling efficiency of the individual pump ports of the six pump port fiber combiner presented in Fig. 10(b) and 10(b) comparison of the experimentally achieved pump coupling efficiencies with the simulation results for fiber combiners with multiple pump ports.

Download Full Size | PPT Slide | PDF

An overview of the experimentally obtained coupling efficiencies with the corresponding simulation results for a fiber combiner with 1, 2, 4 and 6 pump ports is depicted in Fig. 12(b). An agreement of the experimental and simulated results within 1% confirms the applicability of the simulation approach for multiple pump ports. For each fiber combiner a TL of 18 mm, a TR of 6.7 and a PFF with a core NA of 0.15 was applied.

6. Demonstration of 440 W pump power handling

After detailed theoretical and experimental characterization of fiber combiners with multiple pump ports, a pump power handling performance test was conducted. For these investigations each pump port of a 4 + 1x1 combiner was connected to a fiber coupled pump diode (nLight Pearl) with an output power of ~110 W at a wavelength of 976 nm. The PFF and the delivery fiber of the pump diode had a core diameter of 105 µm with a NA of 0.22. At each fiber output end of the IF, a pump light stripper was applied to avoid the Fresnel reflection of the TP, and therefore the TP was not measured. Up to the maximum total pump diode power of 440 W, a coupling efficiency of 90.2% was experimentally determined (Fig. 13 ). In the simulations a slightly higher coupling efficiency of 92.8% was obtained. The difference of 2.6% in simulated and measured pump light coupling must be distributed among TP, PAA and PCT, with simulated values of 3.0, 1.4 and 1.7%, respectively. It can be assumed that the PAA-fraction is higher than 1.4%, since the fibers of the combiner are contaminated with dust particles in spite of intensive cleaning. If we assume for each individual loss mechanism an error of 1% related to the total diode power then PCT was 7.5 W ± 4.4 W, i.e. the coating of the TF and the pump power stripper had to handle this fraction of power.

 figure: Fig. 13

Fig. 13 Combined pump power for a 4 + 1x1 high power fiber combiner, * ratio of coupled power to total diode power in percent.

Download Full Size | PPT Slide | PDF

7. Signal feedthrough of the fiber combiner

Besides the pump power handling and the pump coupling efficiency of a fiber combiner, it is important for fiber laser and amplifier applications to maintain the optical properties of the signal light propagating through the fiber combiner. In particular, during the fabrication of the fiber component, externally induced mechanical stress and perhaps a marginal fraction of thermal diffusion of the core dopants [19] can result in a high signal insertion loss in conjunction with a degradation of the signal beam quality. This behavior was expected for large mode area DC fibers with a very low core refractive index (NA ~0.06), and therefore possible beam quality degradations of the signal feedthrough light was investigated (in Section 7.1).

The uninterrupted signal core in the fiber combiner provides the possibility of passing a signal beam through the combiner in forward and backward direction. However, in the case of a backward propagating signal, the pump diodes need sufficient protection against the signal. Thus, in Section 7.2 we investigate the signal to pump isolation of a 4 + 1x1 combiner in a fiber amplifier setup.

7.1 Signal insertion loss and beam quality

In order to determine possible beam quality degradation and a signal insertion loss caused by the signal feedthrough of the combiner, the setup depicted in Fig. 14 was used. A signal at a wavelength of 1064 nm was launched into the core of a 2.75 m long Ytterbium-doped DC fiber (Nufern YDF-25/250), which is specified with a signal core diameter of 25 µm (NA 0.06) and a pump core diameter of 250 µm (NA 0.46). Thus, the parameters of the passive TF of the combiner were matched to the active fiber. The coiling diameter of the active fiber was 12 cm to maintain near diffraction limited beam quality [20]. The transmitted signal had a power of about 200 mW and was propagating in reverse direction through the fiber combiner. The beam quality measurements were carried out with a Fabry-Perot ring-cavity. With this cavity it was possible to determine the power fraction in higher-order transversal cavity modes with respect to the Gaussian TEM00 mode by scanning the length of the ring-cavity over a free spectral range (FSR). A detailed description of the measuring setup can be found in Ref [21]. Due to the use of a polarization sensitive beam quality measurement, a half- and a quarter-wave retardation plate in conjunction with a polarization beam splitter (PBS) were used. The determined polarization extinction ratio was better than 17 dB after the propagation of the signal through the active fiber and the fiber combiner.

 figure: Fig. 14

Fig. 14 Setup for beam quality measurements, TF: target fiber, PBS: polarization beam splitter.

Download Full Size | PPT Slide | PDF

Before the fusion splice between the active fiber and the 4 + 1x1 combiner, the power in higher-order modes of the active fiber was determined. This measurement served as a reference beam quality for the active fiber. The mode scan in Fig. 15(a) shows the logarithmic normalized intensity over a free spectral range for the reference beam with a power in higher-order modes of 3.1%. This results in a fundamental fiber mode power of at least 96.9% for the reference beam. For the signal feedthrough of the fiber combiner, a power in higher-order modes of only 5.1% was found (Fig. 15(b)).

 figure: Fig. 15

Fig. 15 Normalized transmitted intensity through a premode cleaner as a function of the ring-cavity length in units of a free spectral range for (a) the reference beam and (b) the signal feedthrough beam of a 4 + 1x1 combiner.

Download Full Size | PPT Slide | PDF

Consequently, the signal feedthrough fiber (0.7 m long TF) only led to an increase in power in higher-order transversal modes of maximal 2%. Furthermore, it must be considered that additional power transfer to higher-order transversal modes can also be caused by the fusion splice between the active DC fiber and the TF. Hence, good preservation of the signal beam quality, in conjunction with the low signal insertion loss of less than 3%, provides an excellent high power fiber component for monolithic fiber laser and amplifier systems.

7.2 Signal to pump isolation

The signal to pump isolation (SPI) is defined as the ratio of the amplified signal power to the signal power, which propagates in the PFF towards the pump diodes. The SPI is especially important if the signal propagates through the fiber combiner in reverse direction. In this case, it is necessary to obtain sufficient signal light protection for the pump diodes. To investigate SPI, a slightly modified setup of Fig. 14 was used as shown in Fig. 16 . A 2.5 m long active fiber (Nufern YDF-25/250) was seeded with a signal power of ~1 W at a wavelength of 1064 nm. The active fiber was coiled with a diameter of 10 cm. For counter-propagating pumping of the amplifier only two pump ports of the 4 + 1x1 combiner were used. The pump power for each pump port was about 20 W at a central wavelength of 976 nm. The remaining two pump ports were used to determine the SPI in dependence of the amplifier output power. A dichroic mirror was inserted to measure at each pump port only the signal light and not the reverse propagating pump light.

 figure: Fig. 16

Fig. 16 Setup for the signal to pump isolation measurement of port 3 and 4, TF: target fiber, TP: transmitted pump power of the fiber combiner.

Download Full Size | PPT Slide | PDF

The SPI depends on the fraction of power propagating in the cladding of the active DC fiber. Thus, besides the signal insertion loss of the fiber combiner itself, SPI depends on the losses due to fiber coiling of the active DC fiber [18], the mode field adaptation between the active DC fiber and TF of the combiner, the quality of the fusion splice, the free-space coupling of the seed signal and additionally the fraction of amplified spontaneous emission (ASE).

The determined SPI with respect to the amplified signal power for the four pump ports is shown in Fig. 17 . A SPI between 27 and 32 dB was obtained for amplified signal powers between 4 and 18 W. The ASE suppression of the fiber amplifier was 35 dB. The decrease of the SPI at low amplified signal power can be explained by a constant fraction of seed power coupled into the cladding of the active fiber due to free space coupling. In our experiment, an isolation of more than 27 dB was sufficient to protect the pump diodes against optically induced damage. In Ref [15] such a 4 + 1x1 high power combiner was used in a counter-pumped fiber amplifier configuration up to an average output power of 300 W, revealing a SPI in the range of 30 dB. Isolation values above 30 dB are feasible by optimization of all parameters influencing the signal to pump isolation, for example, a slight increase of the coiling diameter with a still acceptable beam quality.

 figure: Fig. 17

Fig. 17 Signal to pump isolation (SPI) of the 4 pump ports in respect to the amplified signal power. The measurement data were connected by lines for clarity.

Download Full Size | PPT Slide | PDF

A further improvement of SPI as well as beam quality, especially in the case of counter-propagation pumping, can be realized by direct lateral fusion of the IFs to an active fiber avoiding the fusion splice at the high power output of the active fiber. In addition, the reduction of the fiber length leads to less fiber nonlinearities for continuous wave single-frequency and pulsed laser systems.

8. Conclusion

In conclusion, an advanced optical design of an all-fiber high power fiber combiner, based on side-coupling, was presented. Six fiber coupled pump diodes, with a total pump power of 150 W, were combined with an efficiency of 89.6%. The maximum power handling of 440 W with a pump coupling efficiency of 90.2% was achieved for a fiber combiner with four pump ports. Even a fiber combiner with a single pump port results in a pump coupling efficiency of 95%. The experimental results show excellent agreement with the ray tracing simulations. The analysis of the pump light loss mechanisms of the fiber combiner indicates that the thermal load, in form of power leakage into the coating of the target fiber (PCT), can be less than 2% of input pump power independent of the number of pump ports. The signal feedthrough characterization revealed a signal insertion loss of less than 3%, a signal to pump isolation (SPI) of more than 27 dB and an excellent preservation of the signal beam quality. Hence, the developed fiber component meets the requirements for efficient pump light combining as well as high power signal transmission in forward and in reverse direction as presented in Ref [15]. Consequently, this fiber combiner offers the potential to realize monolithic fiber laser systems with output power levels in the kilowatt range.

Acknowledgments

We would like to thank the Albert Einstein Institute Hannover for the successful cooperation in the field of single-frequency laser systems. We also thank the German Research Foundation (DFG) for funding the Cluster of Excellence “Centre for Quantum Engineering and Space-Time Research” (QUEST).

References and links

1. D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007). [CrossRef]  

2. C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W, single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett. 36(5), 618–620 (2011). [CrossRef]   [PubMed]  

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

4. C. Headley III, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005). [CrossRef]  

5. A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007). [CrossRef]  

6. D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995). [CrossRef]  

7. J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003). [CrossRef]  

8. F. Hakimi and H. Hakimi, “A new side coupling method for double-clad fiber amplifiers,” Conf. Lasers and Electro-Optics, 116 (2001).

9. A. B. Grudinin, D. N. Payne, P. W. Turner, L. J. A. Nilsson, M. N. Zervas, M. Ibsen, and M. K. Durkin, “Multi-fiber arrangements for high-power fiber lasers and amplifiers,” U.S. Patent 6826335, (2004).

10. F. Gonthier, “Novel designs for pump and signal fiber combiners,” Proc. SPIE 7580, 758019, 758019-6 (2010). [CrossRef]  

11. C. Jauregui, S. Böhme, G. Wenetiadis, J. Limpert, and A. Tünnermann, “Side-pump combiner for all-fiber monolithic fiber lasers and amplifiers,” J. Opt. Soc. Am. B 27(5), 1011–1015 (2010). [CrossRef]  

12. V. P. Gapontsev and I. Samartsev, Coupling arrangement between a multi-mode light source and an optical fiber through an intermediate optical fiber length,” U.S. Patent 5999673 (1999).

13. Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007). [CrossRef]  

14. F. Gonthier, M. Garneau, and N. Vachon, “Multimode fiber outer cladding coupler for multi-clad fibers,” US Patent 7933779 B2 (2011).

15. T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012). [CrossRef]  

16. C. T. Chang and D. C. Auth, “Radiation characteristics of a tapered cylindrical optical fiber,” J. Opt. Soc. Am. 68(9), 1191–1196 (1978). [CrossRef]  

17. W. T. Welford, Aberrations of Optical Systems (IOP Publishing Ltd, 1986), Chap. 2, 4 and 5.

18. Y. F. Li and J. W. Y. Lit, “Transmission properties of a multimode optical-fiber taper,” J. Opt. Soc. Am. A 2(3), 462–468 (1985). [CrossRef]  

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

20. M.-J. Li, X. Chen, A. Liu, S. Gray, J. Wang, D. T. Walton, and L. A. Zenteno, “Limit of Effective Area for Single-Mode Operation in Step-Index Large Mode Area Laser Fibers,” J. Lightwave Technol. 27(15), 3010–3016 (2009). [CrossRef]  

21. P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007). [CrossRef]   [PubMed]  

References

  • View by:

  1. D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
    [Crossref]
  2. C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W, single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett. 36(5), 618–620 (2011).
    [Crossref] [PubMed]
  3. D. J. DiGiovanni and A. J. Stentz, “Tapered fiber bundles for coupling light into and out of cladding-pumped fiber devices,” U.S. Patent 5864644 (1999).
  4. C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
    [Crossref]
  5. A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007).
    [Crossref]
  6. D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
    [Crossref]
  7. J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
    [Crossref]
  8. F. Hakimi and H. Hakimi, “A new side coupling method for double-clad fiber amplifiers,” Conf. Lasers and Electro-Optics, 116 (2001).
  9. A. B. Grudinin, D. N. Payne, P. W. Turner, L. J. A. Nilsson, M. N. Zervas, M. Ibsen, and M. K. Durkin, “Multi-fiber arrangements for high-power fiber lasers and amplifiers,” U.S. Patent 6826335, (2004).
  10. F. Gonthier, “Novel designs for pump and signal fiber combiners,” Proc. SPIE 7580, 758019, 758019-6 (2010).
    [Crossref]
  11. C. Jauregui, S. Böhme, G. Wenetiadis, J. Limpert, and A. Tünnermann, “Side-pump combiner for all-fiber monolithic fiber lasers and amplifiers,” J. Opt. Soc. Am. B 27(5), 1011–1015 (2010).
    [Crossref]
  12. V. P. Gapontsev and I. Samartsev, Coupling arrangement between a multi-mode light source and an optical fiber through an intermediate optical fiber length,” U.S. Patent 5999673 (1999).
  13. Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
    [Crossref]
  14. F. Gonthier, M. Garneau, and N. Vachon, “Multimode fiber outer cladding coupler for multi-clad fibers,” US Patent 7933779 B2 (2011).
  15. T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012).
    [Crossref]
  16. C. T. Chang and D. C. Auth, “Radiation characteristics of a tapered cylindrical optical fiber,” J. Opt. Soc. Am. 68(9), 1191–1196 (1978).
    [Crossref]
  17. W. T. Welford, Aberrations of Optical Systems (IOP Publishing Ltd, 1986), Chap. 2, 4 and 5.
  18. Y. F. Li and J. W. Y. Lit, “Transmission properties of a multimode optical-fiber taper,” J. Opt. Soc. Am. A 2(3), 462–468 (1985).
    [Crossref]
  19. M. Kihara, M. Matsumoto, T. Haibara, and S. Tomita, “Characteristics of thermally expanded core fiber,” J. Lightwave Technol. 14(10), 2209–2214 (1996).
    [Crossref]
  20. M.-J. Li, X. Chen, A. Liu, S. Gray, J. Wang, D. T. Walton, and L. A. Zenteno, “Limit of Effective Area for Single-Mode Operation in Step-Index Large Mode Area Laser Fibers,” J. Lightwave Technol. 27(15), 3010–3016 (2009).
    [Crossref]
  21. P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007).
    [Crossref] [PubMed]

2012 (1)

T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012).
[Crossref]

2011 (1)

2010 (2)

2009 (1)

2007 (4)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007).
[Crossref] [PubMed]

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007).
[Crossref]

2005 (1)

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

2003 (1)

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[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]

1995 (1)

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

1985 (1)

1978 (1)

Alam, M.

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

Andrejco, M. J.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

Auth, D. C.

Böhme, S.

Brar, K.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

Chang, C. T.

Chen, X.

Dajani, I.

Danzmann, K.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007).
[Crossref] [PubMed]

DiGiovanni, D. J.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

Faucher, M.

A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007).
[Crossref]

Fishteyn, M.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

Glick, Y.

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

Goldberg, L.

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

Gonthier, F.

F. Gonthier, “Novel designs for pump and signal fiber combiners,” Proc. SPIE 7580, 758019, 758019-6 (2010).
[Crossref]

Gray, S.

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]

Headley, C.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

Jauregui, C.

Katz, O.

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[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]

Kliner, D. A. V.

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

Koplow, J. P.

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

Koplowitch, T.

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

Kracht, D.

T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012).
[Crossref]

Kwee, P.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007).
[Crossref] [PubMed]

Lavi, R.

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

Li, M.-J.

Li, Y. F.

Limpert, J.

Lit, J. W. Y.

Liu, A.

Lovelady, M.

A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007).
[Crossref]

Machewirth, D. P.

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

Mann, J.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[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]

Mermelstein, M. D.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

Moore, S. W.

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

Nafcha, Y.

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

Neumann, J.

T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012).
[Crossref]

O'Connor, M.

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

Ripin, D. J.

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

Samson, B.

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

Sayinc, H.

T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012).
[Crossref]

Séguin, F.

A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007).
[Crossref]

Seifert, F.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007).
[Crossref] [PubMed]

Shamir, Y.

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

Sintov, Y.

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

Tankala, K.

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

Theeg, T.

T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012).
[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]

Tünnermann, A.

Vergien, C.

Walton, D. T.

Wang, J.

Wang, Q.

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

Wenetiadis, G.

Wetter, A.

A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007).
[Crossref]

Willke, B.

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007).
[Crossref] [PubMed]

Yablon, A. D.

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

Zenteno, L. A.

Zeringue, C.

Electron. Lett. (1)

D. J. Ripin and L. Goldberg, “High efficiency side-coupling of light into optical fibres using imbedded v-grooves,” Electron. Lett. 31(25), 2204–2205 (1995).
[Crossref]

IEEE J. Quantum Electron. (1)

J. P. Koplow, S. W. Moore, and D. A. V. Kliner, “A new method for side pumping of double-clad fiber sources,” IEEE J. Quantum Electron. 39(4), 529–540 (2003).
[Crossref]

IEEE Photon. Technol. Lett. (1)

T. Theeg, H. Sayinc, J. Neumann, and D. Kracht, “All-fiber counter-propagation pumped single frequency amplifier stage with 300 W output power,” IEEE Photon. Technol. Lett. 24(20), 1864–1867 (2012).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Proc. SPIE (5)

C. Headley, M. Fishteyn, A. D. Yablon, M. J. Andrejco, K. Brar, J. Mann, M. D. Mermelstein, and D. J. DiGiovanni, “Tapered fiber bundles for combining laser pumps (Invited Paper),” Proc. SPIE 5709, 263–272 (2005).
[Crossref]

A. Wetter, M. Faucher, M. Lovelady, and F. Séguin, “Tapered fused-bundle splitter capable of 1kW CW operation,” Proc. SPIE 6453, 64530I, 64530I-10 (2007).
[Crossref]

D. P. Machewirth, Q. Wang, B. Samson, K. Tankala, M. O'Connor, and M. Alam, “Current developments in high-power monolithic polarization maintaining fiber amplifiers for coherent beam combining applications,” Proc. SPIE 6453, 64531F, 64531F-7 (2007).
[Crossref]

F. Gonthier, “Novel designs for pump and signal fiber combiners,” Proc. SPIE 7580, 758019, 758019-6 (2010).
[Crossref]

Y. Sintov, Y. Glick, T. Koplowitch, O. Katz, Y. Nafcha, Y. Shamir, and R. Lavi, “A novel side coupling technique for rugged all-fiber lasers and amplifiers,” Proc. SPIE 6552, 65520R, 65520R-9 (2007).
[Crossref]

Rev. Sci. Instrum. (1)

P. Kwee, F. Seifert, B. Willke, and K. Danzmann, “Laser beam quality and pointing measurement with an optical resonator,” Rev. Sci. Instrum. 78(7), 073103 (2007).
[Crossref] [PubMed]

Other (6)

F. Gonthier, M. Garneau, and N. Vachon, “Multimode fiber outer cladding coupler for multi-clad fibers,” US Patent 7933779 B2 (2011).

W. T. Welford, Aberrations of Optical Systems (IOP Publishing Ltd, 1986), Chap. 2, 4 and 5.

V. P. Gapontsev and I. Samartsev, Coupling arrangement between a multi-mode light source and an optical fiber through an intermediate optical fiber length,” U.S. Patent 5999673 (1999).

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

F. Hakimi and H. Hakimi, “A new side coupling method for double-clad fiber amplifiers,” Conf. Lasers and Electro-Optics, 116 (2001).

A. B. Grudinin, D. N. Payne, P. W. Turner, L. J. A. Nilsson, M. N. Zervas, M. Ibsen, and M. K. Durkin, “Multi-fiber arrangements for high-power fiber lasers and amplifiers,” U.S. Patent 6826335, (2004).

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1
Fig. 1 Schematic side view of a side-pumped double-clad fiber including important ray paths.
Fig. 2
Fig. 2 (a) Pump coupling efficiency (CE) with respect to the taper ratio (TR) and the converging taper length (TL) and (b) a comparison of the pump coupling efficiencies without intermediate fiber (IF) and with IF for different fiber parameters, IF Ø: IF cladding diameter.
Fig. 3
Fig. 3 Pump coupling efficiency with respect to the taper ratio at a converging taper length of (a) 5 mm and (b) 20 mm for a PFF with a pump light input NA of 0.15, 0.22 and 0.30.
Fig. 4
Fig. 4 The loss mechanism and the total pump power loss of the fiber combiner for (a) a TL of 5 mm and (b) a TL of 20 mm at different taper ratios. The losses in percent were calculated with respect to the total input pump power. Please see Fig. 1 for TP, PCT and PAA.
Fig. 5
Fig. 5 The ratio of power leakage into the cladding of the target fiber (PCT) to the total input pump power against the taper ratio for a TL of 20 mm.
Fig. 6
Fig. 6 Coupled and transmitted power measured for a fiber combiner with one pump port with (a) a TL of 9.5 mm (TR of 2.6) and (b) a TL of 18 mm (TR 6.7), * ratio of coupled or transmitted power to total diode power in percent.
Fig. 7
Fig. 7 Fiber combiner with multiple pump ports, PFF: pump feeding fiber with a piece of coreless intermediate fiber (IF) as described in Fig. 1, TF: target fiber, TP: transmitted power.
Fig. 8
Fig. 8 Simulated coupling efficiency for a pump combiner with up to 6 pump ports for (a) a TL of 20 mm and (b) a TL of 10 mm for a pump light input NA of 0.22.
Fig. 9
Fig. 9 Simulated losses for a pump combiner with a TL of 20 mm and a TR of 6 providing up to 6 pump ports. Please see Fig. 1 for TP, PCT and PAA.
Fig. 10
Fig. 10 (a) Combined and transmitted power measured for a fiber combiner with 4 pump ports and (b) combined pump power measured for a fiber combiner with 6 pump ports, * ratio of coupled or transmitted power to total diode power in percent.
Fig. 11
Fig. 11 Microscope image of (a) the top view and (b) the cross section view of a fiber combiner with 4 pump ports.
Fig. 12
Fig. 12 (a) Pump coupling efficiency of the individual pump ports of the six pump port fiber combiner presented in Fig. 10(b) and 10(b) comparison of the experimentally achieved pump coupling efficiencies with the simulation results for fiber combiners with multiple pump ports.
Fig. 13
Fig. 13 Combined pump power for a 4 + 1x1 high power fiber combiner, * ratio of coupled power to total diode power in percent.
Fig. 14
Fig. 14 Setup for beam quality measurements, TF: target fiber, PBS: polarization beam splitter.
Fig. 15
Fig. 15 Normalized transmitted intensity through a premode cleaner as a function of the ring-cavity length in units of a free spectral range for (a) the reference beam and (b) the signal feedthrough beam of a 4 + 1x1 combiner.
Fig. 16
Fig. 16 Setup for the signal to pump isolation measurement of port 3 and 4, TF: target fiber, TP: transmitted pump power of the fiber combiner.
Fig. 17
Fig. 17 Signal to pump isolation (SPI) of the 4 pump ports in respect to the amplified signal power. The measurement data were connected by lines for clarity.

Tables (1)

Tables Icon

Table 1 Overview of the fiber parameters.

Metrics