Fibers with asymmetrical bend compensation offer to completely remove the tradeoff between mode area and single-modedness, with potentially huge impact on high-power amplification. These fibers would be difficult to fabricate, but are the only fundamental-mode strategy that can remove the bend-distortion limitations on mode-area scaling. Here, we show that even imperfect fibers can achieve essentially complete HOM suppression for areas of 2000 square microns or larger. Ultimate performance limits due to finite cladding size and fabrication imperfections are calculated.
©2011 Optical Society of America
The rapidly increasing power obtainable from fiber amplifiers and lasers has been enabled in large part by large mode area (LMA) gain fibers . While available powers are now sufficient for fiber lasers to displace some competing technologies, further power scaling is needed for some applications. Limitations intrinsic to conventional fibers must overcome to achieve even higher power output in a pure fundamental mode .
Several problems limit the mode size that can be achieved in a fiber. The main tradeoff is that large-mode fibers tend to have multiple unwanted modes, and a related degradation of beam quality. Stripping these unwanted modes [3,4] helps significantly, but does not completely remove this tradeoff. Despite significant effort, achieving robust single-mode performance has been difficult, even when straight-fiber layout and free-space coupling are used . Another key obstacle is bend distortion—the contraction and displacement of a mode induced by coiling the fiber [6–8]. Bend distortion becomes increasingly severe for larger cores, so that for practical coiled fibers, simply scaling up conventional core designs is not a viable approach to achieving mode areas much larger than 1000 µm2.
There is one strategy for avoiding bend distortion completely: if the fabricated profile is pre-compensated for the bend-induced index perturbation, then light will ideally see the desired profile . This asymmetric bend-compensated (ABC) strategy, in the limit of ideal fabrication, would completely remove the tradeoff between mode area, macrobending loss, and single-modedness. The strategy is difficult to implement—it requires fabrication of an asymmetric fiber and deployment of the fiber in a fixed bend orientation. However in contrast to other advanced strategies for fundamental-mode area scaling [9–11], it removes the key obstacle of bend distortion, allowing much greater scaling of mode area in a compact, coiled device. This approach is thus an alternative to amplification in very pure higher-order modes, which is naturally immune to bend distortion [12–14] and can also achieve very large mode area. However, ABC does not require an output mode conversion in applications where a Gaussian-like output is desired. We recently confirmed numerically  that the ABC strategy scales to very large areas, but the specific designs studied there had only modest suppression of higher-order modes.
This paper explores the limits on performance of the ABC approach, and the ways in which a real fiber inevitably deviates from an ideal structure. We find that extremely large areas and robust single-modedness can be achieved by assembling a preform of reasonable granularity and size. We also show that there is a tradeoff between mode area and the index control needed. In particular, we find that remarkably robust single modedness—essentially complete (~100dB) suppression of higher-order modes (HOMs)—can be achieved with very large fiber area (Aeff~2000µm2 or larger) in the desirable regime of coiled fiber amplifiers (Rbend = 15cm, 5m length), with challenging but achievable fabrication requirements. This is in stark contrast with other design strategies, where single-moded operation at much smaller areas requires careful management of fiber layout and input launch. The ultimate limits of area determined by fabrication precision are discussed.
2. Bend distortion
Bends play a crucial role in large mode area fiber design—not only because of loss. Figure 1 shows that for conventional designs (SIF with contrast ncore-nclad = 0.0008), as one increases the core size, the mode area eventually sees minimal increase. For realistic bend radii, mode area is in practice limited to about 1000µm2. This bend impact on mode area has been experimentally confirmed .
Bend distortion also has a crucial impact on gain competition by pushing the fundamental mode out of the center of the core. As mode area becomes larger, loss-suppression of HOMs becomes nearly impossible, and gain-suppression of higher-order modes by tailoring the dopant profile  is increasingly important. However, gain tailoring fails drastically if the dopant profile design fails to take bend distortion into consideration, and eventually becomes impossible for highly distorted modes .
Parabolic designs help significantly—in part because the fabricated gradient cancels the bend-induced gradient at the center of the displaced mode . Mode displacement and area reduction are mitigated, but still ultimately limit scalability in parabolic fibers. Holes are useful for controlling HOM suppression, but are certainly no guarantee of single-modedness . Leakage-channel type fibers experience bend distortion similar to others , and so fail to provide gain suppression.
3. Bend-compensated designs
The ABC strategy is illustrated conceptually in Fig. 2 (a-b) . The fabricated profile has a gradient that cancels the bend induced perturbation, so that the equivalent index determining the mode shape is a perfect step-index profile (or whatever other profile we design), at least within the region of the compensation. Figure 2 (c-d) illustrates how we might implement this as a finite number of constant-index cells.
In the ideal limit, it is clear that a fabricated ABC profile can result in whatever equivalent index profile we want. That is, in the limit of fine-grained cells, a large bend-compensated cladding, precise index control, and a known bend, we simply fabricate,.
Here, γ is 1 according to the geometrical conformal mapping , and may include a stress correction. The x-axis is defined to point towards the outside of the bend. The bend perturbation can only be subtracted if the orientation is known, and so the fiber must be wound so that the gradient faces in the desired direction over the fiber length during use. This is challenging, but is clearly achievable in high-performance amplifier and laser applications where careful fiber layout is the norm.
In the limit of perfect index control, there is no need for simulations, and the familiar tradeoffs between area, bend loss, and multi-modedness vanish: as is well-known , a SIF can be rigorously single-modeded for arbitrarily large area. Further, there can be no macrobend loss if the equivalent index of the entire cladding is below the mode index. If light sees a perfect SIF (equivalent) profile, then only secondary considerations (e.g., microbending) limit mode area. Clearly a real fabricated ABC fiber will have finite size, finite granularity, and imperfect control of the index of each cell. Below, we explore the impact of these on fiber performance.
4. Cladding size and suppression of higher-order modes
Several ABC designs were constructed and simulated with cell spacing L, core diameter Dcore = 5L (“19-cell” core), and cladding size either 12L (Dclad = 2.4Dcore) or 18L (Dclad = 3.6Dcore, as in Fig. 2c), assuming a fairly large but practical coil size, Rbend = 15cm. In the illustrative design of Fig. 2c with L = 10, the bend-compensating gradient corresponds to steps along the x-axis of around nsilγx/Rbend, or around 8×10−5 as shown in Fig. 3 . A small core contrast (for the approximate SIF profile, red dashed) of 9×10−5 is needed to maximize leakage of HOMs while providing an acceptable calculated bend loss for the fundamental mode, 0.1dB/m. The simulations confirm that very large area (Aeff=2160µm2) is compatible with large suppression of HOMs (HOM Loss ~140 times the fundamental loss).
The advantages of the ABC strategy are better understood by comparing the performance tradeoffs for different fiber types. Several ABC fibers are compared to traditional designs in Fig. 4a . The three-way tradeoff between bend loss, HOM suppression, and effective area is summarized there by locking all fiber designs to a calculated bend loss of 0.1dB/m at Rbend = 15cm and plotting relative HOM suppression (HOM loss/fundamental loss) vs. Aeff. For example, the family of step-index fibers has two degrees of freedom (core size and contrast). For each core size the contrast is selected to satisfy the 0.1dB/m bend loss requirement, so that only one degree of freedom remains. These core contrast values are plotted in Fig. 4b as a function of core radius, along with effective area. Thus, the SIF (red) and parabolic (blue) designs reduce to simple curves in Fig. 4a. The mode areas are calculated at the bend radius 15cm—that is, in the actual configuration of the fiber during operation. These are more relevant than the straight-fiber areas often quoted in design papers, and can easily be smaller by a factor of 2 or more. The lowest-loss of the HOMs is used in the calculation.
These curves confirm the point illustrated by Fig. 1, that SIF designs cannot be scaled significantly above 1000µm2 for typical coiling requirements, because of a tradeoff with HOM suppression. We note that this curve applies to ideal SIF fibers. The actual contrast values are quite small, and these ideal fibers would be challenging to make with conventional fabrication. Typically, fibers with higher contrast have been used, requiring tighter bends to strip higher-order modes, further degrading the bend distortion and single-modedness. Parabolic fibers show a significantly improved tradeoff, but are still limited in area if bend-loss suppression of HOMs is required.
The simulated ABC designs (black and green circles) illustrate a qualitatively different type of behavior, confirming that the strategy essentially removes the tradeoff with area. As the core size is increased by scaling L (and the contrast adjusted to meet the loss requirement), mode area increases with little impact on the HOM suppression ratio. The HOM suppression is essentially determined by the relative size of the cladding (Dclad/Dcore) alone.
This is what we might expect based on a simple analogy: to understand the impact of the finite extent of the compensated inner cladding region, think of Fig. 3(b) as approximating a 3-layer “w-fiber” with high-index outer cladding starting at 85microns. For example, we can compare the relative tunneling losses of the HOM and fundamental for an unbent w-fiber with outer cladding index equal to the core index (the precise outer index should not matter much), and with Dclad/Dcore similar to the ABC fiber. This simple 1d calculation has been included as a guideline in Fig. 4a (dashed black and green lines), and is quit a useful rough estimate of the more correct (and much more complicated) 2D calculations (black and green circles). Intuitively, the selectivity of the HOM suppression increases with the size of the cladding, since there is more cladding that the fundamental needs to tunnel through to escape.
ABC fibers can thus remove a fundamental limitation on area that constrains other strategies. They can achieve mode areas in the 2000-3000µm2 range with a level of single modedness—and thus beam quality—analogous to conventional fibers with 600-700µm2. In the Aeff~1000µm2 regime, SIF and parabolic designs are not only very difficult to make with conventional fabrication methods, they fail to provide robust HOM suppression even when fabrication is perfect. For example, a 5m long SIF with Aeff~1000µm2 and <0.5dB total bend loss can achieve at most a meager 2-3dB of HOM bend-loss suppression. A parabolic fiber can approach a respectable 10-15dB of suppression, although actual performance will inevitably be worse than these idealized calculations. In any case, these are well short of total suppression, and confirm the actual experiences of real-world users: good beam quality is achievable in hero experiments, but relies heavily on very careful management of input launch, fiber layout, and handling.
Leakage channel fibers (LCF) are an alternative advanced microstructure fiber type, proposed to allow better area scaling. The most common type, with six holes in a single layer around the core, has been included in Fig. 4a (brown). Center-to-center hole spacing varied from 40 to 56 microns, and hole size was adjusted for each design to provide 0.1dB/m loss. The LCF designs achieve an HOM suppression ratio below 10 in our calculation, roughly consistent with previous work . Thus, their performance (as defined in this particular comparison) is comparable to the ideal SIF family. Ongoing work points to possible improvements, for example, it has been proposed that LCFs would achieve much higher HOM suppression by taking advantage of cladding-mode resonances . In any case, area scaling for the LCFs is limited if we avoid highly bend-distorted mode profiles, as illustrated in Fig. 5 (for the LCF with 56µm hole spacing). In an amplifier, the highly displaced mode would suffer serious gain-interaction impairments , since most of the gain-doped area (e.g., dashed circle) does not see the signal light.
The calculations for ABC fibers are in stark contrast. With >100 times relative suppression (and 0.5dB total bend loss), they show “complete” >50dB suppression of HOMs for areas Aeff>2000µm2 (or even Aeff>3000µm2). The mode in Fig. 5 has an excellent shape and no displacement, and so a gain-doped region (e.g., dashed) can be tailored for high gain overlap and high gain selectivity. The ultimate limit of area scaling will be determined by the precision of index control in each cell, as discussed below.
5. Sensitivity to fabrication
The impact of fabrication imperfection on performance was tested by taking each of the three Dclad=3.6Dcore target designs of Fig. 5 and adding a random perturbation to the index of each element. Figure 6 summarizes the impact in terms of the main performance tradeoff. Independent Gaussian random perturbations (with standard deviation 5×10−5) were added to each cell in half of the structure y>=0. For simplicity, symmetric perturbations were assumed for the cells with y<0. Four randomly perturbed structures were generated for each target design, and for each the bend radius was adjusted slightly so that the fundamental loss met the target (0.1dB/m). As one would expect, fabrication sensitivity increases as core size increases: at large area the core contrast becomes very small, and is easily overwhelmed by the random variation in index. The smaller-area fibers, however, are reasonably robust: Performance was relatively unchanged for the Aeff~1310µm2 fiber. Two of the perturbed Aeff~2160µm2 fibers performed essentially as-designed. The performance for the other two, although very degraded, is still much better than the ideal performance (assuming perfect fabrication) of competing technologies, including leakage channel fibers. For the largest Aeff~3280µm2 design, the perturbed profiles significant degrade mode shape, making one of the fibers unusable (dashed), but three of the four perturbed fibers show excellent performance. Intensity profiles for the Aeff~2160µm2 fibers are shown in Fig. 7 . They show distortion, but maintain large area and reasonably small displacement, allowing effective gain overlap.
Previous fundamental-mode large-mode-area fibers generally fall in two categories: practical, robust systems with mode area well below ~1000µm2 (in coiled configuration), and hero fibers that can be operated in single-mode regime only with great difficulty. The proposed asymmetrical bend-compensated fibers would be challenging to fabricate, but offer robust single-moded operation. The limits of area scaling have been explored by calculating the robustness to fabrication errors, and indicate that mode area of 2000µm2 or greater is achievable while maintaining robust single-moded operation. These calculations demonstrate a viable strategy for a practical, 30cm diameter coil size, but also raise the possibility of a much more compact arrangement; since the bend perturbation is canceled, any coil size would be achievable with sufficient fabrication precision.
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