1. Introduction

Fiber amplifiers and lasers continue to achieve ever higher powers, displace competing technologies, and make possible previously unattainable performance in material processing, directed energy, and other applications. While thermal management, pump combining, beam combining, and other techniques play crucial roles, the heart of a fiber laser is the gain fiber, and large mode area fiber design is essential in removing nonlinear limits: once intensity reaches a nonlinear limit, scaling up power requires spreading that intensity over a larger area. Many advanced design strategies have been proposed [1–4], and some have led to impressive demonstrations of large mode area, and yet the path towards scalable area remains unclear for the most demanding applications.

Many systems require a diffraction limited output with reasonable input coupling tolerances, and coiling of the gain fiber to a manageable package size. The fiber should have large mode area (LMA) and low bend loss, and it is increasingly clear that it should support very stable single-moded operation: Eliminating competing modes has always been desirable for improving efficiency, reducing the thermal management problem of dumping power in unwanted modes, etc. More recently, it was discovered that a thermally driven mode-coupling mechanism is a new nonlinearity that can limit power of pulsed and cw sources [5]. As power increases, this mechanism leads to an abrupt degradation of mode quality, so that higher-order modes (HOMs) can dominate the output. Mode instability can be limiting even for mode field diameters as small as 27microns [6], and highlights the importance of more robust approaches to single-modedness.

The traditional approach to robustly single-moded operation is to make all higher-order modes (HOM) very lossy—that is, make the fiber intrinsically more single-moded. Another interesting approach is, counter-intuitively, to use a fiber with many modes, but carefully launch and amplify a specific higher-order mode that is resistant to mode-coupling by bend perturbations [3]. It is not known whether such HOM amplifiers have any resistance to mode-coupling instabilities. On the other hand, fibers with HOM suppression were demonstrated to mitigate the mode-coupling instability [7]. That is, while the dynamics driving modulation instability are thermal, use of a fiber with sufficiently robust single-modedness increases the threshold for the instability by suppressing the modes, much as wavelength filtering can suppress Raman nonlinearities. Both approaches will need to be studied further, but here we focus on designs with intrinsic, robust single-modedness. We target very high levels of HOM suppression in order to significantly offset the large mode-instability gains estimated in the literature (e.g. 10’s or 100’s of dB/m [5],). The resulting designs should enable significant increases beyond current mode-instability limitations on power.

Here we propose a novel class of fiber designs that provide scalable area, robust suppression of HOMs, and excellent bend loss: symmetric bend compensated (BC) fibers essentially remove the tradeoff between these three requirements. These designs achieve improved single-modedness similar to asymmetric bend-compensated (ABC) fibers, which we have previously proposed [8,9], but without the difficulty of fabricating and utilizing asymmetric fibers. The current proposed designs do not require any special management of bend-orientation when coiling the fiber, and can be fabricated with conventional (symmetrical) deposition methods, assuming high precision (δn~10⁻⁴) in the deposition.

2. Bend compensation and transformation optics

The designs proposed here beat the usual performance tradeoffs by recognizing the importance of bend perturbations. Bend loss has long been part of LMA design [10], but it was only recently recognized that bends place crucial limitations on the other elements of the main performance tradeoff [8,9,11,12]: the more tightly a fiber is coiled, the more it must resist not only bend loss, but also reduction of mode area and degradation of selectivity in HOM suppression. Bend perturbations are so essential that, without them, performance is limited only by fabrication precision.

The original bend-compensation proposal [8] is a simple example of a “transformation optics” [13] design approach: the standard model [14] of a bend is to account for path length differences introduced by the bend using an equivalent index profile equal to the fabricated profile plus a bend-induced index tilt. Previous approaches carefully design and fabricate a material index profile, only to have it grossly perturbed by bends. The transformation-optics strategy [8] is simply to design the index profile needed in the equivalent-index space, and then define the fabrication-target profile using the standard bend transformation. In the case of a constant fiber coil, this is conceptually very simple: pre-compensate the profile by subtracting the bend-induced tilt [Fig. 1]. If fabrication imperfection, microbends, etc., can be neglected, performance is essentially perfect; light sees no bend since its perturbation has been subtracted out, and thus all bend loss and bend distortion are eliminated. An analogous solution was recently presented to the more sophisticated problem of mode-matching sections of planar waveguides with varying curvature [13].

 

Fig. 1 Bend-compensation concept: since bend perturbations place the primary limits on performance, a fiber that pre-compensates the bend can achieve much better optical properties. A schematic (left) shows a material index with gradient designed so that the equivalent-index in a bent-fiber configuration (right) attains the desired profile (e.g., a step-index profile).

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While fully pre-compensating a profile may be simple conceptually, and can achieve extremely high performance in simulations [8], it requires difficult fabrication of an asymmetric index profile. This should be possible given recent impressive accomplishments of microstructure fibers [7,15,16]. However, the fabricated tilt only compensates the bend assuming it is oriented correctly, and so an ABC fiber would have to be carefully coiled with orientation control. Thus this performance comes at a high cost, and is suitable only where ultimate area scaling of robustly single-moded fiber is needed. The extension of this concept to symmetric BC designs removes these disadvantages in cases where more moderate areas are sufficient. The basic intuitive argument is simple: ABC designs simultaneous overcome bend distortion of the mode shape (by pre-compensating the core) and degradation of single-modedness (by pre-compensating the cladding). For moderately large mode area, bend distortion plays a much less important role, and pre-compensating the core is unnecessary. Bend-compensating the key portion of the cladding requires only a symmetrical index gradient, and is sufficient to drastically improve performance.

Figure 2 illustrates schematically how bend-compensation de-couples HOM suppression from fundamental-mode bend loss. Figure 2 (left) shows that for a conventional fiber, the potential to selectively suppress HOMs degrades as bends become tighter: At loose enough bends, the index in the entire cladding can fall below the fundamental mode index (an arrow indicating leakage loss is present only for HOM, and not for the fundamental) and so even simple SIF designs can have “complete” selectivity of HOM loss, if precisely the right core contrast is used. At tighter bends, this selectivity degrades. The fundamental and HOM modes must tunnel through comparable distances to find the high-index portion of the cladding, and so losses (indicated by arrows) are more comparable. In a fiber with BC cladding (right) selectivity is restored: the tunneling distance for the fundamental is engineered to be much larger than for the HOMs, so that large HOM loss and small fundamental loss can be achieved simultaneously.

 

Fig. 2 In a conventional, un-compensated design (left), tighter bends lead to degradation of selectivity of the HOM loss. The tighter the bends and the larger the mode size, the more the fundamental and HOMs see a tunneling barrier of comparable width. A bend-compensated cladding (right) restores selectivity, since the compensated portion confines the fundamental but not HOMs. The width of the tunneling barrier seen by the fundamental can thus be engineered independently.

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Figure 3 (a-b) further illustrates the essential design tradeoff for a conventional design. A step-index fiber (black) can easily be designed to meet a target mode area (e.g. 657μm² at 1060nm) and level of HOM suppression (dashed, e.g., 100dB/m at D_bend = 30cm). The problem is that HOM suppression and fundamental bend loss are tied together; to achieve effective single-modedness at a large area, the core contrast must be extremely low, resulting in very high bend loss. If we increase the contrast (red) to lower the bend loss (solid), the HOM suppression degrades.

 

Fig. 3 For conventional step-index profiles (a) of a given core size, one faces a tradeoff: core contrast can be chosen to lower fundamental-mode losses (b,solid) or increase HOM losses (dashed), but not both. Construction of bend-compensated designs (c) from conventional fiber with the same core profile beats this tradeoff: Calculated losses illustrate de-coupling of bend-loss and single-modedness, since fundamental mode-losses can be reduced orders of magnitude (at 30cm bend diameter) with little change in HOM losses.

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Symmetric BC designs can be constructed from the same nominal step-index fiber (SIF) design (black, with 100dB/m at D_bend = 30cm), as shown in Fig. 3 (c-d), by starting with the SIF and adding a BC trench of increasing width to the cladding [Fig. 3c]. Mode area is a local property of the core, and is essentially unchanged (changing from 657μm² to 654μm²). The bend-compensation ensures that the HOMs can still penetrate through the cladding, and so single-modedness is also preserved. The trench does provide additional confinement of the fundamental, and so BC designs can achieve improved bend loss as the width of the BC region is increased, free of the usual tradeoff. This is confirmed by simulation results in Fig. 3d, showing loss vs. bend diameter for the fundamental (solid) and HOMs (dashed), where black curves are for the SIF and green, blue, and red have increasing BC region width, as in Fig. 3a. At the design diameter of 30cm, the HOM suppression shows little degradation due to the BC region, while the fundamental-mode bend loss drops orders of magnitude, indicating negligible loss on a length scale relevant for amplifiers.

3. Single-mode operation with scalable area

Symmetrical BC profiles were designed for a range of core sizes, including the profile in Fig. 4 (a). The strategy described in the previous section is not restricted to cores with simple step-index profile; in this section we use a parabolic-profile in the core (which provides some resistance to bend distortion [8,17]) and add a negative tilt in the cladding designed to cancel a bend with diameter 30cm. The graded region extends to 100 micron radius. Simulations show that this fiber has 0.01dB/m fundamental bend loss at 1040nm, with highly selective HOM suppression >100dB/m. The ratio of higher-order mode to fundamental loss, 10⁴, is much larger than has typically been targeted in the design literature: we focus on this regime of robust HOM suppression because it allows essentially complete removal of HOMs (e.g., 200dB total HOM loss in 2m) and very low loss of the fundamental (e.g., 0.02dB in 2m). Overcoming mode instability may require several 10’s of dB HOM suppression, while signal loss <~1% is extremely valuable in multi-kW applications due to thermal issues. Our design thus achieves some margin for real fibers to perform worse than ideal designs. The performance tradeoff of mode area vs HOM loss is compared (b) for design types, each with the same 0.01dB/m fundamental loss. The results demonstrate that the symmetric BC strategy essentially removes the tradeoff between mode area and selectivity of HOM suppression, allowing robust single-modedness at large areas. Step-index and parabolic profile fibers are used for comparison. A similar kind of comparison was used in [9], and illustrated the scalability of area of asymmetric BC fibers, far beyond the current symmetrical designs in Fig. 4 (although when comparing, we must note that in [9], designs with larger 0.1dB/m fundamental loss were considered, and the ratio of HOM to fundamental mode loss was 100-200). The approaches are complementary, with the symmetric designs more suitable when mode area >>1000 μm² is not needed.

 

Fig. 4 (a) Index profile of a proposed symmetric BC design. (b) Performance tradeoff compared with conventional designs. (c) Equivalent index profile with R_bend = 15cm, for target design (black) and four profiles with irregularity. (d) Performance of imperfect fibers.

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Since the usual performance tradeoff has been removed, an obvious question is what now limits the achievable performance. One answer is that there is a new tradeoff between fabrication precision and mode area. This is shown in the sensitivity analysis of Fig. 4 (c-d), which repeats the calculation of one of the target designs of Fig. 4(a), adding random index ripples of order 10⁻⁴ to model fabrication errors. These simulated irregularities were not azimuthally symmetric, but did have symmetry across the bend axis, to speed the calculation. The equivalent index profiles, which include the bend perturbation, are plotted in Fig. 4(c), with irregular profiles (blue) surrounded the ideal target (black). The cancelation of tilt in the compensated cladding is illustrated by the flat region on the outside of the bend (positive position). In Fig. 4(d), the bend radius of each fiber is adjusted to give the same fundamental bend loss (0.01dB/m), and simulated HOM loss and A_eff are summarized in the tradeoff plot (circles radiating from the target design). Robust single-modedness is still achieved even with this level of fabrication error; the performance is degraded, but still much better than the conventional designs. We note that the comparison to SIF here is entirely unfair, since the SIF performance indicated assumes ideal fabrication of very low-index-contrast profiles.

Single-modedness is not determined solely by loss selectivity, even in a fiber with no low-index outer layer. Furthermore, in a cladding-pumped configuration, the presence of a pump-guiding outer cladding means that true leakage losses are zero. Loss selectivity may still be a rough proxy for mode-coupling losses, and experience shows that a loss-based single-modedness analysis is still a useful guideline in explaining which double-clad fibers act single-moded. In either case, gain competition can play an important role, and depends in part on what fraction of each mode sees the gain region [10,18]. Thus we show mode intensity profiles of the proposed design in Fig. 5. The fundamental mode is well confined to the core (left), while the two LP₁₁-like modes spill out into the cladding. These results suggest higher-order modes highly susceptible to mode-coupling losses, and illustrate that (in addition to any loss) gain will selectively suppress the HOMs, since they will overlap poorly with the gain dopant in the core.

 

Fig. 5 Mode intensity profiles show that the fundamental mode (left) is much better confined to the core than LP11 modes (center and right), and will thus be preferentially amplified by gain in the core.

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7. Conclusion

We propose a new class of fibers that have bend compensation in only part of the cladding. These designs are symmetrical: they can be fabricated using conventional deposition methods with improved tolerances, and can be utilized without onerous bend management or splicing requirements. They thus overcome the main obstacles of our previously proposed asymmetric bend compensated fibers, and are scalable to >1000μm² mode area.

Simulations indicate that, even with reasonable fabrication imperfections and yield, these designs should achieve extremely selective HOM suppression, with the ratio of calculated HOM loss to fundamental loss >1000 on a dB scale (e.g. “complete” 50dB of HOM suppression and <0.05dB of fundamental loss). Such fibers would be ideal for scaling up power in applications where mode-instability is currently limiting, and for sources suitable for beam-combining [19].