1. Introduction

Multicore fiber (MCF) strategies have been presented as a way of surpassing the limits of large mode area (LMA), and thus allowing higher power in fiber amplifiers and lasers. Recent papers on LMA MCF follow quite different approaches; one paper [1] asserted that MCF could be designed and fabricated that are single-moded and vastly exceed the tradeoff of bend loss vs. Aeff for comparable single-moded step-index fibers (SIFs). This assertion is remarkable because, in contrast to other strategies, for example [2–5], there seems to be no intuitive physical mechanism behind the proposed advantage.

This paper presents simulations of the specific fiber analyzed in [1], and of a more general class of LMA MCF. It shows that the specific fiber is not single moded. A SIF “equivalent” is identified that has essentially identical performance in the tradeoff of mode area, bend loss, and degree of multimodedness. The more general class of MCF is compared to SIF by fixing the bend loss and plotting various measures of higher-order mode (HOM) suppression vs effective area. This analysis suggests that this class of MCFs can at best approach the performance of SIF, while some designs in this class do significantly worse.

2. Analysis of specific design in Ref [1]

The design presented by Vogel has a triangular arrangement of 19 identical cores in a uniform cladding. Core-to-core spacing is 5.5μm, and each core has diameter 2.0μm and numerical aperture 0.108. Figure 1 shows the present calculation of effective index and effective area, done using a 2D vector finite-difference mode solver [6]. The stars are values taken from the text of [1] and are in agreement (confirming that the same input fiber specification was used).

 

Fig. 1 (Color online) Mode calculations of proposed multi-core fiber (solid) compared to a comparable step-index fiber (dashed).

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The present calculation shows a bound higher-order mode (labeled LP₁₁), and so the fiber is clearly not single-moded in the strict sense. Of course, a few-moded fiber can be operated in an effectively single-moded regime [7], for example by bending the fiber enough to remove the HOMs. In fact, the HOMs are so weakly guided for this particular fiber that no intentional perturbations would be needed to achieve effectively single-mode operation—loose coiling and unintentional perturbations would suffice. But then it is unfair to compare (as in [1]) the bend loss of the proposed MCF to a truly single-moded SIF. Instead, a fair SIF comparison design has core radius 12.7μm and n_core-n_clad=5.6 × 10⁻⁴, so that the effective area and effective indices of LP₀₁ and LP₁₁ are very close to the MCF, as shown in Fig. 1. This is fair because the fibers have the same effective area, the same index-mismatch n₀₁-n₁₁ governing LP₀₁-LP₁₁ coupling, and are comparably close to “cutoff” (with the same n₁₁-n_sil). Figure 2 shows that the MCF and SIF have nearly identical fundamental bend loss, and the same bend-induced HOM suppression. Bend loss was calculated at 1040nm using a standard equivalent index model [8], with no stress correction.

 

Fig. 2 (Color online) Bend loss for the proposed MCF and a comparable SIF are plotted for the fundamental and two LP₁₁ modes (with lobes oriented along or across the bend).

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The existence of an equivalent SIF with comparable bend loss was also shown in [9] for an MCF with larger-NA cores, along with a procedure for systematically identifying “equivalent” SIF parameters. Since the mode shapes are also comparable [1], the guided light essentially cannot resolve the individual cores; all of the optical properties are essentially equivalent, and one can think of this MCF simply as a SIF fabricated in an unconventional way. Fabrication imperfection plays an increasingly important role in performance as core size increases, and so unconventional fabrication methods are of interest in the push towards large mode areas. Thus one of the most interesting potential advantages demonstrated in previous microstructured fibers (e.g [10].) has been control of dopants difficult to achieve by conventional deposition methods.

3. General class of 19 identical cores in a uniform cladding

We can look more generally at the design space of this class of MCFs with core diameter d, spacing L, and index contrast n_core-n_clad, assuming 19 identical cores in a triangular lattice. To allow fair comparison of the A_eff-vs-HOM-suppression design tradeoff, we restrict all designs to the same fundamental bend loss (in this case 0.1dB at bend radius 15cm). For each core spacing and core filling ratio d/L, there is a unique choice of index contrast selected to meet the bend loss =0.1dB/m, plotted in Fig. 3(a) as a function of 5L (the effective diameter of the composite core). The basic tradeoff can be plotted as effective area (including bend distortion [2,11]) vs. HOM bend loss (for the lowest-loss HOM R_bend=15cm), as in Fig. 3(b). The specific choice of tolerable bend loss, radius, etc., is arbitrary, but is representative of what may be relevant to a real amplifier. Figure 3(b) shows that all of the MCFs studied have performance comparable or worse than SIFs. Performance is similar to SIF when either the mode area is small, or when the cores are closely spaced. The latter case is intuitive: as d/L approaches 1, MCF performance approaches the SIF tradeoff because the fiber profile is becoming SIF-like. When d/L becomes small, the system looks more like a weakly-coupled collection of local waveguides. In the limit of weak coupling, the higher-order (super)modes would be approximately as well guided as the fundamental, and so it makes sense that selective suppression of HOMs becomes worse as we approach this limit. It is interesting to note that for the smallest d/L= 0.2, bend distortion is so severe that effective area decreases as the core size is increased from 5L=40μm to 5L=50μm. While these MCF fibers fail to exceed the SIF performance, it is certainly not a fundamental limit: Performance for single-core fibers with parabolic [2] index profile is also include ed in Fig. 3(b), and is significantly better at large area.

 

Fig. 3 (Color online) (a) Core contrast as a function of core radius required to fix bend loss at 0.1dB/m. (b) Performance tradeoff for this simple MCF family and for SIFs.

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While HOM loss is a very common indicator of single-modedness in fiber design papers, it has no straightforward interpretation when additional pump-guiding features are included in the outer cladding (as required in cladding-pumped amplifiers). Figure 4 plots two other important metrics of HOM suppression vs. effective area, and shows similar trends. Phase mismatch (n^eff ₀₁- n^eff ₁₁) between LP₀₁ and the lowest-loss HOM can be thought of as the resistance to mode coupling. Mode coupling resistance is the same or slightly worse for an MCF as for a SIF of the same A_eff, while parabolic designs show an improvement. Fractional displacement is defined as$\overline{x}/\left(2\sqrt{A_{eff}/\pi }\right)$, that is, the intensity-weighted average displacement $\overline{x}$of the mode (due to bend distortion) normalized by a mode diameter. This is an important indicator of gain competition: if the mode is significantly displaced by bend distortion, then there is no possibility of achieving gain suppression of HOMs with a confined dopant [12,13]. The curves again indicate that this class of MCF performs at best the same as SIF as area is increased, while parabolic fibers perform significantly better. Again the worst performance is for small d/L. This seems to follow the intuitive picture of weakly-guided distant cores: as the supermode becomes more peaked in the cores, a bend perturbation can more easily localize the mode to the outer cores. It is also interesting to note that the specific MCF of [1] falls in the small-area regime, where the curves for all the simulated fibers merge. Thus the MCF strategy performs best in the regime where conventional commercial approaches are already adequate.

 

Fig. 4 (Color online) (a) Resistance to mode coupling vs mode area. (b) Tradeoff of mode displacement and effective area.

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The designs sampled are not exhaustive, but reasonably span the space, indicating that this class of MCF does not improve the basic tradeoff between bend loss, mode area, and single-modedness. Rigorously single-moded and effectively single-moded regimes exist for these fibers, but these regimes do not ensure any new mechanism for overcoming the SIF tradeoff. Multicore strategies to LMA fiber have been proposed based on a variety of other advantages: for example, producing a core dopant profile difficult to fabricate by conventional means [10], or as a platform for interesting and useful nonlinear dynamics [14]. These other advantages are not addressed by the calculations in this paper, and are promising areas for future research.