1. Introduction

Traffic in datacenters has dramatically increased in recent years to constitute a dominant fraction of the overall communication traffic [1]. Within datacenters, transceivers based on 850 nm multi-mode (MM) vertical-cavity surface-emitting lasers (VCSELs) and graded-index (GRIN) multi-mode fibers (MMFs) currently represent the lowest-cost solution for short-reach applications. However, as line rates of datacenter traffic increase, VCSEL-based MMF links are increasingly threatened by single-mode fiber (SMF) links so much so that Facebook has decided to eliminate MMFs in its new datacenters. The reasons are twofold. First, high-speed VCSELs, although technically feasible [2], have lower output powers and are expected to be more expensive. Second, perhaps more importantly, high line rates call for the use of large-bandwidth OM4 fibers, with manually-selected optimized refractive-index profiles [3], which are about 4 times more expensive than SMFs. Several methods have been proposed to reduce the group delay spread (GDS) and improve the bandwidth of GRIN MMFs, for example, using dispersion-compensated MMFs [4]. However, all these methods are inflexible and complicated, therefore expensive as well.

Strong mode mixing is another method to reduce the GDS and improve the bandwidth of MMFs [5,6]. When mode groups in MMFs are strongly coupled, the majority of a signal pulse would have travelled on all mode groups with nearly equal probability, thus reducing GDS due to modal dispersion [7,8]. The reduction of GDS alleviates inter-symbol interference and thus improves the BER performance at the receiver. Taking advantage of the unique distribution of the effective indices of parabolic GRIN MMFs, we propose to use one uniform long-period grating (LPG) with a fixed grating period to achieve strong coupling among all mode groups. The LPGs were placed along the MMF with approximately uniform spacings, leading to reductions in GDS. Theoretically the GDS is proportional to $1/\sqrt{N}$ (where $N-1$ is the number of LPGs) when the total length is the same [7]. We present experimental results demonstrating the conversion of an OM3 MMF (300 m at 10 Gb/s [9]) to an OM4 MMF (400 m at 10 Gb/s [9]) with a negligible excess loss of 0.2 dB using simple mechanical LPGs. The proposed approach can benefit from more densely populating LPGs along the fiber. These fibers can be easily manufactured by inscribing LPGs concurrent with fiber drawing [10].

2. Experimental setup

We measured the performance of the MMF fibers using the experimental setup as shown in Fig. 1(a). An evaluation board (EVB) was used as the electrical interface for the VCSEL-based MM transceiver. A bit error rate tester (BERT) was used to generate a 10Gb/s pseudo-random bit stream (PRBS) of length 2³¹-1 for intensity modulation of the VCSEL transmitter. The output of the VCSEL transmitter was connected to the spool of MMF. The output from the MMF fiber was fed into the receiving port of the transceiver which was connected to 1) the BERT to measure the bit error rates (BERs), and 2) an oscilloscope to measure eye diagrams. Several segments of fibers were extracted out through re-spooling to allow the application of the LPGs. The MMF in this work is a commercial OM3 fiber of length 300 m (the reach specification of OM3 fibers at 10 Gb/s) or longer. The LPGs were placed along the MMF with approximately uniform spacings. The spacings between 2 LPGs and the ends of 400 m-long (530 m-long) MMFs were 120, 120, 160 m (180, 160, 190 m); The spacings between 4 LPGs and the ends of 400 m-long (530 m-long) MMFs were 80, 100, 60, 80, 80 m (120, 120, 100, 80, 110 m). Although uniform spacing was preferred, the spacing disparities were the result of lack of control in our re-spooling process. The refractive index profile of the OM3 fiber was measured and plotted in Fig. 1(b), along with the calculated effective indices of the 18 mode groups (black lines) at a wavelength of 850 nm. The graded-index profile and the trench can reduce the GDS and bending loss. The effective index differences between neighboring mode group pairs, and the corresponding phase-matched LPG periods are nearly equal, as shown in Fig. 1(c). As a result, a uniform LPG with a fixed grating period can be used to couple all mode groups in the MMF to reduce the GDS. In the current experiment, a mechanical LPG was used, which consists of a replaceable plate with gratings cut into it and an upper flat steel plate. The steel plate has an adjustable screw for applying pressure to the fiber [11]. With increased pressure, the coupling efficiency between neighboring mode groups increases due to increased index contrast of the LPG on the fiber, accompanied by a larger loss due to coupling into cladding modes. Since no pressure monitoring capability was provided by the grating manufacturer, we instead use the pressure-induced insertion loss of the grating(s) to indicate the strength of mode coupling.

 

Fig. 1 (a) Experimental setup. BERT: bit error rate tester, Scope: oscilloscope, LPG: long-period grating. (b) Measured refractive index profile and calculated effective indices of the 18 mode groups of the OM3 MMF at a wavelength of 850 nm. (c) Computed effective index differences between neighboring mode group pairs, and corresponding phase-matched LPG periods at a wavelength of 850 nm.

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3. Experimental results

The native 300 m OM3 MMF can indeed support error-free transmission at 10 Gb/s, meeting the specification for OM3 fibers. However, when the length of the native OM3 MMF was increased to 400 m, BER increased to around 10⁻⁸; the corresponding eye diagram is shown in Fig. 2(a). Therefore, the bandwidth of the native OM3 MMF is between 3000 and 4000 $MHz*km$. After 2 mechanical LPGs were applied, error-free transmission was restored on the 400 m OM3 MMF; the corresponding eye diagram is shown in Fig. 2(b), revealing appreciable improvement over that in Fig. 2(a). Similarly, the BER for transmission over a 530 m native OM3 MMF is around 10⁻³ but can be restored to error free with the application of 4 LPGs, revealing an improved bandwidth larger than 5300 $MHz*km$ with the help of LPGs; the corresponding eye diagrams are shown in Figs. 2(c) and 2(d), respectively.

 

Fig. 2 Eye diagrams (a) without LPGs and (b) with 2 LPGs, for 400 m MMF. Eye diagrams (c) without LPGs and (d) with 4 LPGs, for 530 m MMF. The width and height of eye openings as functions of the LPG-induced loss, for (e) 400 m MMF and (f) 530 m MMF.

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The eye diagrams in Fig. 2 also show that the GDS can be greatly reduced with the help of LPGs. The width or height of eye openings can be used to infer the GDS of the MMFs. Larger GDSs would increase the temporal variance of rising and trailing edges, leading to smaller widths or heights of eye openings. Figure 2(e) shows that the widths and heights of eye openings increase as the loss induced by LPGs, and thus mode coupling, increase when 2 LPGs and 4 LPGs were applied on the 400 m MMF. Compared with 2 LPGs, 4 LPGs can achieve the same width or height of eye openings with smaller losses. This is expected as more LPGs would curtail modal group delay more effectively. Similarly for the 530 m long OM3 MMF, as shown in Fig. 2(f), the width of eye opening can be improved by nearly twofold using either 2 LPGs or 4 LPGs.

The BER of the signal received by the transceiver was also measured using a BERT. We first measured the back-to-back BER vs. received power as a reference. The BER performances at 300 and 400 m transmission with and without applying LPGs are plotted together with the back-to-back BER in Fig. 3(a). It can be seen that the modal dispersion-induced power penalty at 10⁻⁹ BER for the 400 m transmission is about 9.8 dB and error-free transmission was not possible. When 4 LPGs are applied, the above modal dispersion-induced power penalty was reduced to about 3.5 dB.

 

Fig. 3 (a) BER as a function of the received power for back-to-back, 300 m (without or with LPGs) and 400 m MMFs (without or with LPGs). (b) BER as a function of the loss induced by LPGs, for 400 m MMF and 530 m MMF. (c) BERs for different lengths of MMF, without, and with 2 or 4 LPGs.

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The BERs as functions of the total losses incurred by the LPGs to reduce the modal dispersion-induced power penalty are shown in Fig. 3(b) at transmission distances of 400 and 530 m with the transmitter power fixed at −1.5 dBm. The BER after 400 m MMF can be easily improved to below 10⁻¹² using LPGs with a total loss smaller than 0.2 dB; using 4 LPGs can better improve the BER with smaller loss compared with using 2 LPGs. Similarly, for 530 MMF, 4 LPGs can improve the BER to below 10⁻¹² with a loss of 2.4 dB loss. To achieve error-free transmission at 530 m, 4 LPGs must be used. The reason why 2 LPGs cannot achieve error-free transmission is that GDS of mode groups in the MMF was accumulated over too long a distance before mode groups are scrambled. Figure 3(c) compares the BERs as functions of the fiber length when 2 LPGs or 4 LPGs are used with the transmitter power also fixed at −1.5 dBm.

It is important to confirm that performance improvements are indeed due to grating-induced mode mixing, rather than due to mode filtering. The best way to do this is encircle flux testing to measure the mode power distribution. Due to lack of the equipment, we performed two additional tests to verify the cause of performance improvements. First, we used fiber bendings as mode strippers on the MMF and observed the resulting changes in the eye diagram and BER. Both the eye diagram and BER deteriorated with bending. Second, if the performance improvements using the LPG were due to pressure-induced mode filtering, the performance would be independent of the grating period. To this end, we changed the angle between the MMF and LPG from the optimum position and observed deteriorations in the eye diagram and BER. Based on the two tests above, we deduce that mode mixing is the cause of GDS reduction.

4. Fabrication tolerance

Our method of converting OM3 to OM4 MMFs takes advantage of the nearly equal effective index differences between neighboring mode group pairs in GRIN MMFs. The effective index differences obviously depend on the refractive index profiles of these fibers, as does modal dispersion. For our method to be attractive, the tolerance on refractive index profiles must be less stringent than for OM4 fibers.

For a GRIN fiber with a core index distribution, as shown in Fig. 4(a), satisfying $n^2=n_1^2-2n_1^2\Delta {\left(r/a\right)}^{\alpha }$ (where $\Delta =n_1^2-n_2^2/2n_1^2$, $n_1$ and $n_2$ are the refractive indices of the core and cladding, $r$ is the radial position, and$a$ is the core radius), the $\alpha$ value is an important factor determining the effective index differences between neighboring mode group pairs. An index trench is usually added to reduce bending loss. Here we fix the width and the depth of the index trench at 5$\mu m$and $\text{5}\text{.5}\times {\text{10}}^{-3}$, respectively, but vary the position of the trench and investigate how this position affects the effective index difference. First, we discuss the effect of the core index profile. Figure 4(b) plots the effective index differences between neighboring mode group pairs at a wavelength of 850 nm for different values of $\alpha$with a trench immediately outside the core, which is the case for existing OM4 MMFs. As can be seen, for the optimum value ${\alpha }_{opt}=1.97$, the effective index difference is almost a constant between all neighboring mode group pairs, while the effective index difference either decreases or increases with mode order when $\alpha <1.97$ or $\alpha >1.97$. Specifically, for $\alpha =1.9$ ($\alpha =2.1$), the range of effective index differences between neighboring mode group pairs from mode group 1 to mode group 18 is about $4.\text{3}\times {\text{10}}^{-5}$ ($6.8\times {10}^{-5}$). The black curve in Fig. 4(c) shows the range of effective index differences or corresponding matched LPG periods as a function of $\alpha$for GRIN profiles of existing MMFs [black curve in Fig. 4(a)]. It is important to determine the range of $\alpha$ for which our method of using uniform LPGs to reduce modal group delay spread works efficiently, and to compare that range with what is required for OM4 fibers. As a reference, the tolerance on $\alpha$for conventional OM4 fibers is around 0.02 [12,13].

 

Fig. 4 (a) Refractive index profiles without or with trench shift. (b) Effective index differences between neighboring mode group pairs for 3 different $\alpha$values, for the index profile without trench shift. (c) Range of effective index differences or corresponding matched LPG periods as a function of the $\alpha$ value, without or with trench shift. (d) Coupling efficiency between two modes, as a function of effective index difference or corresponding matched LPG period, for $\kappa =50/m$, with perfect phase-matched index difference at $7.6\times {10}^{-4}$.

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Next, we present the effect of the position of the index trench. To reduce the range of effective index differences, we varied the position of the trench and found that shifting the trench away from the core by 1$\mu m$yields the smallest range of effective index differences or corresponding matched LPG periods, as shown in the red curve in Fig. 4(c). It was found that shifting the trench away from the core can reduce the effective index differences between higher-order mode group pairs.

The fabrication tolerance of $\alpha$ depends on the acceptable range of effective index differences or corresponding matched LPG periods, which in turn depends on the coupling coefficient $\kappa$. Figure 4(d) plots the coupling efficiency between two modes as a function of the effective index difference or corresponding matched LPG period for a coupling coefficient of $\kappa =50/m$,with perfect phase-matched index difference at $7.6\times {10}^{-4}$. This value of coupling coefficient is approximately the same as in our experiment in Section 3, and was deduced from the impulse response, which indicated that complete mode coupling occurred over the total coupling length of 3.5 cm for the mechanical grating [14]. To achieve a coupling efficiency >50%, the range of effective index differences must be smaller than $2.7\times {10}^{-5}$ or the range of LPG periods must be smaller than 40 $\mu m$, as shown in Fig. 4(d). This range of effective index differences or LPG periods corresponds to a tolerance on $\alpha$ value around 0.11, which is >5 times greater than the tolerance on $\alpha$for conventional OM4 fibers mentioned above.

5. Conclusions

In conclusion, we experimentally demonstrate low-cost and low-loss conversion of OM3 MMFs to OM4 MMFs using strong mode mixing by periodically embedding simple LPGs for datacenter applications. OM3 MMFs can be converted to OM4 MMFs with only 0.2 dB loss over 400 m for 10 Gb/s transmission. Error-free transmission at 10 Gb/s can be extended to 530 m if higher losses can be tolerated. The experiment was done using a specific transceiver and on a specific OM3 MMF. So the improvement in bandwidth may be different with a different transceiver or OM3 MMF. To verify consistent channel performance, additional tests using different transceivers and OM3 MMFs should be conducted. The proposed approach can benefit from more densely populating LPGs along the fiber. These fibers can be easily manufactured by inscribing distributed LPGs concurrent with fiber drawing [10] leading to better performances and lower costs. Better index profile designs can provide a large $\alpha$ fabrication tolerance. Therefore, the approach presented in this paper could potentially extend the longevity of VCSEL-based MMF links for datacenter applications.