PHOTONICS 1254
IEEE TECHNOLOGY LETTERS, VOL. 19, NO. 16, AUGUST 15, 2007
Mode Coupling in Plastic Optical Fiber Enables 40-Gb/s Performance
Arup Polley and Stephen E. Ralph
AbstractWe report 40-Gb/s capability of 50-m core plastic optical ber using differential modal delay measurements and power penalty due to intersymbol interference computations. The results are explained via a comprehensive multimode ber model that includes mode coupling (MC) and differential modal attenuation (DMA). We show that strong MC can enable 40-Gb/s transmission for reach in excess of 100 m even in the presence of irregularities in the refractive index prole that prevent 10-Gb/s performance without MC. Furthermore, we show that DMA effects are negligible and that the mode power distributions are not a good indicator of bandwidth. Index TermsOptical ber communication.
I. INTRODUCTION RADED index plastic optical ber (GI-POF) has shown the potential for high-speed data transmission over shortreach links [1]. Strong mode coupling (MC) [2][4] and differential modal attenuation (DMA) [5] have both been reported to be effective in improving POF bandwidth. Indeed, 11 Gb/s has been demonstrated in GI-POF for distances of 100 m [1]. However, the achievable performance of modern GI-POF has not been explored and the sensitivity of the performance benets of MC in the presence of index prole irregularities has not been reported. We show that 40 Gb/s over 100-m GI-POF is achievable [6], [7] using any launch condition. We explain the results using a comprehensive multimode ber (MMF) model using the previously reported MC strength without the need to invoke DMA. We also show that knowledge of the mode power distribution (MPD) is not necessarily a good indicator of bandwidth. We, therefore, focus on the temporal behavior of GI-POF and demonstrate that 40 Gb/s should be readily achievable in any variety of MMF provided that the index prole meets modest accuracy constraints and that the required MC, quantied here, is present.
Fig. 1. Experimentally measured DMD of 200-m length of 50-m core GI-POF. The deconvolved DMD is 50 ps and thus supports 40 Gb/s.
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II. EXPERIMENTAL RESULTS The high-resolution impulse response of 200-m 50- m core GI-POF from Chromis Fiberoptics is determined using 16-ps
Manuscript received December 15, 2006; revised May 14, 2007. The authors are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA (e-mail: [e-mail]; [e-mail]). Color versions of one or more of the gures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identier 10.1109/LPT.2007.901743
pulses at 850 nm launched via single-mode ber at different offsets from the ber core center (Fig. 1). The receiver is a commercial 50- m MMF photodetector followed by a digital sampling scope with a net bandwidth of 25 GHz. The differential modal delay (DMD), dened as the temporal width at 25% of the maximum intensity across all offset responses, is 66 ps and is limited by the receiver; the maximum difference between the peaks is 2 ps and the deconvolved DMD is 50 ps. The deconvolved response for 0- m offset is 29-ps full-width at half-maximum (FWHM). The variation in FWHM across all offsets is 4 ps thus demonstrating that any launch condition, including overlled launch, yields equivalent performance. Using the deconvolved channel responses, we estimate that the optical power penalty for 200-m GI-POF channel is 4 and 10 dBo for 30 and 40 Gb/s, respectively. The corresponding penalty for 40 Gb/s with 100-m reach is 4 dBo, which is comparable to the 3.6-dBo penalty allotted in the 10-Gb/s Ethernet standard. A 40-Gb/s receiver suitable for MMF may yield lower power penalties than we report here. Eye diagrams and bit-error ratios at 20, 30, and 40 Gb/s conrm the bandwidth performance illustrated by the DMD [7]. III. FIBER MODEL A comprehensive MMF model [8] is used to evaluate the temporal response and evolution of MPDs. The mode solver determines the transverse electric eld proles and group delays of the propagating modes for arbitrary refractive index proles. We use prole irregularities known to exist in GI-POF including pure, but not ideal, -proles and mixed proles where the alpha varies across the radius. We neglect the small material dispersion; however, we use the exact eld proles, hence the
1041-1135/$25.00 2007 IEEE
POLLEY AND RALPH: MC IN PLASTIC OPTICAL FIBER ENABLES 40-Gb/s PERFORMANCE
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Fig. 2. DMD simulation for 200-m GI-POF with average MCCs of 1:7 10 , 0:17, and 5 m [(a), (b), and (c), respectively]. Corresponding MPD [(d), (e), (f)] versus mode group number for launch offsets of 0 mopen circles; 5 mXs; 10 mdiamonds; 15 msquares; and 20 mtriangles.
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optimum is 2.03. We also examine irregularities known to result in severe DMD in silica bers; center peak and center ). The corecladding index delta is 1.5% dip (with and the cladding index is 1.34, corresponding to peruorinated and . GI-POF. The pure proles examined are The center dip and center peak have an index deviation 12% of . The mixed prole has for inner core and for the outer core. The initial MPD is obtained via overlap integrals of the 7- m FWHM Gaussian excitation and the mode proles. The effects of MC and DMA are simulated using the discrete theory of MC [9]. MC in peruorinated GI-POF results from micro-bending at the corecladding interface [3]. Complete mode mixing is assumed within the velocity degenerate mode groups and MC occurs only between adjacent mode groups. Therefore, a set of coupled power equations for different mode groups is solved using a numerical split-step method to obtain the temporal evolution and MPDs of different mode groups. The mode coupling coefcient (MCC) is dependent on the difference in propagation constant between modes, mode proles, refractive index prole, and MC strength parameter [8]. The MCC increases linearly with mode group number for pure alpha index proles although we determine the exact MCC for each mode group of a particular index prole. We identify an effective MCC, given by the average over all mode groups. A mode coupling length (MCL) is dened as the distance re, quired to reach a steady state MPD where and are the two smallest eigenvalues of the coupled power equations. This denition ensures that the eigenstate corresponding to the steady-state MPD is 100 times stronger than the next strongest eigenstate [9]. Numerically, we vary the
effective MCC over a wide range from 0.01 to 1000 m and compute the corresponding MCL. The DMA is also varied and we nd that 0.3 dB/m for the highest mode group produces a net modal attenuation commensurate with the measured loss of 50 dB/km. IV. SIMULATION RESULTS Fig. 2 summarizes the effects of MC on the temporal response launched at and MPD of 200-m 50- m core GI-POF m different offsets. The lowest depicted of MC corresponds to that found in glass MMF [8]. On the other hand, the highest coupling of 5 m corresponds to an MCL of 30 m, and is consistent with that reported for GI-POF which ranges between 2 to 100 m [2][4]. An intermediate MCC of 0.17 m is chosen to illustrate the transition between weak and strong coupling. The temporal response changes dramatically with increasing MC [Fig. 2(a)(c)]. In the absence of signicant MC [Fig. 2(a)], yields a DMD the nonoptimal refractive index prole of 367 ps. We note that this is close to the maximum DMD of 2 ns/km allowed in FDDI grade glass MMF and only supports 10 Gb/s with a restricted mode launch. As the MCC is increased to 0.17 m , energy transfer among the mode groups rst lls the valleys between the discrete mode groups and then increases the width of the response at a particular offset, although the DMD of 331 ps is reduced slightly. Increasing the MCC to 5 m with corresponding MCL of 30 m reduces the DMD to 97 ps. The individual offset responses are also reduced (compared to intermediate coupling) [Fig. 2(c)]. Comparison of Fig. 2(c) with the observed DMD of Fig. 1 reveals that the meam. sured ber has an MCC
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 19, NO. 16, AUGUST 15, 2007
Fig. 3. DMD versus MCC for 200-m 50-m core POFs with different refractive index proles. Loss versus MCC (solid). Inset depicts DMD details at high coupling.
As expected for small coupling, the MPDs at the receiver remain dependant on launch condition [Fig. 2(d)] and are essentially the same as those at the launch. Of course, the leaky mode group loses power, and there is somewhat less power in the higher modes in general. For strong coupling [Fig. 2(f)], all launch offsets yield similar near-equilibrium MPDs after 200 m. Thus, specic launch conditions, which control mode excitation to improve bandwidth, are not effective. The DMD is, therefore, a better measure of available bandwidth. In Fig. 2(f), the increase in power with mode number reects the increasing degeneracy with increasing mode number. Furthermore, the included DMA of 0.3 dB/m does not appreciably reduce the power in the leaky mode nor change the MPD. The intermediate MCC case [Fig. 2(e)] reveals a range of MPDs as the offset is changed and the light emission angle at the receiver depends on the launch condition. Experimentally, it is challenging to distinguish between the MPDs beyond the intermediate coupling regime. This may account for the range of MCL that have been reported. The DMDs for other prole irregularities are summarized in Fig. 3. Although the MPD varies only slightly among the different bers, the temporal response is strongly dependent on the index prole and the DMD varies considerably. The effect of MCC on DMD has a near-threshold-like behavior. An MCC below 0.5 m has little practical impact on DMD yet the near-minimum DMD is reached with an MCC of 10 m or greater. Strong coupling substantially reduces the DMD for all index irregularities [4]. Importantly, the DMD remains dependent on the index prole for all coupling strengths. Optimum performance is obtained by the combination of wellbehaved index proles and strong MC. It is known, and our model demonstrates, that DMD increases approximately linearly up to coupling length , and the DMD at length is given by , where is the DMD at . This result captures the dependence on both the coupling and the index prole. What is interesting is that index
irregularities similar to or somewhat worse than those found in glass MMF, together with coupling typically found in POF, are sufcient to enable 40 Gb/s. Thus, MC should be equally benecial in glass MMF. The detail of the strong coupling limit (inset of Fig. 3) demonstrates that knowledge of the MCL or the MPD is not sufcient and that the temporal behavior, preferably at the intended ber length, is required. We noted that the MCC depends on the strength and nature of the perturbation and the transverse mode prole. We nd that the MCC varies only slightly for the index irregularities considered here. This relative insensitivity results from the insensitivity of the transverse mode proles to t...