Unconventional plastic optical fiber design for very short multimode fiber link

Azusa Inoue; Yasuhiro Koike

doi:10.1364/OE.27.012061

1. Introduction

With the proliferation of smartphones, tablets, televisions, and various monitoring devices, Internet traffic continues to grow toward the next-generation Internet of Things (IoT) era [1]. This growth is being accelerated by the implementation of ultrahigh-definition (UHD) imaging technologies in IoT environments. To accommodate this traffic, core/metro/access networks including datacenter networks have been rapidly developed [2–4]. While UHD videos are highly compressed for their distribution and acquisition through the existing networks, UHD data are decompressed for connections of UHD devices in homes and buildings located in the optical network terminal area. For video formats with 8K (7680 × 4320) resolution, the decompressed data rate is well above 100 Gb/s [5], where multilevel pulse amplitude modulation (PAM) is vital [6,7].

For household applications, optical fiber lengths are typically several meters, and less than or comparable to 30 m. These short optical cables are frequently connected and disconnected by consumers in a manner similar to conventional metal cables. It is essential to develop low-cost optical modules and connectors without the requirement for precise fiber alignment or high manufacturing accuracies. Under these specific conditions, the data transmission quality is degraded by various noise sources (e.g., reflection noise, modal noise, multipath interference noise, and polarization noise), which depend on the condition of the connecting optical fiber in optical modules and connectors. This degradation becomes more pronounced for multilevel modulation schemes such as the 4-level PAM (PAM-4), which is more sensitive to noise than the commonly used PAM-2. Therefore, in contrast to conventional optical data transmission that has developed low-loss, high-bandwidth optical fibers [8], household applications require low-noise optical fiber technologies.

Graded-index plastic optical fiber (GI POF) is a promising optical cable for household applications because of its flexibility, safety, and high bandwidth [9,10], which enables 40-Gb/s data transmission over a 100-m GI POF. Recently, we proposed a low-noise GI POF to achieve stable, robust data transmission in a multimode fiber (MMF) link with a vertical-cavity surface emitting laser (VCSEL) [11]. The GI POF has strong mode coupling that is closely related to the microscopic heterogeneities in the core material, which induce forward light scattering. The strong mode coupling can significantly decrease interferometric noise, including that due to external optical feedback [12], to stabilize PAM transmission through reduction in the amplitude and timing jitter. Although such noise reduction effects can be enhanced by increasing the mode coupling strength, this enhancement involves an increase in the scattering loss through power transition from the guided modes to radiation modes. Scattering loss due to radiative mode coupling is problematic for the long-distance data transmission of existing optical networks, however, for very short-distance applications, this scattering loss is less critical.

In this paper, we introduce an unconventional optical fiber design for household applications utilizing characteristic microscopic heterogeneities that can induce strong mode coupling with sufficiently low scattering loss. The developed GI POF achieves lower-noise data transmission owing to reflection noise reduction through the strong mode coupling compared to the silica GI MMFs for link lengths below 30 m. Moreover, in the low-noise GI POF link, the transmitted signal quality tends to improve with increase in fiber length, despite the increase in attenuation and decrease in bandwidth of the GI POF. This suggests that the GI POF link quality can be further increased by controlling the mode coupling through the microscopic heterogeneous properties of the GI POF core material, depending on the optical link length required for each application.

2. Characteristic mode coupling

POF materials are composed of extremely large polymer coils and are completely different from silica glasses, which are composed of covalent networks [see Fig. 1(a)]. These polymer-specific structures result in density and composition fluctuations at different scales. Low-noise GI POF core materials have microscopic heterogeneities that can induce random mode coupling by the forward scattering of guided light in the GI POF. This intrinsic mode coupling in the GI POF can be described as follows [13]:

\frac{\partial P_{i}}{\partial z} = \sum_{j = 1}^{N} h_{i j} (P_{j} - P_{i}),

where

P_{i (j)}

is the ensemble-averaged mode power and

N

is the total number of propagation modes. In the GI POF, the coupling coefficient

h_{i j}

, i.e., the coupling strength between modes

i

and

j

, is given by

h_{i j} = 〈 δ ε_{r}^{2} 〉 \frac{ε_{0}^{2} ω^{2} π^{3 / 2} a^{3}}{8} \exp (- \frac{Δ β_{i j}^{2} a^{2}}{4}) \iint {| E_{i}^{*} \cdot E_{j} |}^{2} d x d y .

Here,

E_{i (j)}

is the transverse electric-field vector for mode

i (j)

,

Δ β_{i j}

is the propagation constant difference between the modes

i

and

j

,

ω

is the angular frequency of guided light,

ε_{0}

is the vacuum dielectric constant, and

δ ε_{r}

is the relative dielectric constant fluctuation. As shown in Eq. (2), the coupling coefficient depends on the microscopic heterogeneous properties of the correlation length

a

and the mean square fluctuation

〈 δ ε_{r}^{2} 〉

, which correspond to the measures of the fluctuation size and amplitude, respectively. The coupling coefficients barely depend on the differences in the propagation constant between the guided mode pairs, because

\exp (- Δ β_{i j}^{2} a^{2} / 4) \approx 1

for a typical correlation length

a

of the low-noise GI POF core [9,13]. This indicates that the mechanism of mode coupling in the GI POF is fundamentally different from that of the microbending-induced coupling in the silica GI MMFs. It is difficult to directly observe and evaluate the microscopic heterogeneities in the actual GI POF core because the fluctuations are too small to measure. Therefore, we estimated the coupling coefficients and microscopic heterogeneous properties of our fabricated low-noise GI POF (described below) using the developed coupled power equation for analyzing the frequency response of the GI POF [14]. This estimation suggests that the GI POF core has considerably large microscopic heterogeneities, whose correlation lengths

a

are 400–1900 nm for

〈 δ ε_{r}^{2} 〉

of the order of 10⁻⁸–10⁻⁷, as shown in Fig. 1(b).

Fig. 1 (a) Schematic of microscopic structures of GI POF core materials. (b) Estimated correlation length $a$ vs. mean square of relative dielectric constant fluctuation $〈 δ ε_{r}^{2} 〉$ of microscopic heterogeneities in fabricated low-noise GI POF core.

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Using the co-extrusion method [15,16], we fabricated a low-noise GI POF with the specific microscopic heterogeneities, whose properties depend on the material, polymerization conditions, and heat treatment [17,18]. The low-noise GI POF had a core diameter of ~50 μm, numerical aperture (NA) of ~0.2, and GI profile index-exponent of ~2.0, which is almost the same as that of the reference silica GI MMF. The low-noise GI POF has an attenuation of ~6.4 × 10⁻² dB/m and a bandwidth of ~210 GHz·m, whereas the silica GI MMF has an attenuation of ~2.3 × 10⁻³ dB/m and a bandwidth above 2650 GHz·m (device limit of the component analyzer). Note that the loss and bandwidth of the GI POF are sufficiently low and high, respectively, for household applications, where most link lengths are below 10 m. We evaluated the characteristics of the mode coupling in the GI POF by measuring the near-field patterns (NFPs) and far-field patterns (FFPs) of the output beams from the GI POFs. These measurements were performed for center launching using an 852-nm single longitudinal mode laser pigtailed with a polarization-maintaining single mode fiber (SMF). The laser has a linewidth of 10 MHz, a mode field diameter (MFD) of 5.3 μm, and an angled physical contact connector. Figure 2 shows the corresponding output-beam diameters and divergence angles of the silica GI MMF and low-noise GI POF as functions of the fiber lengths. The output beam parameters were estimated according to the definitions with the second-order moments of the NFPs and FFPs [19]. The silica GI MMF exhibited almost the same NFPs and FFPs for all fiber lengths. The NFPs of the silica GI MMFs were similar to those of the launched modes. On the other hand, as shown in the inset of Fig. 2(a), the low-noise GI POF exhibited speckle NFPs, whereas the silica GI MMF did not exhibit speckle because of negligible mode coupling. This speckle NFP of the GI POF is attributed to the strong mode coupling that induces random power transition between all the guided modes, which, in contrast with microbending-induced coupling, is stronger for the lower principal mode groups. This strong mode coupling increased the diameters and divergence angles of the speckle output beams, and this effect became more pronounced for longer fiber lengths.

Fig. 2 (a) Beam diameters and (b) divergence angles of optical fiber output beams as functions of fiber length. From left to right, the insets show the NFPs and FFPs of the input beam and the output beams from the 10-m silica GI MMF and 10-m low-noise GI POF. The beam parameters were estimated according to the second-order moment method. The scale bars for the NFPs and FFPs are 10 μm and 5°, respectively.

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3. Low-noise GI POF link

Figure 3 (a) depicts the experimental setup consisting of a fiber, a 12-GHz GaAs photodiode (PD), and an 850-nm multimode VCSEL, which was directly modulated with 10-Gb/s non-return-to-zero (NRZ) data (pseudorandom bit-sequence with a pattern length of 2³¹–1) at a bias current of 5 mA. The VCSEL had a bandwidth of ~9 GHz and an average relaxation frequency of ~6 GHz. Its output beam was coupled to a fiber with an antireflection (AR)-coated lens for the center launching condition, where the input beam diameter and divergence angle were smaller than the fiber core diameters and NAs, respectively. The output beam from the fiber was collimated and focused on the PD with AR-coated lenses. All the output beams from the fibers were in the PD active area for all the evaluated fibers, as confirmed by a charge coupled device (CCD) camera [see Fig. 3(b)]. Thus, the transmission quality could be evaluated with negligible coupling loss and modal noise, which is defined as power fluctuations due to the partial detection of a beam with a fluctuating speckled pattern [20]. We measured the bit error rates (BERs) of the data transmitted through the low-noise GI POF and silica GI MMF for a very low modulation voltage of 0.07 V; this voltage is less than or comparable to the minimum symbol-level difference in PAM-4 with the VCSEL, whereas the modulation voltage is typically 0.35–0.4 V for the NRZ (PAM-2). For such significantly low input-signal levels, the BER is sensitive to noise, which depends on the alignment of the fiber end-faces with the VCSEL and PD. Therefore, we evaluated the MMF link quality by measuring the BER under precisely aligned conditions of the optical components.

Fig. 3 (a) Experimental setup. A broadband dichroic mirror with negligible polarization dependence is located between the fiber and PD to monitor the PD irradiated by the output beam. The dichroic mirror barely influences the transmission quality because the reflectivity of the mirror is almost the same for all the oscillation wavelengths of the VCSEL modes. (b) Microscopic images of PD active area irradiated with output beam from silica GI MMF and low-noise GI POF with fiber lengths of 30 m.

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As shown in Fig. 4(a), the silica GI MMFs had BERs around 10⁻⁴ regardless of the fiber lengths. Such high BERs are mainly due to the low modulation voltage or low input signal-to-noise ratio (SNR). However, the BERs were reduced significantly by using the low-noise GI POF for all fiber lengths below 30 m. Moreover, this improvement tended to be more pronounced with an increasing fiber length up to 10 m, despite the increase in the loss and decrease in the bandwidth. These features suggest that the improvement can be attributed to the strong mode coupling of the low-noise GI POF, which may decrease noise in the MMF link. The GI POF enabled lower BERs or higher SNRs for longer fiber lengths, resulting in the lowest BER or highest SNR for a fiber length of 10 m. For fibers longer than 10 m, this BER improvement effect was decreased by the increased attenuation and decreased bandwidth, however, despite this, the BER for the low-noise GI POF remained lower than that of the silica GI MMF up to 30 m.

Fig. 4 (a) BERs and (b) received optical powers for 10-Gb/s NRZ data transmission through MMF links with silica GI MMF and low-noise GI POF as functions of fiber length.

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To investigate the BER improvement in detail, the temporally averaged noise spectra of the optical links were measured for various fiber lengths, as shown in Figs. 5(a) and 5(b), which are the spectra measured for different frequency ranges and resolution bandwidths (RBWs). These spectra suggest that the dominant noise mechanism is reflection noise due to the external optical feedback in the MMF link. Both fibers exhibited periodic peaks with equal spacing corresponding to the round-trip frequencies $ν_{R}$ of two imaginary external cavities with external reflectors at the fiber output face and PD [see Fig. 5(a)]. The peak spacing decreased with the increasing fiber length, according to $ν_{R} = c / 2 l_{0}$ , where $ν_{R}$ is the peak spacing, $l_{0}$ is the external cavity optical length, and $c$ is the velocity of light [21,22]. Therefore, the spikes are external-cavity-mode beatings, indicating the generation of external cavity modes and anti-modes due to external optical feedback from the reflectors. Each peak may include beatings with slightly different $ν_{R}$ values, which correspond to the optical feedback from the fiber output face and PD. In Fig. 5(a), such an underlying peak structure can be observed as a peak separation that is more pronounced at higher frequencies for fiber lengths of 1–5 m. For silica GI MMFs, the noise spectra had more complex structures with other small peaks, whose generation mechanism is currently under investigation using the laser rate equation, considering the external optical feedback. However, for all fiber lengths, peaks with considerably lower powers were observed for the low-noise GI POF than for the silica GI MMF. This reduction in the power of periodic peaks due to external-cavity-mode generation is attributed to the strong mode coupling of the low-noise GI POF [11,12]. This strong mode coupling can decrease the self-coupling fractions of the light back-reflected into the VCSEL cavity, by changing the field pattern, degree of polarization, and degree of coherence of the back-reflected light through roundtrip guidance.

Fig. 5 (a) Average noise spectra of optical links with silica GI MMF (green) and low-noise GI POF (red) for various fiber lengths; the RBW is 1 MHz. (b) Corresponding spectra measured for wider frequency range; the RBW is 10 MHz. The noise spectra were obtained by averaging the scanned spectra over 1000 scans. The reference plane corresponds to an electrical noise power of −60 dBm.

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The silica GI MMF links also exhibited a pronounced envelope peak at ~1.5 GHz, which is barely observable in the low-noise GI POF links. A similar envelope peak was observed for the 1-m low-noise GI POF, but this envelope peak level was significantly lower than that of the 1-m silica GI MMF. In VCSEL-based MMF links subject to external optical feedback, this envelope peak tends to grow into periodic envelope peaks with increasing feedback levels, significantly increasing the BER [12]. As shown in Fig. 5(b), approximately periodic envelope peaks were observed for the silica GI MMF, with the clearest peaks at a length of 5 m. However, such a critical destabilization of the periodic envelope peak generation can be avoided by using the low-noise GI POF for all the link lengths. This stabilization by the low-noise GI POF is likely due to suppression of external cavity formation through the strong mode coupling [12]. This effect may be the dominant mechanism underlying the lower BER, which was improved by replacing the silica GI MMF with the low-noise GI POF, as shown in Fig. 4(a).

4. Conclusion

In conclusion, we have proposed an unconventional optical fiber design utilizing the strong mode coupling of the GI POF to achieve low-noise data transmission for emerging household applications. The developed GI POF with characteristic microscopic heterogeneities achieved significantly higher-quality data transmission than silica GI MMFs. This is owing to reflection noise reduction through strong mode coupling with sufficiently low scattering loss for very short MMF links. Moreover, in the low-noise GI POF link, the transmitted signal quality tends to improve for longer fiber lengths, despite higher attenuation and lower bandwidth, whereas an increase in the fiber length decreases the BER improvement effect for fiber lengths above 10 m. This feature suggests that, by controlling the mode coupling using the microscopic heterogeneous properties of the GI POF core material, we can optimize the data transmission quality for a given optical link length per application requirements. This novel concept for optical-fiber design will pave the way for the proliferation of optical fiber in households.

Funding

The Strategic Promotion of Innovative Research and Development (S-Innovation).

Acknowledgements

This paper is based on the results of a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO) of Japan.

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Unconventional plastic optical fiber design for very short multimode fiber link

Abstract

1. Introduction

2. Characteristic mode coupling

3. Low-noise GI POF link

4. Conclusion

Funding

Acknowledgements

References

Cited By

Figures (5)

Equations (2)

Optics Express