1. Introduction

Balanced microwave photonic links exhibit superior microwave and radio frequency (RF) gain and noise performance compared to conventional analog links; both outputs of their Mach-Zehnder intensity modulators (MZMs) are detected by balanced photodetector pairs, doubling the link’s photocurrent and cancelling common mode noise [1]. However, these gain and noise improvements come at a cost. First, balanced links are generally more complicated to construct since two separate and precisely RF phase/optical path length matched single-mode fiber (SMF) spans are required (Fig. 1(a)). Second, in operation, environmental perturbations can cause differential refractive index variations via the stress and thermo-optical effects, changing the optical path lengths of the two separate fibers and adversely affecting the link’s gain and noise canceling performance (i.e. by ‘unbalancing’ the link). Specifically, the thermo-optical effect can change the propagation delays by up to 40ps/km/K in standard SMF at 1550 nm [2–4]. These errors may be negligible over short distances and low RF frequencies, but they could become non-negligible at higher frequencies and over longer propagation distances. For example, two 1-km SMF spans with only a 0.1 K temperature differential will be differentially delayed by 4ps. At 1 GHz this temperature differential will induce only a 1.44° phase error between the two spans. However, at 25 GHz this corresponds to a detrimental 36° phase error. Of course, co-location of the SMF spans within jacketed cables help to mitigate these effects [5]. Additionally, alternate mitigation techniques include the use of specialized fiber coatings [3] or by using, for example, hollow-core photonic bandgap fibers [4]. Here, multicore fibers (MCFs) present another possible solution toward mitigation of RF phase errors in longer distance balanced links.

 

Fig. 1. a) Diagram of a conventional balanced link based on two separate spans of SMF. b) Diagram of the balanced link based on multicore fiber and the cross-section of the four core fiber (not to scale). VOA: variable optical attenuator, φ: optical phase shifter, BPDs: balanced photodetectors.

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In a MCF-based balanced link, the two outputs of the MZM are simply space-division multiplexed (SDM) into and out of the separate cores of a single MCF (Fig. 1(b)) rather than two separate SMFs (Fig. 1(a)). Since a majority of the link consists of a single span of MCF, it is significantly easier to construct compared to its SMF counterpart; only the short uncommon fiber paths in the link’s front and back-ends must be RF phase matched. Moreover, in past studies the dynamic inter-core differential optical delay, or dynamic ‘skew’, due to temperature fluctuations have been shown to be an order of magnitude less in multicore fibers compared to two separate SMF spans [6–9]. With their possible greater resilience to environmental effects and ease of construction, MCFs have the potential to extend the reach of balanced links into the realm of long-haul analog link applications [10], such as radio-over-fiber [11,12], military radars [13,14], and radio telescopes [15–17], while still keeping them practical to construct and operate.

In the field of microwave photonics, MCFs have been demonstrated in several signal processing applications [18,19], such as sampled delay lines [20,21] and optoelectronic oscillators [22], to name only a few. Surprisingly, however, balanced links based on MCF have not been thoroughly investigated, especially for longer propagation distances. Notably, a 20 m balanced link based on dual-core fiber was demonstrated recently, with promising results [23]. In this work, we extend the MCF length to one km, demonstrating a viable balanced link based on a single span of commercially-available homogeneous four core MCF. Its RF gain and phase stability over temperature was measured and compared to an equivalent length SMF-based balanced link. In addition, the inter-core RF crosstalk of the MCF was measured.

2. Experimental setup

The MCF-based balanced link consisted of a λ=1557 nm laser source followed by a dual output MZM (Fig. 1(b)). The laser’s linewidth was 59 kHz. Both outputs of the MZM were connected to fan-ins/fan-outs (Fibercore: Optofan 3D – 4 Channel) which space-division multiplex the optical signals from the two separate SMFs into separate cores of the MCF (Fibercore: SM4C-1500). From manufacturer specifications, the optical insertion loss of the multiplexers were ≤1.3 dB per channel and the optical crosstalk was ≤ -40 dB between channels. The MCFs’ identical single mode cores are arranged in a square configuration with a mean 50µm spacing between adjacent cores (cross-section shown in Fig. 1(b)). The MCF propagation loss was 1.76 dB/km, considerably larger than SMF. After propagation through the MCF, the optical signals were then de-multiplexed back into separate SMFs, individually-attenuated, and then phase-shifted in order to balance the link, i.e. to compensate for any differential optical attenuation and delay between the two separate paths. The optical signals were then detected by a pair of photodetectors (Discovery Semiconductors: DSC2-50S) whose photocurrents were subtracted using an 180° RF hybrid (Krytar). For comparison, a 1 km balanced link based on two separate SMF spans was also constructed (see Fig. 1(a)). The exact same front-end and back-end components (laser, MZM, VOAs, Φs, PDs, and RF hybrid) were used for both links. Importantly, to be more representative of a balanced link, the two SMF spans were spooled simultaneously ‘side-by-side’ on the same mandrel in order to co-locate the two fibers as close as possible. The single MCF span and the dual spans of SMF were then removed completely from their spools, leaving only loosely coiled fiber.

The RF gain and phases of the links were measured using an Agilent E8361 network analyzer. In MCF, it is well known that optical crosstalk can occur between the cores during propagation and at discrete points (e.g. at splices and components). If appreciable, the optical crosstalk could cause gain and phase fluctuations in the RF domain which could adversely affect the performance of a balanced link. Here, we define the RF XT as the ratio of RF power at a chosen frequency, Ω, received from a MCF core that initially only contained continuous wave (CW) light vs. the RF power received from a core that initially only contained RF modulated light: $X{T_{RF}} = {P_{CW}}(\mathrm{\Omega } )/{P_{Mod}}(\mathrm{\Omega } )$. The RF XT was measured by splitting the optical signal immediately after the laser using a 50:50 fused fiber coupler. One of the coupler’s outputs was sent through the modulator path, whereas the other bypassed the modulator and was routed through an optical attenuator and then into another core of the MCF, i.e. the CW path. The CW path’s optical power was attenuated to be equal to the modulated path’s power, representative of a balanced link. Each separate path was detected by a single PD and the RF signal was subsequently amplified. The RF signals were generated using an Agilent N5183A analog signal generator and detected using an Agilent N9030A electrical signal analyzer. Finally, the RF differential phase stability over temperature, i.e. the difference in phases between the two arms of the MCF link as the temperature was varied, was quantified by placing the uninsulated SMF and MCF fiber coils inside a temperature-controlled chamber. The temperatures were measured using thermocouples attached to the outermost layer of the spooled fiber using polyimide tape. It is important to note that the thermocouples are only measuring the T’s of the surface of the spooled fibers in very small area (3 × 2 mm) and are not representative of the overall fiber temperature. Only the fibers themselves were inside the chamber, the fan-in/fan-outs and all other components were outside the chamber in an insulated box. Each arm of the links were alternately attenuated using the VOAs to individually measure their RF phases, ${\varphi _{i,j}}$ (where i,j are the MCF core numbers) at a single RF frequency of Ω as the temperature of the chamber was slowly varied. The RF differential phases were then calculated as $\mathrm{\Delta }{\varphi _{ij}} = {\varphi _i} - {\varphi _j}$. The ideal link with ‘perfect’ phase stability would have a $|{\mathrm{\Delta }{\varphi_{ij}}} |= 0$.

3. Experimental results and discussions

3.1 RF gain improvement

The measured RF gain(s) (S₂₁) of the MCF balanced link are plotted in Fig. 2 for the balanced pair, G_BP, and single cores (or arms) of the link, G₁ and G₄, where the subscript corresponds to the core number (see core labeling and positions in Fig. 1 b). For a RF photonic link, the RF gain is proportional to the squared ratio of the received photocurrent, I_DC, and the modulator efficiency, V_π (${G_{RF}} \propto I_{DC}^2/V_\pi ^2$) [1]. Since I_DC is doubled for the balanced pair (G_BP in the figure), there is a four-fold or 6 dB improvement in gain compared to the single arms of the link, G₁,₄. In the figure G_BP shows +6 dB improvement across nearly the entire measured frequency range. The small frequency-dependent oscillations are due to the frequency response of the RF hybrid as well as the unequal responses of the PDs. The gains were approximately the same for all other core combinations and are not shown. Of course, the SMF link exhibits the same +6 dB improvement relative to its single arms. Critically, however, the MCF link exhibits significantly lower RF gain when directly compared to the SMF balanced link (i.e. given the same optical input power) since there are additional insertion losses from the multiplexers and from propagation through the MCF itself. For this MCF and components, the RF gain was ≈12 dB less than the SMF link due to the additional ≈6 dB optical loss. In application this could be compensated for, to some degree, by using a higher power source and/or adding an optical amplifier.

 

Fig. 2. RF gain or S₂₁ of the MCF link for the balanced pair (G_BP, black line) and single cores (G₁, G₄, blue & green lines). G­_BP shows the approx. the expected +6 dB improvement compared to the single arm gains of G₁ and G₄ across the entire measured RF frequency range. All other core combinations showed the same improvement.

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3.2 Inter-core RF crosstalk

Plotted in Fig. 3(a)) are the measured RF output powers received from cores c₁, c₂, c₃, and c₄ while measuring a fixed RF frequency over a chosen time interval, commonly called a ‘zero-span’ measurement. A Ω=10 GHz modulated optical signal was launched into c₁, whereas the CW light was either launched into the adjacent cores, c₂,₃, or the diagonal core, c₄. As can be seen in Fig. 3(a)), the RF powers received out of c₂,c₃, and c₄ were all at least 60 dB below the RF power received out of c₁. The received RF powers fluctuated randomly over the course of the measurements due the stochastic nature of optical crosstalk in MCF [24,25]. Figure 3(b), (c), and (d) displays the RF XT histograms calculated from the measured RF powers over time (Fig. 3(a)). The XT measured at other RF frequencies were similar in magnitude and are not shown. Interestingly, the mean XT between the diagonally-opposite cores (c₁ →c₄) was only 9 dB less than the adjacent cores (c₁→c₂,₃). Assuming the XT originated from only propagation, the diagonally-opposite cores should have exhibited significantly lower XT compared to the adjacent cores [26]. Hence, these measurements suggests the XT in this particular link may be dominated by sources other than propagation.

 

Fig. 3. a) The RF power at Ω=10 GHz received out of each core over a 120s interval: c₁ contains the RF modulated signal (black line) which corresponds to ${P_{Mod}}(\Omega )$ in the definition of RF XT, whereas c₂ (blue line), c₃ (cyan), and c₄ (green) initially contained only CW light, corresponding to ${P_{CW}}(\Omega )$. After propagating through 1 km of MCF, there is measurable RF power at Ω in the CW paths due to optical XT. The noise floor is also shown (red).

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Figure 4 reveals the origins of the RF XT for this particular link. It displays the means and standard deviations of the RF XT at 10 GHz through a short link comprised of the two multiplexers connected by a single MCF-to-MCF splice and a MCF length of only 10 m. The splice was performed three separate times by manually-rotating the fibers while attempting to maximize the optical output powers from each core. After each splice, the short link exhibited RF XTs in the -70 to -60 dB and -80 to -70 dB ranges between the adjacent and diagonal cores, respectively. Figure 4(b)) shows the same measurements for the full MCF link, comprised of the two multiplexers connected by two MCF-to-MCF splices and 1 km of MCF. Given there is comparable XT in the 10 m span of MCF compared to the 1 km span, we can reasonably conclude that the RF XT in this particular link is dominated by XT occurring at localized points, e.g. at the multiplexers and the MCF-to-MCF splices, rather than distributed XT due to propagation.

 

Fig. 4. a) Mean and standard deviations of 10 GHz RF XT zero-spans through only the multiplexers, 10 m of MCF, and one MCF-to-MCF splice performed 3 separate times. Schematic shown below the figure. b) Mean and standard deviations of the same through the multiplexers, 1 km of MCF, and two higher quality MCF-to-MCF splices. Mean and standard deviations were determined from the linear scale RF XT data and converted back to dB-scale.

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Regardless of the XT’s origins, XT levels of -60 dB or below through 1 km of MCF could be considered negligible for most conventional link applications (-60 dB corresponds to a RF XT to signal power ratio of only 10⁻⁶). In our case, the RF XT was relatively constant since it was dominated by contributions from the multiplexers and splices rather than through propagation. However, with longer propagation distances and/or if better multiplexers and splices were used, the XT could be dependent on many more factors including the mode propagation constants, core-to-core separations, and the bending radii and the twisting rates of the MCF [24,25]. Hence, the measured XT levels in a MCF-based balanced link could also exhibit dependence on the layout of the fiber itself if the localized sources of XT are mitigated. Nevertheless, even with measurable XT, MCF is a comparatively better single fiber alternative for use in balanced links than, for example, few mode fiber, which exhibits severe RF gain fluctuations due to intra-core mode-coupling [27].

3.3 RF differential phase stability

Figure 5 displays the measured differential RF phases, $\Delta {\varphi _{ij}}$, at 25 GHz over a 3 hour period as the temperature (T) was periodically-varied for both the MCF and SMF-based balanced links with the fibers coiled. The T-profiles (time vs. T) are shown on the right axis of Fig. 5 a) and b), ramping up and down by 13°C over a period of 60 mins. The measured differential phase fluctuations are due to the induced thermal differentials and strain differentials between the fiber cores via the thermo-optical and stress-optical effects, as detailed in [28]. Interestingly, each of the MCF’s core pairings in Fig. 5 a) exhibited different Δφs despite nearly identical T-profiles. The differential phase between c₁ and c₄, $\Delta {\varphi _{14}}\; $, fluctuated the least with an absolute max phase error of only ${|{\Delta {\varphi_{14}}\; } |_{max}}$≈5°, whereas $\Delta {\varphi _{23}}\; $ fluctuated the most with ${|{\Delta {\varphi_{23}}\; } |_{max}}$≈13°. At 25 GHz, these Δφs correspond to differential skews of $|{\Delta {t_{14}}} |$≈0.55ps and $|{\Delta {t_{23}}} |$≈1.44ps, on the same order as the previous studies [6–9]. In a balanced link, a 13° offset at 25 GHz will cause only a 0.2 dB reduction in RF gain. The adjacent core phase errors, $|{\Delta {\varphi_{12}}} |\; $ and $|{\Delta {\varphi_{13}}} |$, both ranged between 5° and 13°. Notably, c₂ and c­₃ are diagonally-opposite cores and are orthogonal to the diagonal connecting c₁ and c₄. For comparison, $\Delta {\varphi _{SMF}}$ is shown in Fig. 5 b) and exhibited a ${|{\Delta {\varphi_{SMF}}} |_{max}}$ of only ≈7°. Hence, in stark contrast to [8,9], the SMF spans did not exhibit an order of magnitude larger differential phase errors/skews than the MCF. Instead, their phase errors/skews were comparable.

 

Fig. 5. a) The differential RF phases, Δφ_i,j, between cores i and j of the MCF-based link at 25 GHz over a 3 hour period. b) Δφ between the two spans of SMF at 25 GHz over the same period of time. Their nearly identical T-profiles are also shown (grey dotted lines, right scales).

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Why is there such a large disparity? The most important distinction here is that our two spans of SMF were co-located as close as possible together and removed from their spool (i.e. more representative of a balanced link in application), whereas in the other cited studies the two SMF spans were kept on physically-separate spools. Even with careful environmental isolation and common insulation, separate spools can still exhibit non-negligible temperature differentials which could easily ‘exaggerate’ the measured skews between the SMFs, as was noted as possible in [8]. Moreover, the spools themselves can also complicate the measurements since their thermo-mechanical expansion and contraction, in combination with the fiber’s orientation(s) and tension(s), can also contribute to the measured differential skews. Co-locating the SMF spans and removing the fiber from the spools at least enables a fairer in laboratory comparison between the cores of the MCF and two separate SMFs. Regardless, these measurement at least reveal that the MCFs have promising RF phase stability for higher frequency and longer distance balanced links, but they may not necessarily have better phase stabilities compared to two carefully co-located SMF spans. In fact, commercially-available ‘loose-tube’ optical fiber cables have exhibited less than 1° phase error for frequencies up to 18 GHz under T differentials of up to 40° C [28]. However, the heated cable lengths in that study were only 1 to 5 m. Hence, it is unclear if the induced RF phase error would still remain low for a much longer cable span. Nevertheless, the MCF span may still be more resilient to installation and manufacturing errors which otherwise would cause the SMF spans to separate within their cables. In the end, the best comparison would be between ‘deployed’ MCF and SMF cables in the field which, unfortunately, were beyond our resources at the time of this work.

4. Conclusion

We have demonstrated a one km balanced analog photonic link based on a single span of MCF. In contrast to other studies, the MCF and SMF spans both exhibited comparable differential phase fluctuations with temperature. The disparity can be resolved by considering fiber configurations; our dual spans of SMF were co-located as close as possible together and removed from their spools to be more representative of balanced links in application. Regardless of the SMF link’s performance, the MCF-based link exhibited low RF XT, acceptable RF phase stability at higher frequencies and, critically, is significantly easier to construct compared to its SMF counterpart. Of course, the simplified construction does comes at a cost; there is significantly higher optical loss and measurable XT between the cores that is dependent on the specific SDM components and MCF used, the number and quality of splices, and the fiber layout. Hence, it will be prudent to test future MCF-based balanced links with their fiber span configured as close as possible to their intended applications. Nevertheless, the measurements here demonstrate that space-division multiplexing into and out of the cores of a single MCF is a viable alternative architecture for balanced analog photonics links, warranting further investigations.