Selective coupling a single pair of cores in a photonic crystal fiber with multiple, initially decoupled, cores is demonstrated through the use of a technique to locally post-process the fiber cross section. Coupling occurs when the hole between the selected core pair is collapsed over a short fiber section, which is accomplished by heating the section while the hole is submitted to an air pressure that is lower than that applied to all other holes in the microstructure. The demonstrated couplers present an estimated insertion loss of ~1 dB and exhibit spectral modulations with a depth of up to 18 dB and a high polarization sensitivity that can be exploited for polarization splitting or filtering in space-division-multiplexed optical interconnection and telecommunication links.
© 2012 OSA
Multicore fibers have received increased interest in recent years for their numerous application as, e.g., variable optical attenuators , sensors [2–4], gain media in high-power or high-energy pulsed lasers and amplifiers [5, 6], nonlinear media in supercontinuum sources [7, 8] and multi-pixel image fibers for endoscopic imaging . More recently, however, space-division multiplexed optical telecommunications has emerged as one of the most important and exciting fields of application for multicore fibers, with significant increases in system capacity expected [10–15]. So far, up to 112 Tb/s transmission rates over 76.8 km have been demonstrated, using 160 polarization-division multiplexed quadrature phase-shift keying (PDM-QPSK) 107 Gb/s channels, in each of the 7 cores of a fiber . Multicore fibers have also been suggested and demonstrated for optical interconnection . A number of fiber components, such as tapered fiber connectors [11, 12, 14] and arrays of detectors and vertical-cavity surface-emitting lasers (VCSELs) [11, 13, 15, 16], have been developed and used as enabling technology. Due to their extreme design flexibility, photonic crystal fibers (PCFs) are very attractive candidates for the development of multicore fibers and components, with several of multicore PCFs already demonstrated [2, 5–8, 16–20], including demonstrations aimed at space-division multiplexing in telecommunication  and interconnection  systems.
Although some of the proposed multicore fiber communication systems rely on coupling between cores  (and some devices rely on such a coupling to accomplish, e.g., channel splitting  or nonlinear switching ), for most demonstrated systems it is crucial that the cores remain decoupled along the whole transmission link to avoid channel crosstalk. Nevertheless, local coupling between cores at specific system positions may be important for, e.g., channel multiplexing/demultiplexing, re-routing or multicasting. A few methods for locally coupling initially decoupled cores in multicore fibers have been reported in the literature. It is possible, e.g., to obtain coupling segments by local tapering the fiber  or the region around a single-core/multicore fiber splice . Coupling is also obtained if the multicore fiber is spliced with a segment of a fiber with a single core whose diameter encompasses several cores [2, 3]. However, all these methods invariably cause the coupling of all neighboring cores, being virtually impossible to choose which cores become coupled and which remain decoupled.
In this paper, we demonstrate the feasibility of selectively coupling a single core pair in a multicore PCF. While the method is quite general, in this paper it is applied to a PCF with a line of three equally-spaced and initially decoupled cores. The method relies on the selective collapse of the hole between the cores to be coupled, using the technique to locally alter the fiber cross-section that was previously demonstrated by Witkowska et al. . It is noted that this technique has been previously employed to demonstrate cores with complex shapes , mode converters  and modal Mach-Zehnder interferometers , all in single-core PCFs. To the best of our knowledge, the technique has so far not been described for use with multicore fibers, except in a brief and preliminary report by our group .
2. Experimental setups
To obtain the proposed coupling structure, the fiber post-fabrication processing technique described in  was used. In it, holes can be selectively collapsed upon fiber tapering if the air pressure is raised in all holes that are to remain open. This is accomplished by sealing the entrance to the holes to be collapsed, so that they remain at room pressure while a fiber section is heated. In our case, to seal the entrance of the hole to be collapsed, i.e., the hole between the two cores to be coupled, a UV curable polymer was used, which was deployed via a micropipette . The fiber tip with the sealed hole entrance was then connected to a nitrogen pressure cell, while all the holes were sealed in the opposite tip. The fiber was then placed in a tapering rig, where it was brushed with a temperature-controlled isobutane and oxygen flame that moved along the fiber axis using a DC motor, Fig. 1 . In our case, the aimed change in the fiber cross section was sufficiently small so that tapering was not required . The fiber was, therefore, not pulled during the whole process.
The cross section of the silica multicore PCF that was employed in the proof-of-principle experiments reported here is shown in Fig. 2(a) . It consists of three solid cores (numbered sequentially in the Fig.), each with a diameter of 2.4 µm, that are immersed in a 2.2-µm-pitch matrix of 1.8-µm diameter holes. The holes are separated from each other by a single hole, which leads to a core pitch of 4.4 μm. This pitch is expected to be appropriate to avoid inter-core crosstalk in interconnects , but in telecommunication systems larger pitches and more holes between cores are necessary . In this case, no major technical challenge would prevent the proposed method to be employed to collapse multiple holes, either in the same or in subsequent sections along the fiber.
It was found that the following processing parameters were adequate for collapsing the selected hole while leaving the rest of the microstructure nearly unchanged. Nitrogen pressure: 5 Bar; brushed fiber length: 5 mm; brushing time: 100 s. Figure 2(b) shows an image of the cross section of one post-processed PCF at the point in which the hole collapsed. Although some undesired microstructure distortion is visible, the average pitch and hole diameter near the cores are 2.0 µm and 1.8 µm respectively, which is close to the original values. Figure 2(c) schematically shows a longitudinal cut to the post-processed fiber, from which the local collapse of the hole between cores 1 and 2 can be seen. Note that for all optical experiments the collapse region was far from both fiber tips.
Figure 3 shows the experimental setup used to optically characterize the post-processed PCFs. Light from a supercontinuum source spectrally extending from 550 nm to at least 1700 nm traversed a polarizer (operating range: 650-1700 nm), used to linearize and to control the source state of polarization, and was then coupled into the fiber under characterization with the use of a 60 × objective lens. Unless otherwise stated in the text, all measurements were undertaken with an input polarization that is parallel to the line that connects the three cores. A 40 × objective lens subsequently imaged the fiber output tip on a beam profiler. The latter could be replaced with a multimode fiber (core diameter of 300 µm) connected to an optical spectrum analyzer (OSA) so that the transmission spectrum of each individual core was recorded. Bandpass filters and a neutral density attenuator were added to the setup after the second objective lens for some of the measurements with the beam profiler.
4. Results, analysis, and discussion
As a control experiment, a 7-cm-long section of the unprocessed multicore PCF was characterized with the setup shown in Fig. 3. While the beam profiler measurements showed that all three cores could be separately excited, measurements with the OSA revealed no spectral modulation in the transmission spectra, both of which demonstrate that the cores were decoupled from one another in the spectral region covered by the supercontinuum source. The absence of modulation also shows that single core modes can easily be excited despite the fiber not being strictly single moded. Coupling light into one core purposely at an angle, on the other hand, reveals a modulation with a 3.5-nm period at ~900 nm (for a 7-cm-long fiber; spectrum not shown), which can be attributed to beating between the two lower-order modes. A modal index difference of 3 × 10−3 can, therefore, be estimated. A longer (1 m) fiber section was also characterized with a 980-nm laser, with no appreciable coupling between cores detected.
Processed sections of multicore PCFs (with ~7-cm lengths) were then characterized. Figure 4 shows images of one fiber output under three different excitations (no filter was used in the fiber output). Figure 4(a) shows an image obtained with the input objective lens defocused, so that all cores are illuminated and from which the position of the three cores can be identified. Figure 4(b) shows the output image when light was focused and coupled solely into core 3. As with the unprocessed fiber, it can be seen that light remains in core 3, indicating that it remains decoupled from the other cores. Figure 4(c) shows the output image when light was focused and coupled into core 2. In this case, light always exited the fiber via cores 1 and 2; it was not possible to obtain light from these cores separately regardless of the input coupling conditions. The same trend was observed throughout the characterized spectral range. It is, therefore, concluded that processing couples cores 1 and 2, while leaving core 3 decoupled. This selective core pair coupling condition would not be possible to achieve using previously demonstrated methods, which couple all neighboring cores indiscriminately.
The mechanism that leads to coupling of the core pair is similar to that of the modal Mach-Zehnder interferometer reported in  (in that case for a single-core PCF with a collapsed hole next to it) and can be described as follows. As light is launched into core 1 or core 2, it excites its fundamental mode and travels along the fiber until it reaches the section with the collapsed hole, for which the core structure is significantly altered and comprises core 1, core 2 and the collapsed hole between them (see Fig. 2(b)). At this point, the traveling field distribution ceases to be a guided mode, becoming a superposition of guided (and, potentially, radiation) modes of the modified structure. Because each mode has a different propagation constant, they dephase leading to an evolution of the transverse field distribution. If, for simplicity, one can assume that only the first two modes of the modified structure are excited, the initial field distribution will be periodically recovered at propagation distances for which the relative phase between modes is a multiple of 2π. If the length of the collapsed hole region coincides with one of these distances, the propagated wave perfectly recouples to the core along which it was originally traveling. On the other hand, for distances over which the relative accumulated phase is an odd multiple of π, the field distribution becomes the mirror image of the initial distribution (assuming that a symmetric mode and an anti-symmetric mode are excited in the modified fiber section), having its maximum aligned with the other core. If the length of the collapsed hole region coincides with one of these distances, light will couple to the core that was initially not excited. For other collapsed lengths, fractions of the light intensity will couple to each of the coupled cores. We note that this mechanism is different from that usually used in fiber couplers, which rely on evanescent field coupling.
It can be shown  that, as phase accumulation depends upon the wavelength, λ, the described coupling dynamics generates a spectral modulation whose period, Δλ, is given by
Figure 5 shows the transmission spectra of cores 1 (red) and 2 (black) for two different post-processed fiber samples. These spectra were normalized with respect to that of core 3 (green in Fig. 5(a)) so as to remove the spectral distortion (alignment-dependent intensity decrease towards the extremes of the measured range) that was observed as a consequence of chromatic aberration in the characterization setup. It is noted that, as expected, in both Figs. cores 1 and 2 present spectral modulations with the same pitch and with a π relative phase. In Figs. 5(a) and 5(b), respectively, the modulation depths are of up to 18 dB and 16 dB, while the modulation periods are 56 nm and 127 nm at 900 nm. The differences in these modulation characteristics are attributed to slight variations on the hole collapse conditions and, especially, on the collapsed length. The faster, low amplitude, modulation observed in both spectra (7.0 nm and 8.4-nm modulation period at 900 nm in Figs. 5(a) and 5(b), respectively) may be tentatively explained as the result of Fabry-Perot resonances in bubbles formed at the beginning and end of the collapsed hole section (as a consequence of possible non-uniform heating at these positions).
From Eq. (1), one can see that the modulation period varies with wavelength both because of its explicit spectral dependence and because the modal indices, and therefore Δneff, depend on the wavelength. Figure 6 shows the value of the experimentally obtained modulation period for a wide spectral region, obtained in another produced coupler. The observed monotonic variation indicates the suitability of the model that takes into account only two modes within the modified waveguide. The right-hand side vertical axis in the Fig. shows the spectral variation of Δneff that is obtained with the use of Eq. (1), assuming L = 5 mm. The observed Δneff increase with wavelength, as well as its 10−3-10−2 order of magnitude, is in line with those observed in similar structures [25, 27]. Assuming the Δneff dependence on the wavelength to be approximately polynomial, from Eq. (1) one expects, to a first approximation, Δλ to be proportional to λb. It was found that b = −1 yields the best fit to the experimental data (black curve in Fig. 6), from which a cubic Δneff dependence on λ is concluded. The best cubic fit to Δneff is seen as a green curve in Fig. 6 and, indeed, fall on the experimental points.
It is noted that the supercontinuum light source presented a relatively low spectral power density in the 1550-nm region. For this reason an external cavity laser that was tunable in the 1510-1640 nm range was used for the periodicity measurement in this longer wavelength region. Note that despite the different characterization method, the modulation period, and therefore the Δneff value, both shown in Fig. 6, fall on the fitting curves, as expected.
The 1550-nm tunable laser was also used for estimating the insertion loss of the device. To this end, the laser was tuned to one of the transmission peaks of one core and the optical power was measured before the input lens and after the output lens (cut-back measurements were not possible due to the short device length), yielding a total loss of 4.1 ± 0.6 dB. The same loss in an unprocessed fiber section of same length was measured to be 4.4 ± 0.6 dB. An insertion loss no greater than 0.9 dB can, therefore, be inferred, which is adequate for practical use. The low insertion loss also indicates that coupling to radiation modes in the beginning and end of the collapsed hole section is minimal.
As can be seen from Fig. 2(b) the modified core structure has an extremely elongated shape along the line that connects the three cores. A high birefringence is, therefore, anticipated, which is expected to affect the inter-core coupling and, consequently, the obtained transmission spectra. Figure 7 shows data obtained as the input fiber polarization is varied. Figure 7(a) shows the transmission spectra of one of the cores as a function of the polarizer angle. It can be noted that the spectral modulation period depends on the polarization. With an angle of 0° (i.e., along the line that connects the three cores) the modulation period, around a wavelength of 800 nm, is ~60 nm, changing to ~95 nm at 90° (i.e., polarization orthogonal to the line that connects the cores).
It is also interesting to note that certain spectral points (e.g., around 800 nm) present a transmission minimum at one polarization axis and a maximum at the other, which can be exploited as a polarizer or polarization beam splitter. Figure 7(b) presents the normalized transmission at 800 nm for both coupled cores as a function of input polarization angle. Over 14 dB polarization extinction ratio is achieved in each core, with each orthogonal polarization coupling to a different core. Figure 7(c), as well as the online movie (Media 1), shows images of the fiber output for various input polarization angles also at 800 nm. It can be seen that, as the polarization is scanned, light oscillates from one core to the other, corroborating the data of Figs. 7(a) and 7(b). Polarization splitting is, therefore, demonstrated.
A method that allows locally coupling selected core pairs of multicore PCFs was demonstrated and applied to a three-core fiber. The coupled cores presented the spectral modulation that is typical of fiber couplers, with a modulation depth of up to 18 dB. This modulation presented a high polarization sensitivity, which can be exploited for the production of polarization beam splitters. At given wavelengths a polarization extinction ratio of over 14 dB was achieved. The demonstrated couplers may find application as important components in next generation optical telecommunication links and in optical interconnects that use space-division multiplexing in multicore fibers for increased capacity.
This work is supported by CNPq (including funding from INCT FOTONICOM), FAPESP (INCT FOTONICOM) and Fundo Mackenzie de Pesquisa. R. M. Gerosa acknowledges CAPES for his scholarship.
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