1. Introduction

Although twin-core fiber (TCF) has been researched for more than 30 years [1], it is not like single-core fiber (SCF), which has been used to realize many available optical fiber devices, e.g. fuse-tapered directional coupler and fiber Bragg grating. In fact, there are still many potential applications to be exploited for TCF. And most of them are based on the strong coupling characteristic between the two matched or mismatched cores in TCF. One of the basis applications is the directional coupler, of which the splitting ratio can be conveniently controlled by adjusting the length of the matched TCF section or by adjusting the bending-induced detuning of TCF [2]. Another application is high isolation comb filter [3]. So it is possible to make TCF-based optical interleaver. The third popular device is band-pass and band-stop filter [4, 5], which are made of mismatched TCF, in which the phase-matching condition is satisfied for special wavelength by appropriate fiber (or fiber grating) design. The last, but important and complex application, is fiber-Bragg-grating-assisted and TCF-based optical add/drop multiplexer [6], which could be used in Frequency Division Multiplexing [7].

These devices have not been widely used in practice just because it is difficult to simultaneously access the two close cores of the TCF. The usually method for accessing TCF is connecting the core of SCF to one of the cores of TCF by special splicing technology [8]. Obviously, the method couldn’t provide full functions of the foregoing devices since full function optical directional coupler, interleaver, band-pass and band-stop filter must have two output ports and full function optical add/drop multiplexer must have the input port, the drop port, the add port and the output port.

Other applications of TCF include gain flattening in erbium-doped TCF amplifier [9] and TCF-based sensor [10]. Their performances will be improved greatly by accessing both close TCF cores.

There are a few existing methods for accessing both close cores of TCF. The first uses mature planar optical circuits for separating the two close optical fields launched from TCF and V grooves for attaching TCF and SCF pigtails. However, the insert loss and cross-talk will be serious because of material absorption, scattering, noncircular index profile of waveguide and difficulty of accurately, cheaply and repeatedly aligning the fiber pigtails to the device [11]. The second is based on two tapered SCFs in a twin-hole capillary of low index [11]. The problem is that the core radii of the tapered SCFs will be much smaller than those of TCF, especially when the core distance of TCF is much smaller than the center distance of the twin-hole of capillary. So, serious insert loss and cross-talk are difficult to avoid. The last method is implemented by fabricating a fused tapered coupler by using a piece of mismatched TCF and a normal SCF [12]. However, this method can’t be used in the case of matched TCF.

On the other hand, Zhu, B. et al. fabricated a tapered seven-core connector for connecting seven pieces of SCF to seven-core fiber with the core distance of 38 μm [13]. So it is possible to access both far apart cores of TCF by end-face connecting. By using the content, we proposed a connector for simultaneously accessing the two cores of the TCF through two SCFs. The insert loss and the cross-talk are very low according to the simulation. Two cascaded pieces of collinear four-core fiber (CFCF) are used for separating the two close output optical fields of the TCF and the center distance of the optical fields is increased greatly. One gemini fiber segment with pigtails is used to guide the separated optical fields to two SCFs. For demonstrating the feasibility of the strategy, a CFCF is fabricated and two adjacent SCFs are fused bonded together and stretched by flame-brushing technique [14]. Moreover, the paths of the two optical fields are both reversible. So many TCF-based full function devices (e.g. directional coupler, filter and add/drop multiplexer) could be realized with the assistance of the connector.

2. Structure of the connector

The generic schematic of the connector is shown in Fig. 1 . For all the CFCFs in this paper, all the four cores are collinear and each pair of cores (upper or lower) are phase-matched. So the CFCF could be called dual-pair-core fiber (DPCF). Particularly, for the first piece of CFCF spliced with TCF, the phase velocities of the two pair of cores are different. So it is called asymmetric DPCF in the paper. For the other piece of CFCF, the distance between the inner two cores is so large that the transverse coupling between them could be neglected. So it is called far apart DPCF in the paper. To implement the connector, the TCF is firstly spliced to an asymmetric DPCF and the two cores of the TCF are aligned to be concentric with the inner two cores of the asymmetric DPCF respectively. The asymmetric DPCF is then spliced with a far apart DPCF with the outer two cores of the asymmetric DPCF concentric with the inner two cores of the far apart DPCF respectively. Finally, the far apart DPCF are spliced with one gemini fiber segment with the outer two cores of the far apart DPCF concentric with the two single-mode cores respectively.

 

Fig. 1 Schematic of the TCF to two pieces of SCF connector.

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The first optical field (represented by red color) launched from the TCF is butt-coupled into the second core of asymmetric DPCF. There is no transverse coupling between the inner two cores of asymmetric DPCF since they are mismatched. So, all the power is transverse coupled into the first core of asymmetric DPCF at the splicer between asymmetric DPCF and far apart DPCF. Then the first optical field is butt-coupled into the second core of far apart DPCF. There is no transverse coupling between the inner two cores of far apart DPCF still, since they are far apart enough. So, all the power is transverse coupled into the first core of far apart DPCF at the splicer between far apart DPCF and gemini fiber segment. The first optical fields can be butt-coupled into the first core of the gemini fiber segment now. Finally, it is guided into one normal SCF through transition segment. The path of the second field (represented by blue color) is similar. Obviously, the optical paths are both reversible in the connector, i.e. they will not affect each other.

3. Theory

Coupled-mode theory is usually applied to describe the optical wave propagation phenomena in the TCF or multi-core fiber. However, the eigenmodes calculated out by finite element method are used through the paper because the eigenmode interference method is more accurate than coupled-mode theory. In addition, it is more accurate and effective for numerical analysis of butt-coupling of two pieces of fiber by eigenmode theory and mode-matching principle. There are two eigenmodes (even and odd modes) for coherent light in TCF and four eigenmodes in DPCF. Figure 2 shows the electric field profiles of the eigenmodes on the central axes connecting the cores.

 

Fig. 2 The index profile and eigenmodes of (a) TCF, (b) asymmetric DPCF, (c) far apart DPCF.

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The simulated index profile is also illustrated in Fig. 2. All the fibers have step-indices with identical core diameter of 8 μm and identical cladding index of $\text{1}\text{.444}$at the optical wavelength of 1.55 μm. So the phase velocity of every core is only dominated by therefractive index of the core. For the asymmetric DPCF, the center-to-center distance of the right pair of cores is bigger than that of the left pair, and the refractive index of the right pair of cores is smaller than that of the left pair. So the two pairs of cores have the same coupling length of L_a = 0.0546m. However, the two pairs of cores of the far apart DPCF have the same interval, the refractive index and the coupling length of L_f = 0.0499 m. Actually, the length of the DPCF could be odd multiples of the coupling length. According to the mode-matching principle, one can get the conclusions: the two left (right) eigenmodes of far apart DPCF are mainly excited by the two left (right) eigenmodes of asymmetric DPCF and the power of the left (right) SCF is mainly excited by the two left (right) eigenmodes of far apart DPCF.

Both the power of the even and odd eigenmodes of TCF is supposed to be 0.5 in the simulation, which is approximately coincided with many phase-matched TCF devices. The powers of the excited eigenmodes of DPCFs and SCFs are shown in Fig. 3 with respect to the phase difference of the two eigenmodes of the matched TCF at the splice point between TCF and asymmetric DPCF. The ratio of the power concentrated in the right core to that in the left core is approximately equal to 1:0, 0.5:0.5, and 0:1 when the phase difference is 0, 0.5π, π respectively. From Fig. 3(c), the power of the eigenmodes in TCF is successfully divided and launched into two SCFs with the maximum crosstalk of −37 dB and the maximum power loss of 0.056 dB. The center distance of the two fields launched from the TCF is extended to 92.95 μm which is the center distance of the two outer cores of the far apart DPCF. And it is possible to widen further the interval by cascading more pieces of far apart DPCF.

 

Fig. 3 Excited power of eigenmodes in (a) asymmetric DPCF, (b) far apart DPCF, and (c) SCFs.

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It is noted that, unlike the planar optical circuits method and tapering SCF method [11], the transferred power of the proposed connector will be wavelength dependent since the transverse coupling coefficients are approximately linear functions of wavelength in two DPCFs [10]. The normalized output spectrums of left and right SCF are shown in Fig. 4 .

 

Fig. 4 Normalized output power of left and right optical field.

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4. Experiment

For demonstrating the feasibility of the strategy, a CFCF is fabricated by means of groove & stack & draw method. The CFCF preform is firstly prepared by side-grooving on a largediameter pure silica rod; then the rectangular groove is filled with four small-diameter Ge- doped silica rods and other small-diameter pure silica rods; finally, they are fixed in a pure silica tube, as shown in Fig. 5(a) . The cross section of the drawn fiber is shown in Fig. 5(b). We intended to make it as asymmetric DPCF.

 

Fig. 5 The CFCF cross section of (a) preform (b) drawn fiber.

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Limited by our experimental conditions, until now the phase mismatching, between the two inner cores of asymmetric DPCF, is satisfied by the core radius difference rather than the core refraction index difference. In our experiment, the molar ratio of Ge and Si elements of the four cores is 0.0271. The diameter and the center-to-center distance of the left (right) pair of cores are 7.34 μm and 27.35 μm (6.3 μm and 30.72 μm) respectively. And the center distance of the inner two cores is 15.86 μm. So both pairs of cores should have the same coupling length of 10cm at the wavelength of 1.5μm. However, the eigenmode profiles calculated with finite element method are not like the simulated sample in Fig. 2, as shown in Fig. 6 . The even (odd) eigenmodes are not even (odd) symmetric any more. As a result, the left (right) pair of cores will not exchange power completely, and there is serious cross-talking between the inner two cores. In addition, the two coupling lengths will not be equal. So the fiber can’t be used as asymmetric DPCF. Although we could change the radius and the interval of the four cores slightly to make even (odd) eigenmodes more even (odd) symmetric and coupling lengths identical, it is difficult to avoid serious cross-talking of the device. So, it is faster and more efficient to design asymmetric DPCF of different core index than different core radii.

 

Fig. 6 The index profile and eigenmodes of the experimental sample

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Another key technology is how to attach two SCFs to the far apart DPCF. The tapered multi-core fiber connector in Ref. 13 has good use for reference of our problem. Two adjacent SCFs are fused bonded together and stretched by the flame-brushing technique [14] to form one gemini fiber segment, as show in Fig. 7 . By accurately controlling the fiber stretch and the flame movement, the core interval of the two SCFs can be set to an extremely high degree of accuracy to match the outer core spacing of far apart DPCF. In addition, the produced pigtailed Gemini fiber segment [15] is uniform and long enough to facilitate splicing. Finally, splice among TCF, CFCF, gemini fiber segment can be implemented by manual mode of polarization maintaining fusion splicer, with the assistance of transmission power detection system for orienting cores.

 

Fig. 7 The cross section of the gemini fiber segment.

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5. Conclusion

As the conclusion, we proposed a connector for connecting TCF and two SCFs with low power loss and low cross-talk by two kinds of CFCF. We believe that the connector can be applied in many devices based on TCF and that the proposed approach can be popularized for other multi-core fiber devices.