1. Introduction

Most fibre-based advanced photonics technologies use single-mode (SM) fibres. SM operation in fibre allows better control and understanding of the propagating light. One of the areas where SM fibres are essential is in sensor technology. The majority of all-fibre sensors are based on fibre Long Period- and Bragg-Gratings. These sensors exploit the resonance properties of the sole propagating fundamental mode along the fibre. The interest in SM polymer optical fibre (POF) gratings lies in strain sensing and monitoring in engineering and medical applications [1]. This arises from existing interest in the use of polymer fibres for such applications [2,3], with PMMA fibres used for strains of up to 15% [4,5]. The high elastic limit of polymers and the ability to have low-loss single-mode fibres in the visible makes SM POF uniquely useful in such strain sensing applications.

Whilst SM fibre technology is abundant in silica, POF technology has focused almost entirely on large-core multimode, step- and graded-index fibres. The best state of the art low loss POF fibres are generally fabricated by co-extrusion, such as perfluorinated fibres [6]. The extrusion method, even though very good for large-core fibres, is not suitable for the fabrication of the very small cores required for SM operation. In general, achieving true SM operation in polymer fibres down to the visible regime is not straight forward due to the non trivial process of doping drawable polymers to the required refractive index and maintaining good optical quality. The fabrication of small doped polymer cores is intrinsically difficult due to much higher dopant diffusion seen in polymers [7] compared to silica doped cores. In spite of these problems, all-solid SM POF have been fabricated [8,9], but they are typically SM only in the infrared, suffer from high loss (in excess of 10’s dB/m), and are generally not commercially available [6]. The most successful approach for SM operation in the visible in polymer fibres is the use of microstructured polymer fibres (mPOF) which can be designed to be SM at any wavelength [10,11]. Another recent approach is a hybrid fabrication technique between commercial perfluorinated POF and mPOF technology. A standard graded-index perfluorinated large-core multimode fibre was inserted into a PMMA cladding with holes (the air holes were needed due to the much lower refractive index of the perfluorinated polymer, n = 1.34, compared to PMMA, n = 1.49) and drawn to fibre together until the large multimode fibre was reduced to form the SM core of the final fibre [12]. However, this fibre was also designed for operation in the IR.

In general polymer rods/tubes with tailored refractive indices are not commercially available or indeed easy to fabricate. On the other hand, different off-the-shelf drawable polymer materials can be purchased in an affordable and accessible manner from many different manufacturers. Some of the most common polymers are, PMMA (n = 1.49), Polystyrene (n = 1.59), Polycarbonate (n = 1.58) and Zeonex 480R (n = 1.53). A SM step-index fibre can be made by using these raw polymers in a straight-forward manner, however due to the high refractive index differences between these, the core sizes needed for SM operation would have to be extremely small, making the fibres impractical compared to their silica counterparts.

An interesting alternative for the fabrication of SM fibres is to have a composite core formed by an array of evanescent-field coupled cores. If the individual cores are are sufficiently small and appropriately spaced, the resulting multicore fibre (MCF) can be tailored to behave as a true SM waveguides with a single-mode, composite core. Such MCF waveguides were initially reported in silica to behave as SM waveguides in the IR, with the aim of increasing the effective mode area for fibre amplifiers and lasers [13]. However, a later report demonstrated that those waveguides were not operating in a SM regime but in a few-moded one [14]. Large-core MCFs having quasi-SM behaviour have been exploited in fibre laser applications. In those waveguides the SM propagation was achieved by phase locking [15,16] and self-organizing [17] of the fundamental supermode, but not by a true cut-off mechanism within the fibre core (the fibre was again few-moded).

This paper presents an analysis of the behaviour of these composite core waveguides, investigating the core-spacing and size required in order to achieve true SM operation down to 650 nm by using off-the-shelf polymer materials. We use PMMA and Zeonex 480R polymer for the analysis as well as for the fabrication of the final all-solid SM polymer fibre. A characterisation of the final fibre showing the onset of SM operation is also presented.

2. Multicore composite core for SM operation

The composite core under study is a multicore structure formed by 19 identical Zeonex 480R cores hexagonally arranged in a PMMA cladding, such that they interact strongly. Here we distinguish the composite core from a collection of non-interacting cores. In order to study the modal behaviour of the composite core in terms of the individual core sizes (d) and spacing (Λ), two analyses were undertaken: firstly we studied the composite core by keeping the individual core sizes constant and increased the spacing between them; secondly we analysed the modal behaviour of the composite core by varying the individual core sizes while fixing the spacing. Hence, we calculated modes of the composite core at different wavelengths and different d/Λ ratios. RSOFT, a generalized mode solver based on the Finite Element Method (FEM) by a full-vector implementation was used. The guidance in the composite core is achieved by the strong coupling between all the very weakly guiding (submicron) individual cores. In general, the number of modes, their modal effective index (n_eff) values and cut-offs of the composite core are related to the number of individual cores, their confinement properties and the separation between them.

For the first part of the analysis we began by considering the case of a standard SM step-index fibre made of Zeonex/PMMA. The refractive indices of PMMA and Zeonex are 1.4894 and 1.5226 at 650nm respectively. The size of the core needs to be D = 1.522 µm to be SM. To study the behaviour of a composite core we divided this solid core into 19 adjacent (i.e. with a d/Λ = 1) Zeonex submicron cores with the same total area. The size of the composite core can be considered to be 4.5 times the spacing (4.5 × Λ). Hence the submicron cores were calculated by dividing the diameter of the standard core by 4.5 (d = D/4.5), resulting in a composite core with d/Λ = 1, d = 345 nm and Λ = 345 nm (Fig. 1 (top right)). The independent Zeonex submicron cores are not effective waveguides on their own with a V-parameter or normalized frequency (V = πd/λ (n_co²-n_cl²)^1/2) of about 0.5 [18].

 

Fig. 1 (left) Dispersion plots for the fundamental mode (LP₀₁) of the composite cores with different d/Λ ratios while fixing multicores size constant. (right) Schematic of the studied multicore composite cores and calculated LP₀₁ modes at 810 nm for the different d/Λ ratios, at the same scale.

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To characterise resulting composite core, we calculated its fundamental mode (LP₀₁) for five different d/Λ ratios (1, 0.8, 0.6, 0.4 and 0.2; with Λ = 345, 431, 575, 863 and 1725 nm respectively) for the wavelength range 0.65 to 1.05 µm. The d/Λ ratios are obtained by changing the spacing between the submicron cores while keeping their size constant i.e. d = 345 nm as shown in Fig. 1. The composite core is obviously SM for all the d/Λ ratios for this part of the analysis. The modal n_eff of the LP₀₁ for the different composite cores versus wavelength is shown in the plot of Fig. 1. For d/Λ = 1 the behaviour of the core is very similar to that of the 1.552 µm solid core, as expected. In Fig. 1 we can see how the fundamental mode guided by the composite core can be tailored to virtually any range of n_eff values (i.e. waveguide dispersion) and mode field diameters (MFD) (see Fig. 1(right)), just by simply choosing the right pitch. For example, by choosing d/Λ = 0.4, a total increase in MFD of 4.84 times can be achieved. Obviously the limitation of the MFD and dispersion properties will be set by the actual confinement loses of the composite core. It can be seen that the dispersion properties of the composite waveguide versus the wavelength have a more pronounced slope towards shorter wavelengths where the confinement of the core is stronger, i.e. the waveguide dispersion is more dominant than the material dispersion. On the other hand, for lower d/Λ ratios the overall dispersion tends to approximate the slope of the material dispersion itself (of PMMA in this case), clearly indicating a much weaker waveguide confinement.

So far in our study of the composite core behaviour we have just discussed the effect of the multicore parameters in an already SM composite core. For the second part of our analysis we studied a fixed-size larger multimode composite core. In order to do this, we fixed the spacing between the 19 individual cores while changing their size, hence achieving the different d/Λ ratios from 1 to 0.2. As a starting point for the size of our composite core we chose a D = 4.2 µm. This size was chosen to be the same as that of standard silica SM fibres that are SM at 650 nm, e.g. Thorlabs SM600. As in the previous analysis, we divided the 4.2 µm core into 19 adjacent identical Zeonex cores, resulting in a composite core with d/Λ = 1, Λ = 933 nm and d = 933 nm (see Fig. 2 (top right)). We then calculated the modes of the composite core for five different d/Λ ratios (1, 0.8, 0.6, 0.4 and 0.2; with d = 933, 746, 373, 186 nm respectively) for the wavelength range 650 to 1050 nm. The d/Λ ratios were achieved by varying the individual core size while keeping the pitch constant i.e. Λ = 933 nm as sketched in Fig. 2(right). In this case the effective size of the composite core remained approximately constant for all the filling fractions.

 

Fig. 2 (left) Dispersion plot for the fundamental modes (LP₀₁) of the composite cores with different d/Λ ratios while keeping core to core spacing constant. (right) Schematic of the studied multicore composite cores and calculated LP₀₁ and LP₁₁ modes at 810nm for the different d/Λ ratios, at the same scale.

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In the graph of Fig. 2 we can observe the expected similar dispersion behaviour of the waveguide fundamental modes to the previous results when varying the composite cores filling fraction. For larger d/Λ ratios above 0.4 the composite cores are multimoded as can be seen by the calculated mode profiles for the LP₀₁ and LP₁₁ modes at 810 nm, shown in Fig. 2(right). In fact, the composite core with a d/Λ = 1 supports 9 spatial modes. As a comparison, we calculated the dispersion of the fundamental mode of a fictitious SM PMMA step-index fibre with similar parameters to that of the Thorlabs SM600, D = 4.2 µm and NA = 0.12 (NA = (n_co²-n_cl²)^1/2) at 650 nm. The fundamental mode dispersion of this fictitious fibre was very close to that of the composite core with d/Λ = 0.4 (see Fig. 2).

To study the dependence of the true SM operation versus wavelength and cores filling fraction, we plotted the two lower order modes’ n_eff vs the d/Λ ratios for three different wavelengths (650, 810 and 1050nm) in Fig. 3 (left). For true SM operation the second mode (LP₁₁) has to fall below the cut-off, in step-index fibres this happens when the n_eff of the mode falls below the refractive index of the cladding. It is clear from the graph in Fig. 3 that for this composite core geometry and size, a d/Λ of less than 0.4 is needed for the waveguide to work in a truly SM regime down to 650 nm. This is strongly dependent on wavelength: considering the 400 nm wavelength range in Fig. 3, which has a fixed composite core size and core/cladding refractive index difference of Δn = 0.033, the d/Λ condition for SM operation ranges from 0.35 to 0.60.

 

Fig. 3 (left) Modal effective indices of the LP₀₁ and LP₁₁ modes versus composite core filling fractions for 650, 810 and 1050nm wavelengths. (right) Mode profiles for LP₀₁ and LP₁₁ at 650, 810, 1050nm wavelengths at the same scale for the d/Λ = 0.4 composite core.

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Effectively, this multicore composite core approach can be used to tailor the n_eff of the modes (i.e. the fibre core refractive index) in the same way that doping technology is used in the fabrication of standard SM silica fibres, and effectively results in a step-index fibre with a core of a tailored refractive index. Like all step-index fibres, the fundamental mode has no defined cut-off, but at long wavelengths stops to be effectively guided. This is also seen for these composite core fibres in Fig. 3, for example at 1050 nm the n_eff of the fundamental mode approached that of the cladding at d/Λ = 0.25, making the fibre an ineffective waveguide. This analysis has identified the range of parameters required to achieve SM operation in such multicore composite-core waveguides.

3. PMMA/Zeonex multicore composite core fibre fabrication

From the modal analysis of the composite core shown above we determined that in order to achieve true SM operation down to 650 nm, the core needs to be around 4 to 5 µm in diameter and to have a d/Λ = 0.4 or less. The materials we used are off-the-shelf PMMA and Zeonex 480R purchased in rod form. PMMA and Zeonex 480R are good compatible materials in terms of processing temperature and dilatation coefficients for co-drawing applications, such as fibre drawing. To create the composite core we employed the same drilling method used in the fabrication of microstructured polymer fibres [10]. A 68 mm diameter solid PMMA preform was drilled to create the structure of the composite core. We drilled 19 identical 3 mm diameter holes in an hexagonal arrangement with a core to core spacing of 7.5 mm giving a d/Λ = 0.4. Then we drew the preform with the empty holes to an intermediate 11 mm diameter preform; at this stage the holes were 500 µm. To create the composite core we drew solid 480 µm Zeonex 480R rods and inserted them into the PMMA intermediate 30 cm length preform (Fig. 4(a) ). The Zeonex 480R rods were inserted in the holes of the PMMA preform under a microscope. The 20 µm hole-to-rod gap proved to be sufficient for an easy and trouble-free assembly of the final PMMA/Zeonex structure.

 

Fig. 4 (a) Neck-down preform showing the 19 480µm Zeonex rods inserted into the PMMA cladding structure for the composite core fabrication. (b) First stage 6mm preform showing the Zeonex/PMMA multicore array. (c) 330µm diameter composite multicore polymer fibre with bottom light core illumination. (d) Optical photograph at high magnification of the 4.5µm composite core showing the 19 submicron Zeonex cores.

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The entire structure was drawn to a 6 mm preform while vacuum was applied to eliminate the gaps between the Zeonex rods and the PMMA cladding, as shown in Fig. 4(b). The final d/Λ obtained in the preform was 0.35. A reduction in d/Λ was expected due to the collapse of the holes during the preform draw and also due to the smaller diameter of the Zeonex rods (480 µm) compared to the holes in the PMMA (500 µm). Once the microstructured core was achieved, the 6 mm preform was inserted into a 12.7/6.35 mm (OD/ID) PMMA jacket and stretched to 6 mm again. Due to the high reduction in diameter needed to achieve the final core size of about 4-5 µm, this sleeving process was repeated 4 times before the final fibre was drawn. Two different fibre diameters were fabricated, 330 (Fig. 4(c)) and 390µm. The core sizes for the 330 and 390 µm fibres were measured using a microscope to be approximately 4.5 and 5.3 µm respectively (measured corner-to-corner of the multicore composite core). Considering the corner-to-corner distance to be equal to 4Λ + d (d = size of submicron cores and Λ = spacing) and a d/Λ = 0.35 in the composite cores, parameters for the cores can be estimated to be d = 362 nm, Λ = 1.034 µm for the 330 µm fibre (Fig. 5(a) ); and d = 428 nm, Λ = 1.222 µm for the 390 µm one (Fig. 5(e)). Considering the final submicron individual Zeonex core size of approximately 360 nm in the final composite core, a total remarkable reduction of almost 200,000 times was achieved from the 60 mm diameter original Zeonex 480R rod.

 

Fig. 5 Optical photographs of (a) 4.5µm composite core of the 330µm fibre; (b) 330µm fibre near- and far-field images of the guided LP₁₁ mode at 550nm in a 1.2m fibre length; (c) calculated LP01 mode profile for the 330µm fibre at 650nm; (d) 330µm fibre near- and far-field images of the guided fundamental mode LP₀₁ at 650nm in a 1.2m fibre length; (e) 5.3µm composite core of the 390µm fibre; and (f) 390µm fibre near- and far-field images of the guided LP₁₁ mode at 650nm in a 1.2m fibre length.

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The optical properties of the composite cores were investigated by using a visible broadband white light source (Thorlabs OSL1). The wavelength selection was done by using 10 nm band-pass filters at the input of the fibre. Light was coupled into 1.2 m lengths of fibre (same length was used for characterizing both fibre sizes) by a 25 × microscope objective lens, while imaging the output of the fibre using a microscope. The light input conditions were chosen to overfill the core size and NA of the composite cores such that all the possible modes of the fibre could be excited. The near- and far-field output of both fibres’ composite cores were imaged to determine their modal properties. Both fibres were characterized using the 10 nm band-pass filters in 50 nm steps, the lower centre wavelength used was 550 nm.

The 330 µm fibre was found to be clearly operating in the SM regime at 650 nm as can be seen by its near- and far-field outputs (Fig. 5(d)). The fibre was bent in order to observe any spatial intensity variations on the mode field profile which would have indicated multimode operation. The 330 µm fibre showed a strong unperturbed SM operation at 650 nm while bending. However, while using the 10 nm band-pass filter centred at 600 nm a slight variation in the spatial intensity mode profile was observed while bending the fibre. This indicated that the second mode LP₁₁ was present, and that the wavelength cut-off for this fibre was somewhere in the range of 605 to 645 nm. We characterized the 390 µm fibre following the same procedure and the wavelength cut-off of the fibre was found to be somewhere in the range of 705 to 745 nm. We further characterised the 330 µm fibre by using a HeNe laser and found that the fibre was definitely operating in the single-mode regime narrowing the range of cut-off to 633 to 645 nm. The fibre losses were found to be 8 dB/m at the HeNe wavelength. We measured the material losses of our Zeonex and PMMA materials at HeNe wavelength to be 6.5 and 0.35 dB/m respectively. Considering our composite core to be ~10% Zeonex and ~90% PMMA at the d/Λ = 0.35, the theoretical composite bulk material loss would be around 1 dB/m. However, as it is clear from the calculated and measured mode profiles, light intensity will tent to localize in the higher refractive index areas, i.e Zeonex. This effect will indeed represent a larger effective bulk material loss than the theoretical 1 dB/m.

In standard SM step-index fibres the core confinement and the cut-off wavelength is determined by the V-parameter. For a fixed refractive index difference between core and cladding (n_co²-n_cl²)^1/2 (i.e. NA), the fibre waveguide modal cut-off properties are related to the core size and the operating wavelength in a linear and opposed way (V~d/λ). This behaviour agrees very well with the calculations plotted in Fig. 3(left), and from which the wavelength and core size dependence can be extrapolated. In the composite core case we can consider the d/Λ ratio (i.e multicore filling fraction) to be the parameter responsible for the final effective refractive index difference between the cladding and the composite core. Hence, in our two fibres with a fixed d/Λ = 0.35, a larger core will imply a longer wavelength cut-off (as observed above) and working at shorter wavelength will lead to operating in a multimode regime. To verify the latter experimentally, we varied the light input conditions to the composite cores (i.e. off-centring and angle) while using 10 nm band-pass filters centred at 550 nm and 650 nm for the 330 and the 390 µm fibre respectively. It was possible to excite almost cleanly the LP₁₁ modes in both fibres, as shown in Fig. 5(b) and (f). As expected the 4.5 µm composite core was multimode at 550 nm and the 5.3 µm core was indeed still multimode at 650nm.

4. Conclusion

A new concept for the realisation of SM polymer fibres using standard available PMMA and Zeonex polymers has been presented. We have shown and analysed multicore composite core geometries for achieving true SM operation down to 650 nm wavelengths. The range of parameters used were not exhaustive, however, this analysis clearly results in a detailed understanding of the parameters and trade-offs. We have shown that this multicore composite core approach can be used to tailor the fibre core properties in the same way that doping technology is used in the fabrication of standard SM silica fibres. Furthermore, this approach could lead to more interesting and complex core index geometries that cannot be achieved with standard doping technologies. Two different core sizes were fabricated and characterized, their cut-off wavelength properties were measured and found to agree with the theory. The fabricated 330 µm SM composite multicore polymer fibre had a very similar core size, MFD and dispersion behaviour to its silica counterpart (i.e. Thorlabs SM600).