1. Introduction

As the key component of fiber-optic endoscopes, fiber arrays or fiber bundles have been widely used in medical diagnoses and surgical treatments [1–4]. Generally, a large number of cores are arranged regularly in the fiber arrays or fiber bundles, with each core serving as an individual channel to transmit one image pixel information. In order to achieve high-resolution imaging, the fiber arrays with high core density are desired, since higher core density means more pixels can be transmitted per unit area of fiber facet. However, high core density tends to bring in stronger inter-core coupling, thus significantly deteriorating the image quality. Over the last decades, several techniques have been exploited to obtain low inter-core coupling and high core density simultaneously. One common method is to design the fiber arrays consisting of either different core-size or different core-shape, thus introducing a small mode mismatch between adjacent cores to reduce the inter-core coupling [5–7]. Most of the currently commercially available fiber bundles adopt this method of design. But experimental results show that the strong crosstalk amongst cores still exist [8]. Another promising way is to enlarge the core-cladding index contrast of the fiber bundles to realize tighter mode confinement, thus reducing the core spacing and increasing the core density simultaneously. But these kinds of fiber bundles face significant technical challenges in fabrication. One giant barrier is the suited pair of materials for the core and cladding which are required to be not only thermal-matched but also with high index contrast [9,10].

In this paper, we proposed a honeycomb pure-silica-core fiber array associated with air hole cladding for high-resolution image transmission. This fiber structure is not only easy to achieve a high core-cladding index contrast due to the high refractive index difference between silica and air, but also beneficial for reducing the difficulty of fabrication since no second material is needed. It is worth noting that the honeycomb structure is widely studied in the field of the photonic crystal fibers, but seldom used for the fiber array design. Recently, a technique for the fabrication of the honeycomb doped-silica-core air-clad fiber bundles has been proposed by the University of Bath [11]. However, detailed numerical calculation or simulation of the fiber design are absent in their paper. Here, we mainly focus on the study and analysis of the impacts of the fiber array’s structure parameters on its inter-core coupling. Numerical simulation results show that, for an optimized fiber array, both a core spacing of 4.33µm and a power coupling ratio of lower than 1% between adjacent cores can be achieved. In this case, the fiber array with the 500µm diameter can realize about 10,000 image pixels.

2. Schematic topology and design principle

Figure 1(a) shows the schematic cross-section of the proposed honeycomb pure-silica-core fiber array. It is composed of circular air-holes (denoted by the white circles) arranged in a hexagonal array in the background of pure silica (the gray part). Each silica core is surrounded by six air-holes. The distance between adjacent air-holes is Λ, which is also named lattice constant. The air-hole diameter is d. The three numbers 1, 2 and 3 represent the core₁, core₂ and core₃, respectively. And we can easily calculate that the distance between adjacent cores is $\sqrt {3} \Lambda $.

 

Fig. 1. (a) Schematic cross section of the proposed honeycomb pure-silica-core fiber array. The white circles represent air-holes, and the gray part represents the background of pure silica. The parameters of d and Λ are air-hole diameter and the lattice constant. Note that the dark spots signify many air-holes and cores not shown. (b) A 24Λ×25Λ rectangle fiber array model used in the calculations.

Download Full Size | PDF

It is obvious that, for an optimized fiber array design, the values of both lattice constant Λ and air-hole diameter d should be determined. So it is of great significance to study the influences of different lattice constants Λ and air-hole diameters d on the crosstalk properties of the fiber array. In general, the strength of the crosstalk among cores can be estimated by calculating the power of the light transferred from the input core to the surrounding cores. In our simulation, in order to study the coupling behaviors of the fiber array, the beam propagation method [12] and the coupled mode theory [13] are performed on a 24Λ×25Λ rectangle fiber array model (as shown in Fig. 1(b), which consists of about 180 cores, in order to reduce the computation time) with length of 50cm. And the calculation step is set at 0.1µm. The detailed simulation process is as follows. Firstly, we launch a Gaussian beam with a diameter equal to that of one single core at the wavelength of 633nm into the center of core₁. Then we measure the Gaussian power oscillations in the core₁, core₂ and core₃ along the fiber length respectively. It should be noted that, before starting the research, we have verified the results calculated based on the 24Λ×25Λ fiber array model are the same as that based on a bigger fiber structure.

3. Fiber design and simulation results

First, the impacts of the air-hole diameter d on the inter-core coupling of the fiber array are analyzed in detail. Figure 2 shows the monitored power of the core₁, core₂ and core₃ as a function of the propagation distance z for the fiber array with the same lattice constant Λ=1.5µm but different air-hole diameters of (a) d = 0.7Λ, (b) d = 0.8Λ and (c) d = 0.9Λ. Here, the green line represents the monitored Gaussian power in core₁, with the red and the blue lines for the monitored Gaussian power in core₂ and core₃ respectively. The monitored power is normalized. From Figs. 2(a)–(c), it is easy to notice that with the increase of the air-hole diameter d, the levels and speeds of the power coupling from the core₁ into the core₂ and core₃ are gradually reduced. According to the simulation results, it can be concluded that for the same lattice constant Λ, increasing the air-hole diameter can decrease the inter-core coupling of the fiber array. Actually, larger air-hole diameter d means higher air-hole filling ratio (d/Λ) which will result in higher core-cladding index contrast, thus improving the ability of the cores to confine the light. Taking into account that the fiber bundle with the air-hole filling ratio d/Λ of larger than 0.9 has been successfully fabricated [14], here we choose d/Λ=0.9 for our fiber array design.

 

Fig. 2. The monitored normalized power of the core₁, core₂ and core₃ as a function of the propagation distance z for the fiber arrays with different air-hole diameters, (a) d = 0.7Λ, (b) d = 0.8Λ and (c) d = 0.9Λ, when the lattice constant Λ is fixed at 1.5µm.

Download Full Size | PDF

Then, the effects of the lattice constant Λ on the inter-core coupling of the fiber array are also thoroughly investigated. Figure 3 shows the monitored power of the core₁, core₂ and core₃ as a function of the propagation distance z for the fiber arrays with different air-hole diameters when the air-hole filling ratio is fixed at d/Λ=0.9. By comparing Fig. 3(a) with Fig. 3(b), 3(c) and 3(d), we can find that the lattice constant Λ also plays a critical role in the inter-core coupling. Especially, when the lattice constant Λ increases from 1.5µm (as shown in Fig. 3(a)) to 2µm (as shown in Fig. 3(b)), it is clear that the curve of the monitored power in core₁ becomes flatter, meanwhile both the maximum values of the monitored power in core₂ and core3 over the whole fiber length dramatically decrease to less than 1%. These results indicate that little energy is transferred from the core₁ to the surrounding cores for the situation of Λ=2µm. If the lattice constant Λ increases further to 2.5µm or 3µm, even less power will be transferred to the core₂ and core₃, but the trend of change is not as noticeable as that in the previous case, as shown in Fig. 3(c) and Fig. 3(d). Based on the analysis above, we can draw a conclusion that increasing the lattice constant Λ is also helpful for the achievement of the low inter-core coupling fiber array.

 

Fig. 3. The monitored normalized power of the core₁, core₂ and core₃ as a function of the propagation distance z for the fiber arrays with different Λ of (a) Λ=1.5µm, (b) Λ=2µm, (c) Λ=2.5µm and (d) Λ=3µm, when the air-hole filling ratio d/Λ is fixed at 0.9.

Download Full Size | PDF

Though we have shown that increasing the lattice constant Λ can lower the power coupling among cores, large lattice constant Λ is harmful for the realization of high core density. To obtain an appropriate value for the lattice constant Λ, we plot the 2D amplitude distributions of the core₁, core₂ and core₃ for the fiber arrays with different Λ of (a) Λ=1.5µm, (b) Λ=2µm, (c) Λ=2.5µm and (d) Λ=3µm when d/Λ=0.9, at the fiber length where the monitored power of the core₂ first reaches the maximum. At this moment the coupling effect between the core₁ and its adjacent cores is the strongest. Specifically, the fiber length for the fiber array with (a) Λ=1.5µm, (b) Λ=2µm, (c) Λ=2.5µm and (d) Λ=3µm are about 7cm, 1.4cm, 3.8cm and 5cm, respectively. These values are obtained based on the simulations results from Fig. 3(a)–(d). In Fig. 4(a), it shows that the maximum amplitude for the core₂ is almost twice of that for the core₁, implying that this fiber array is with high inter-coupling and not suit for image transmission. The Fig. 4(b), 4(c) and 4(d) show that their maximum amplitudes of the core₂ are much less than that of the core₁. In fact, their power ratios between the core₂ and the core₁ are all calculated to be far less than 1%, indicating low crosstalk characteristics. Therefore, we choose Λ=2.5µm as the optimum values of the fiber array for both low crosstalk and high core density, meanwhile leaving enough room for the possible fabrication error. Accordingly, the distance between adjacent cores of the fiber array is about 4.33µm, which is slightly smaller than that of FIGH-10-500N (one of the best commercially available imaging optical fibers) [8]. Here, to get a feel for how much at most the light in core₁ can spread to the nearest cores, the transverse field distributions for the fiber arrays with d/Λ=0.9 and (a) Λ=1.5µm, z = 7cm, (b) Λ=2.5µm, z = 3.8cm are also displayed in Fig. 5(a) and Fig. 5(b), respectively. It is obvious that the coupling strength for the fiber array with Λ=2.5µm is much weaker than that for Λ=1.5µm. And for the optimum fiber array, the maximum power in core₂ is far smaller than the power in core₁. Hence, through the above research, a fiber array design with comparable core spacing to the commercial image fiber as well as ultra-low inter-core coupling has been successfully obtained. To achieve 10,000 pixels with our design, the diameter of the fiber array is approximately 500µm.

 

Fig. 4. The amplitude profiles of the three cores (core₁, core₂ and core₃) for the fiber arrays with d/Λ=0.9 and (a) Λ=1.5µm, (b) Λ=2µm, (c) Λ=2.5µm and (d) Λ=3µm, when the value of the monitored power in the core₂ first reaches a maximum.

Download Full Size | PDF

 

Fig. 5. The transverse field distributions for the fiber arrays with d/Λ=0.9 and (a) Λ=1.5µm, z = 7 cm, (b) Λ=2.5µm, z = 3.8 cm.

Download Full Size | PDF

4. Fabrication method

Considering that two similar air-clad fiber arrays with three different kinds of doped silica cores reported in Ref. [11] have been successfully fabricated by using the multistage unjacketed stack-and-draw techniques, we have reasons to believe that our proposed fiber array also can be realized and easily manufactured by employing the similar method. What’s more, due to the uniform pure-silica-core, the preform of our proposed fiber array may also be prepared by exploiting the drilling-hole method [15]. This process can be generalized as follows: first, a regular hexagon pure silica preform is prepared; then, the air holes are drilled in the preform according to fiber structure shown in Fig. 1. In addition, the preform may still need to be stretched, cut short, stacked together again to form a final preform and drawn to the fiber array with the required fiber diameter. Reference [11] pointed out that less than 5% of the doped silica cores are nonguiding primarily due to fusing with the silica jacket or with each other. We guess this situation will get improved for our fiber fabrication with the pure-silica-core structure.

5. Conclusion

In summary, we have demonstrated and designed a honeycomb pure-silica-core fiber array associated with the air-hole cladding. The high index contrast between the pure-silica-core and the air-cladding guarantees the light tightly confined. Theoretical results have shown that increasing either the air-hole diameter d or the lattice constant Λ is helpful for reducing the crosstalk among cores. For a fiber array with Λ=2.5µm and d/Λ=0.9, a core spacing of 4.33µm and a power coupling ratio of lower than 1% between the adjacent cores can be realized. This fiber array design greatly reduces the difficulty of fabrication compared to other fiber bundles with either different diameters of cores or different kinds of doped-silica cores. This designed fiber array can support multi-mode transmission and is suitable for the optical wavelength of no more than 633nm. We believe this type of fiber would have potential applications in the fields of high resolution imaging such as medical diagnosis [4], high-bandwidth data transmission for image recognition [16] and object tracking [17].