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Abstract
We report on a double negative curvature anti-resonance hollow core fiber, in which, the cladding is constituted of 6 large tubes and 6 small tubes arranged in a staggered pattern. The simulation shows that the loss of the fiber can reach or even exceed the loss of double-clad negative curvature anti-resonance hollow core fibers in short wavelength band, due to the staggered arrangement of two kind of tubes and the double negative curvature on the core boundary. The best single mode performance with a loss ratio as high as 100,000 between LP11 mode and LP01 mode is obtained due to simultaneously inhibited LP11 modes and LP21 modes in the fiber structure. The reason for loss oscillations in long wavelength band and the fabrication feasibility of proposed fiber are also discussed.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Hollow core fibers (HCFs) such as photonic band gap fibers, Kagome fibers and negative curvature anti-resonance hollow core fibers (NC-AR-HCFs) have enabled new applications [1–7] due to their extraordinary properties compared to common solid-core fibers. NC-AR-HCFs have attracted much attentions in recent years, which have many advantages such as simple structure, design flexibility, and broadband transmission.
The cladding of NC-AR-HCF is composed of a single layer of thin-walled circular tubes. There are several transmission bands between the high-loss regions, and the central wavelength of transmission bands are determined by the anti-resonance condition [8]. Negative curvature indicates that the surface normal to the core boundary is oppositely directed from the core.
As early as in the research of Kagome fibers in 2013, Debord et al. proved that the loss of Kagome fibers is strongly dependent on the contour negative curvature of the core-cladding interface, the decrease in radius of negative curvature results in a strong decrease in both the confinement loss and the optical power overlap between the core modes and the silica core boundary [9]. In NC-AR-HCF, the smaller negative curvature radius of core boundary couldn’t be blindly pursued because of the inhibited coupling, ratio between the radius of circular tube and core needs to be cleverly set at the optimal inhibited coupling point, the mode coupling of the fundamental modes (FMs) and the tube modes are inhibited to achieve an optimized confinement loss of FMs [7,10,11]. In order to further study the effect of negative curvature radius of the core boundary on confinement loss of FMs in NC-AR-HCF, elliptical cladding tubes have also been studied, a loss reduction of more than 1 order of magnitude has also been shown theoretically in fibers with elliptical cladding tubes compared to fibers using circular tubes [12–14]. The other way to decrease the confinement loss of NC-AR-HCF is increasing the number of anti-resonance layers. The concept of “double-clad” NC-AR-HCF were presented, Poletti et al. and Belardi et al. proposed NC-AR-HCFs with nested tubes [15,16], Gao et al. reported a NC-AR-HCF with conjoined-tubes [17], in those fibers, two anti-resonance reflections are created due to the double-clad walls, and the loss can be decreased by 2 orders of magnitude. However, elliptical capillary tubes or double-clad means that the difficulty of preparation is further increased.
For the potential advantage of core boundary with small negative-curvature radius is not fully exerted, in this paper, a double negative curvature anti-resonance HCF is proposed for the first time, in which, the cladding is constituted two kind of tubes arranged in a staggered pattern. Further reduction of confinement loss and the surface scattering loss by additional small tubes. The loss reduction of proposed fiber can reach or even exceed the level of double-clad NC-AR-HCFs in short wavelength band. Excellent single mode performance with a loss ratio as high as 100,000 between the higher order modes (HOMs) and FM is obtained.
2. Structure and performance
The cross-section of the proposed fiber is shown in Fig. 1(a). The cladding is constituted of 12 circular tubes which are in contact with each other, i.e., 6 large tubes and 6 small tubes are arranged in a staggered pattern. The core radius rcore is 20 μm, the outer radius of large tubes r1 is 17 μm, the outer radius of small tubes r2 is 13 μm, and the glass wall thickness t are 0.5 μm.
Three loss contributions of proposed fiber were evaluated in Fig. 1(b). The confinement loss (CL) is calculated from FEM method [18],
where is the imaginary part of the mode effective refractive index, is the wavelength. The surface scattering loss (SSL) was caused by surface capillary waves (SCWs) frozen into the fiber as it solidified [19], which is calculated according to the model after calibration [15],where F is the optical power overlap between the core mode and the silica core boundary, is 300, representing the calibration factor at the wavelength of = 1.55 μm [15]. According to the additional small tubes, the optical power overlap between the core mode and the silica core boundary remains less than 0.01%. The random microbend loss (RML) from the coupled power theory model is also considered, the coupling loss with good approximation caused by random microbends between fundamental mode and LP11 mode of the fiber is calculated using the model in [20] proposed by Eric Numkam Fokoua et al.,where is the mode propagation constant of fundamental mode. is the difference of mode propagation constant between fundamental mode and LP11 mode group, is the power spectral density at the spatial frequency , and are the square of the spot radius of fundamental mode and the spot radius of LP11 mode energy state respectively.The total loss of FM remains lower than 1 dB/km in the range of 1150~1500 nm.
It’s important for HCFs to provide effectively single-mode operation, the most common method is exciting the mode coupling between the LP11 modes (the first lowest loss among HOMs) in core and the like-LP01 modes in tube to achieve an optimized confinement loss of LP01 modes in core. However, due to the extremely high optical power overlap between the LP21 modes (the second lowest loss among HOMs) and the LP11 modes, it can only achieve hundreds or thousands of loss ratio between HOMs and FMs as reported in [21,22].
The modal contents in core and tubes of proposed fiber are shown in Fig. 2(a), when the diameter of tubes are around 13 μm and 17 μm, the like-LP01 modes and the like-LP11 modes in tubes precisely coupling with the LP11 modes and LP21 modes in core respectively. The mode field distributions are shown in the Fig. 2(a) below. The total loss of FMs and lowest confinement losses of HOMs are shown in Fig. 2(b), the confinement loss of HOMs remains larger than 2000 dB/km. The calculated loss ratio between confinement losses of HOMs and total loss of FMs is around 100,000 in the range of 1150~1350 nm, which is the highest value to our knowledge.
3. Discussion
As can be seen in Fig. 1(b) that the primary loss mechanism in proposed fiber is CL. The CL of proposed fiber is compared with the confinement losses of other structures, including single-layer NC-AR-HCF with 6 tubes, double-clad NC-AR-HCFs with 6 nested tubes and conjoined-tubes under the same core radius (20μm) and glass wall thickness (0.5μm), the results are shown in Fig. 3.
Fig. 3 Comparison among proposed fiber and other structures. (a) structure of single-layer NC-AR-HCF with 6 tubes (tube radius is 17 μm), (b) structure of double-clad NC-AR-HCFs with 6 nested tubes (outer radius of large tubes is 17μm, outer radius of small tubes is 11μm), (c) structure of double-clad NC-AR-HCFs with conjoined-tubes (tube radius is 17 μm, distance between circle center of two conjoined-tubes is 10μm), (d) simulated attenuation spectra.
It can be seen that the confinement loss of the proposed fiber is basically the same level as that of double-clad NC-AR-HCFs, and reduced more than 2 orders of magnitude at most compared with single-layer NC-AR-HCFs. The reason for the reduction of CL is analyzed. It’s assumed that the staggered arrangement of two kind of tubes effected the CL. When the arrangement of two kind of tubes in the same radial line direction (deviation angle θ = 0 deg), the CL is 0.83 dB/km, as the arrangement offset to the staggered arrangement (deviation angle θ = 33 deg when r1 = 17 μm, r2 = 13 μm), the CL decreases less than 0.1 dB/km. The normalized electric field intensity in radial line direction (the red dot line in Fig. 4(a)) as shown in Fig. 4(b). A part of the energy of FM leaks to the gaps between the large tubes when the deviation angle is small. As the deviation angle increases, the non-overlapping in the radial direction of the gaps between small tubes and the gaps between large tubes increases, the normalized electric field intensity at the gaps between the large tubes, which indicates the CL of FM, decreases about one order of magnitude, therefore, the confinement loss is reduced.
Fig. 4 (a) Normalized electric field intensity in radial line direction, (b) the loss variation for deviation angle changes
However, the confinement loss increases rapidly at the long wavelength band of transmission window due to the existence of nodes [15], large tubes and small tubes can be combined into a variety of structures and guiding a variety of surface modes, which leads to loss increase in the long wavelength band.
In order to quantitatively analyze the effect of the surface mode caused by the nodes on the confinement loss of the proposed fiber in long wavelength band, imaginary fiber which has the same size of core and tubes with the proposed fiber, but the large tubes and the small tubes are not in contact and the gap between them is 0.5 μm. The structure of proposed fiber and imaginary fiber are marked red and black respectively in Fig. 5(a), the comparison of confinement losses is simulated as shown in Fig. 5(a), as the effect of surface modes caused by nodes, the bandwidth of transmission window is degraded by 50% and loss increased at least 2 orders of magnitude in long wavelength band.
A point of practical importance is to ensure that the proposed fiber can be fabricated. The preparation process of NC-AR-HCF is getting more and more mature [7,23], however, one of the main practical challenges in the fabrication of NC-AR-HCF is to achieve the required high uniformity for the gap and position of the non-contact tubular elements over long distances, most of NC-AR-HCFs reported to date seem to qualitatively present non-uniformities.
Nawazuddin et al. provided a solution, a lotus-shaped NC-AR-HCF fabricated by introducing additional smaller diameter capillaries between the original tubes to help maintain a uniform gap and position between the anti-resonance elements [24]. The preparation process of lotus-shaped NC-AR-HCF is also applicable to the proposed fiber in this paper, the large tubes and small tubes are arranged in a staggered pattern, and two kind of tubes support each other to help maintain a uniform gap and position between the anti-resonance elements, which ensures structural uniformity over long distances.
However, some segments in lotus-shaped NC-AR-HCF become straight, which make an illusion that the topology of structure cannot be preserved during fiber draw. In fact, fabricated into a lotus structure is designed, the reason of the reduction of simulated loss with lotus structure is that the effective index of air modes guided in lotus structure are less close to the fundamental core mode, and they can hardly phase match. It is a manufacturing process problem, which is related to the length of hot zone and the drawing temperature. The shorter the hot zone, the lower the drawing temperature, the more intact the structure can be maintained, otherwise, the structure will be seriously deformed. Xiaosheng Huang et al. reported their double-clad NC-AR-HCF, it can be shown that even if the cladding tubes are in contact with each other, the edges are not straightened and the topology is preserved [25].
The fabrication tolerances of nodes on the performance of the proposed fiber are also analyzed. As shown in Fig. 5(b), length of node edge L increase from 1μm to 6 μm, the lowest loss value and the bandwidth (the wavelength range which loss is less than 1 dB/km) becomes deteriorate obviously. While the length of node edge L increasing form 1μm to 6 μm, the average loss in the range of 1150nm~1500nm of are 0.417 dB/km, 0.552 dB/km, 0.460 dB/km, 0.423 dB/km, 5.147 dB/km, and 1.565 dB/km, respectively, and the bandwidth are 300 nm, 300 nm, 400 nm, 450 nm, 300 nm and 250 nm respectively. The average loss and bandwidth are 0.25 dB/km and 400nm respectively in an ideal structure. After comprehensive consideration, it is suggested that performance degradation is acceptable under the condition that the length of node edge is kept below 5μm.
4. Conclusion
In conclusion, we proposed a double negative curvature anti-resonance hollow core fiber, in which, the cladding is constituted of 6 large tubes and 6 small tubes arranged in a staggered pattern. The simulation shows that the loss of the fiber can reach or even exceed the loss of double-clad negative curvature anti-resonance hollow core fibers in short wavelength band, due to the staggered arrangement of two kind of tubes and the double negative curvature of on the core boundary. The best single mode performance with a loss ratio as high as 100,000 between LP11 mode and LP01 mode is obtained due to simultaneously inhibited LP11 modes and LP21 modes in the fiber structure. However, as the effect of surface modes caused by nodes, the bandwidth of transmission window is degraded by 50% and the loss increased at least 2 orders of magnitude in long wavelength band. In addition, the fabrication feasibility of proposed fiber is analyzed, the tubes arranging in a staggered pattern ensure the structural uniformity over long distances. The nodes become straight in reality preparation process that affecting the performance, it is suggested that performance degradation is acceptable under the condition that the length of node edge is kept below 5μm.
Funding
National Natural Science Foundation of China (61535009).
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