A hollow-core antiresonant fiber (HC-ARF) with nested supporting rings (NSRs) is designed and simulated. The HC-ARF with NSRs has advantages and benefits of low loss, large bandwidth, simple structure and a well bending characteristic, in which confinement loss (CL) is ∼ 0.15 dB/km @ 1.55 µm and the bandwidth is ∼ 220 nm @ CL < 1 dB/km. The bending loss (BL) is lower than ∼ 1 dB/km @ bend radius rc > 24 mm at 1.55 µm. Therefore, the HC-ARF with NSRs has potential applications of data transmission, sensing, high power delivery and so on.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Hollow-core antiresonant fibers (HC-ARFs) are a novel kind of hollow core fibers based on the antiresonant effect [1,2]. Due to the special structure and guidance mechanism, HC-ARFs exhibit many advantages such as large bandwidth, low nonlinearity, high damage threshold, ultralow latency and so on [3–5]. Therefore, HC-ARFs have a great potential in the application of power delivery , nonlinearity optics , fiber optic sensors , UV or visible spectral range guidance [9–12] and so on. The antiresonant effect can be described by the so-called antiresonant reflecting optical waveguide (ARROW) model [13–15]. In the ARROW model, the silica or air layers are considered as Fabry–Perot- (FP-) like resonators, which confine light in fiber core with wide antiresonance spectra and low confinement loss (CL). As the transverse sectional of Fig. 1(a) shows, the ideal structure of HC-ARFs is the periodical concentric antiresonant rings (ARRs) of silica and air surrounding the air core [15,16].
However, the ideal structure of HC-ARFs is impractical because the silica antiresonant rings (SARRs) lack the supporting structure in the air antiresonant rings (AARRs). Thus, the additional supporting structure such as silica struts and rings is essential for HC-ARFs [3,17–19]. There are HC-ARF with a hexagram antiresonant cladding , HC-ARF with ‘negative curvature’ core surround , HC-ARF with non-touching antiresonant tube elements arranged around a central core [21,22] and so on. Especially, the state-of-the-art hollow core nested antiresonant nodeless fiber (HC-NANF) with 0.28 dB/km attenuation in the C and L bands has been developed recently .
The additional supporting structure forms new air-silica interface reflection, which is benefit for low-loss compared with the ideal structure of HC-ARFs [17,18]. Unfortunately, the supporting structure would also change the shape and thickness of ARRs, so the antiresonant effects were weakened. The loss of HC-ARFs with unsuitable supporting structure would increase compared with the ideal structure of HC-ARFs [17,18]. Therefore, we focus on designing a suitable and practical supporting structure for ideal structure of HC-ARFs to achieve low-loss guidance.
The nested rings structure is common in HC-ARFs [24–29], especially in negative curvature fibers, which the nested rings with antiresonant thickness arranged around a central core to guide light. In the HC-NANF, the additional nested rings with antiresonant thickness are added in the non-touching antiresonant tube elements to further reduce the fiber loss. However, the bending loss (BL) is still non-negligible, which is measured < 0.1 dB/m for bend diameters ≥ 8 cm and 0.2 dB/m for a 4 cm diameter at 1.55 µm . The feature of large BL limits the application of HC-ARFs in long-haul communication, miniaturized fiber sensing system and so on. In addition, the nested rings with antiresonant thickness are also added in a modified Bragg fiber . However, it is based on the ideal Bragg fiber, as one of Photonic Band Gap (PBG) fibers, so it has large number of rings to form the Bragg effect and the air antiresonant effect is ignored.
In this paper, we provide a practical and simple structure of HC-ARF with nested supporting rings (NSRs) and its design method, which has nested rings to be the supporting structure of HC-ARFs ideal structure. As the Fig. 2(a) shows, the two NSRs with resonant thickness are added in the AARRs to support the SARRs and optimized to avoid affecting the antiresonant effect. According the simulated result, the CL is ∼ 0.15 dB/km @ 1.55 µm and the bandwidth is ∼ 220 nm @ CL < 1 dB/km. In addition, the HC-ARF with NSRs has well bending characteristic compared with common HC-ARFs, which simulated BL is lower than ∼ 1 dB/km @ bend radius rc > 24 mm at 1.55 µm.
2. Fiber design
2.1 Design of the HC-ARF ideal structure
The basic parameters of HC-ARFs ideal structure have λ0, r, t, h, N, which are the central wavelength of fiber, the radius of fiber core, the thickness of SARRs, the thickness of AARRs and the number of ARRs respectively, as Fig. 1(a) shown. We choose λ0 = 1.55 µm. The typical value of r/λ0 is ∼ 10 to 20 , so we design r = 20 µm.
According to the ARROW model, the theoretical values of t and h are calculated by Eq. (1) and Eq. (2) [16–18], where n = 1.444 is the refractive index of silica, m is natural number, neff is the effectively mode index of LP01 mode, u = 2.405 is the first null of the zeroth-order Bessel function.
2.2 Design of the HC-ARF with NSRs
As Fig. 2(a) shows, the characteristic parameters of HC-ARF with NSRs have p, θ and q, which are the thicknesses of NSRs, the angle between AB and CD and the nested depth of NSRs respectively. The points of A, B, C, D are the nested locations. The intensity distributions of HC-ARF with NSRs modes are shown in Fig. 2(b) including airy modes in core or cladding and dielectric modes in SAARs and NSRs.
The additional NSRs would change the FP-like resonance condition of ARRs. In order to reduce the influence of NSRs on the antiresonant effects, the theoretical thickness of p is the silica resonant thickness in Eq. (4), where m, λ and n are same as Eq. (1). According to Eq. (4), p = 744 nm when m = 0 and p = 1488 nm when m = 1. The later value is chosen to design a stable supporting structure of HC-ARF with NSRs. However, the optimized value of p is far from theoretical value because the NSRs are decentered to air core and it also depends on the values of q and θ.
After design the q and θ, p is optimized in Fig. 4. The optimized value of p is around 1275 nm or 1325 nm when q/p = 0.005 and θ = 90° in Fig. 4(a). However, the λ0 is also changed with p, so the CL spectra of HC-ARF with NSRs in different p are simulated in Fig. 4(b). The λ0 increases as p and reaches ∼ 1.55 µm when p = 1325 nm. In this condition, the bandwidth is ∼ 220 nm from 1400 nm to 1620 nm when the CL < 1 dB/km and the CL is ∼ 0.15 dB/km at 1.55 µm. The RL between CLs of HC-ARF with NSRs and HC-ARFs ideal structure with N = 4 is ∼ 14.7 dB at 1.55 µm. The reason is that additional 4 air-silica interfaces from the two NSRs introduce RL ∼ 24 dB from multiple Fresnel reflections. However, the NSRs, which locate in AARRs and nest with SARRs, influence the antiresonant effects. In addition, the NSRs are decentered to air core, so the reflectivities of the NSRs air-silica interfaces in different directions are inconsistent. Therefore, the RL is only ∼ 14.7 dB, which is smaller than ∼ 24 dB.
Besides CL, BL is also a crucial kind of loss for HC-ARFs. The Fig. 5 shows the simulated BLs of HC-ARF with NSRs and HC-ARFs ideal structure with N = 4 on the rc in four mainly bend directions based on Fig. 2(a). Due to the asymmetric structure of the HC-ARF with NSRs, the BLs in down and right bend directions are similar with the BLs in up and left bend directions respectively. When rc > 24 mm, the BLs are lower than 1 dB/km in all four bend directions. The RL of BLs between HC-ARF with NSRs and HC-ARFs ideal structure with N = 4 is ∼ 26 dB at rc = 24 mm. The reduction of BLs is benefit from the increased air-silica interfaces reflection and the phase mismatch between LP01 modes and cladding modes. Thus, the HC-ARF with NSRs has excellent bending characteristic compared with the common HC-ARFs.
We have focused on getting an efficient design of HC-ARF with NSRs for light guidance at λ0 = 1.55 µm and r = 20 µm, despite the design method is universal for other λ0 and r. According to the ARROW model, the HC-ARFs with periodical concentric ARRs are ideal structures of HC-ARFs, so the HC-ARFs ideal structure with N = 4 is designed at first, which CL is ∼ 4.5 dB/km at 1.55 µm. However, it is impractical because there is no supporting structure in the AARRs to support the SARRs. Therefore, the NSRs are added and optimized to support the SARRs and further reduce the CL of the HC-ARF with NSRs on the basis of HC-ARFs ideal structure with N = 4. The optimized result is that the CL is ∼ 0.15 dB/km at 1.55 µm, the bandwidth is ∼ 220 nm when the CL < 1 dB/km and the BL < 1 dB/km when rc > 24 mm at 1.55 µm. The RLs of CLs and BLs between HC-ARF with NSRs and HC-ARFs ideal structure with N = 4 are ∼14.7 dB and ∼ 26 dB respectively. Moreover, even if the structure is asymmetric and the loss of LP01 modes are different, there is nearly no polarization difference between two LP01 modes because the shape of core boundary is circle and the radius of fiber core is large. Due to the intensity distribution of LP01 modes is circular in HC-ARF with NSRs rather than non-circular in negative curvature fibers, the coupling between HC-ARF with NSRs and the fiber with circular intensity distributions of LP01 modes is relatively easy when they have similar radiuses of intensity distribution.
It can be predicted that the fabrication of HC-ARF with NSRs is challenging because of the nested and decentered NSRs structure. According to the practical nested structure of other HC-ARFs, the silica rings would deform because of silica surface tension and the pressure difference in each region. The nested depth q is also an uncontrollable factor and needs to be further researched. Predictably, the extrusion and high precise 3D Printing techniques for other materials could be helpful for fabrication. However, the features of low-loss and large bandwidth make the HC-ARF with NSRs highly advantageous with tremendous potential applications including data transmission, sensing, high power delivery etc. In particular, the feature of low BL is outstanding compared with most of HC-ARFs, which is crucial for many flexible miniaturized applications such as the fiber coil of fiber optic gyroscope or hydrophone and so on. The HC-ARF with NSRs which has low CL and BL over such a wide range of wavelengths is attractive and should be encouraged to further research in this area.
National Natural Science Foundation of China (61575012, 61575013, 61935002).
The authors declare that there are no conflicts of interest related to this article.
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