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Abstract
In reality, an efficient platform for high-power laser delivery is highly important, which can be justified by readily available fiber lasers, and hollow-core fiber can be the best platform for guiding high optical power over long distances. The constraints include designing new cladding geometry, which may lead to a higher laser induced damage threshold in the fiber’s structure, having low losses along with a single mode nature. This article reports a new antiresonant fiber that has a hollow core and a triple-layered cladding configuration with only circular tube elements. The effects of multiple layers corresponding to the number of tube rings in the cladding geometry are well explored, which leads to understanding the physical insight of inter-layers. In comparison to double-layered cladding elements fiber, the proposed fiber significantly reduces loss by an order of two and reveals a minimum leakage loss of 5.82 × 10−5 dB/km at the chosen wavelength of 1.06 µm through the proper arrangement of cladding elements. We achieved a maximal higher order mode extinction ratio of about 104 (indicates the excellent single mode properties) and comparatively a little bending-induced loss of 9.00 × 10−4 dB/km, when the radius of bending is 14 cm. As a result, our studies on new multilayer fiber designs are not only useful for delivering high laser power but also serve as guidelines for the experimental realization of future multilayered cladding fibers.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Specialized fibers, referred as hollow core (HC) fibers, limit light in the hollow interior known as the core [1]. They are able to overcome many limitations of their solid core counterparts due to their distinctive characteristics, which include low loss [2], an increased optical breakdown threshold [3], an extended frequency range, reduced spectral broadening, low nonlinearity, and many more. As HC fibers guide light in the hollow region, it is capable to minimize the material loss that is influenced by host material. This guiding property also helps to significantly reduce the fiber dispersion, and also minimize other types of losses such as surface scattering loss and absorption induced loss [4,5]. As a result, they have garnered substantial attention and fascination to the researchers. HC fibers (HCFs) have several applications in different fields, such as optical fiber communications [6–8], an advanced high-energy beam delivery system [9], gas based light source [10,11], polarization controlling optical devices [12,13], and terahertz guiding [14–16] as a result of the aforementioned promising characteristics. Among the above application areas, it has become an important issue for many researchers to guide and control laser lights with high power, and they chose HC fibers as a better platform for this [17–21]. For instance, Goel et al. used HC fiber platform for delivering high power [18].
The guidance characteristic divides HCFs into groups that are useful for obtaining certain promising qualities [22]. For instance, hollow core photonic bandgap fibers (HC-PBGFs) exploit the photonic bandgap (PBG) phenomenon to trap light within the air-centered core, resulting in reduced transmission loss, constrained bandwidth, and increased dispersion [23]. In HCFs with Kagome structures, the restricted bandwidth may be addressed, and decreased attenuation is shown as a result of the hypocycloid form [24,25]. On the other hand, the HC antiresonant fiber (ARF)’s inhibited guiding mechanism [26] largely depends on the design of their cladding. As a result, light leakage from the HC is prevented by the cladding's design, which creates a significant difference in refractive indices between the core and cladding modes [5]. Therefore, HC-ARFs overcome many limitations due to their advancement [5], including low dispersion along with broad bandwidth, negligible power overlapping [22], low loss [27], etc. These extraordinary features lead this fiber to many applications [28], especially in the area of high-power laser delivery systems. For example, Gu and co-workers found record low loss of 4.3 dB/km on HC-ARF platform for high power laser delivery at 1.0 µm [17]. Moreover, Zhu and co-authors [29] experimentally investigated the laser induced damage threshold on the cladding geometry of AR-HCF at 1 µm of wavelength. Therefore, one interesting way in this area is to engineer the cladding elements of HC-ARFs.
Several cladding geometries are utilized on HC-ARFs for different applications (mostly for communication purposes), and the geometry includes anisotropic anti-resonant (AR) nested tubes [30], anti-resonant ice-cream cone-shaped tubes [31], elliptic anti-resonant tubes (ARTs) [32], etc. As an example, Debord et al. [33] showed untouching eight circular cladding tube elements in a HC-AR fiber with 7.7 dB/km of leakage loss (LL) at a wavelength of 0.75 µm. Besides that, Gao and his colleagues have suggested a fiber that has a LL of 2.2 dB/km at the wavelength of 1.512 µm [34]. In addition, in our previous research, Shaha et al. [35] proposed a nested HC-AR fiber with double cladding elements that exhibits low optical loss, in the year 2020. In our recent works, it is seen that hybrid cladding elements (circular and elliptical) [6] and modified conjoined tubes [8] in the cladding geometry of HC-ARFs have significantly improved the loss performances. Moreover, Wang et al. [36] introduced a two ring ART with curvature of inverse nature and showed what happened at the wavelength of 1.06 µm when an additional ring was added for high power laser applications. Once more, Shaha and colleagues [30] reported a minimal loss anisotropic HC-AR fiber arrangement for reducing the loss to 12 × 10−4 dB/km at an operating wavelength of 1.25 µm. A conclusion can be drawn from the literature that an efficient guiding medium is highly expected to transmit and control high power, and HC-ARF would be the best platform for this. Although many researchers tried to solve the limitations in this fiber platform (high leakage as well as bending losses, weak single mode characteristics, and so on), the study of the effect of increasing the number of layers in the cladding on the HC-ARF platform might be highly demanding. Hence, innovative structures with efficient cladding configurations are eagerly anticipated in HC-ARFs for transmitting and controlling high-power laser light with extremely low leakage and bending-induced loss with superior singular mode characteristics.
With a view to examining the impacts of multi-layer cladding elements on the fiber performances, we studied triple cladding antiresonant hollow core fibers (TC-AR-HCFs) and proposed the best low loss guiding possibility of high-power laser light. It offers extremely minimal leakage loss, comparably minimal bending-induced loss, and excellent single mode performance. Our focusing point is at the wavelength of 1.06 µm where high power lasers are available. We achieved impressive low-level losses: LL and bending loss (BL) are reduced by two and three order, respectively, by utilizing the positive impact of additional third ring or layer of AR tubes surrounding the core because it gives additional negative curvatures to the fiber. A minimum LL, 5.82 × 10−5 dB/km, is calculated at the wavelength of 1.06 µm, and it maintains a loss of ~ 0.08 dB/km in between 0.95 µm and 1.2 µm (250 nm bandwidth). Moreover, this fiber has reduced bending-induced loss (9 × 10−4 dB/km) at 1.06 µm wavelength with a bend radius of 14 cm. The higher order mode extinction ratio (HOMER) formula is assessed for single-mode performance, and so in this work, HOMER has an elevated value of ~104 for a wavelength of 1.06 µm.
2. Fiber design and methodology
Figure 1 reports the studied TC-AR-HC fibers, in a two-dimensional platform, having three cladding layers (i.e., three ART tubes ring). Instead of full geometry, half structures are shown due to the easy presentation. Each of the four possible fiber geometries has a uniform core radius of Dc = 30 µm and a similar thickness for all the circular elements of t = 0.42 µm. Besides that, all the ARTs in three cladding rings are circular, and the diameters of first (near the core), second (in the middle) and third (close to the outer capillary) rings are represented by d1, d2, and d3, respectively. The core, which has a hollow region, is filled with air, and the background fiber material is silica [37] in our fiber design. Figures 1(a)-1(d) show a schematic two-dimensional arrangement of the studied three-layered circular shaped cladding ring geometries. In Figs. 1(a) and (b), the fiber core is surrounded by a total of eight ARTs to form the first and second rings, while the third ring consists of sixteen tubes connected to the outer capillary (connected to the boundary). The total fiber diameter for the first fiber geometry is 79.74 µm (Fig. 1(a)). In Fig. 1(b), the third ring ARTs are rotated by 45° in order to create more nodes or junctions in the third layer. Here, the ratio of d1/Dc and d2/Dc for both the structures (Figs. 1(a) and (b)) are 0.57 and 0.70, respectively. The third ring tubes’ diameter ratio, d3/Dc, is 0.29 for original unrotated fiber structure (Fig. 1(a)) and 0.36 for rotated structure (Fig. 1(b)). The different ratio in third ring tube diameters is due to the fixed total fiber diameter.
Fig. 1. Standardized cross-sectional representation of the considered TC-HC-ARFs. This configuration contains four semi-structures of TC-HC-ARF having (a) eight tubes, and (c) six tubes in the first ring (i.e., close to the core). In each of these diagrams, the core diameter is uniform and represented as Dc, and the uniform thickness of the cladding AR tubes is represented by t. Furthermore, d1, d2, and d3 correspond to the diameters of 1st, 2nd, and 3rd cladding ring, respectively. Third ring tubes are rotated by 45° in Figs. (b) and (d) in order to see the effect of increased nodes in a multi-layer cladding configuration.
On the other hand, Figs. 1(c)-1(d) have six tubes in their first and second cladding rings, and the third ring has twelve tubes connected to the outer capillary (close to the perfectly matched layer (PML)). In Fig. 1(d), the structure is modified by rotating the third ring tubes by 45° compared to the unrotated counterpart (Fig. 1(c)). Here, the ratio of d1/Dc and d2/Dc for both the rotated and non-rotated structures, shown in Figs. 1(c) and 1(d), are 0.63 and 0.88, respectively. The third ring tubes diameter with respect to the core diameter, d3/Dc, is 0.60 and 0.73, respectively, for our discussed unrotated and rotated (third ring tubes) cladding structures. In a nutshell, the dimensions of all four structures studied (two have eight tubes and two have six tubes in both the first and second ring) are uniform except for the diameter of the tubes, and the optimized dimensions are summarized in Table 1. This is happening because we have tried to keep the fiber core diameter fixed for the four considered structures which helps us to compare the performance of the fibers. There is no overlap between the fiber core and any of the tubes. The positioning of the ARTs in the first cladding ring is determined as [26]
where Dc is the fiber core diameter, d1 is the fiber tube diameter for first ring tube, and n is the number of tubes. The parameter g represents the distance or spacing between the tubes in the first ring (close to the core). The tubes in the second and third rings naturally adhere to the previously mentioned rules since their diameters are smaller compared to the diameter of the tubes presented in the literature [26]. Taking into account the thickness of the tubes, denoted by t, which is measured at 0.42 µm, and concentrated on the initial range of effective transmission, the state of resonance is received approximately at a wavelength of 0.87 µm, as indicated by the provided expression as [26] where the refractive indices for silica and air are denoted as nSi and nair, respectively, and the wavelength of the guided light is λ, while w1 represents the effective transmission range possessing only counting or natural values. Here, silica is selected as the material for the tubes surrounding the core (known as cladding tubes), and Sellmeier's equation (material dispersion is already included) is used for defining the properties of the fiber material [37]. Leakage loss, which results from insufficiently confining light inside the fiber core, is a crucial loss that must be estimated. The following equation can be used to determine this loss as [38]
Table 1. Fine Tuned Structural Properties of the Studied Fibers
3. Numerical results and discussion
For modeling and numerical analysis of the proposed structures, commercial software namely COMSOL Multiphysics is used, which works based on the finite element method (FEM). A finite computational domain is selected by implementing a PML boundary that is responsible for absorbing radiating light energy. The background fiber material (silica) is also selected for this layer. A proper selection of mesh is also an important issue. A convergence experiment is first conducted, as shown in Figs. 2(a) and 2(b), on the suggested eight tube non-rotated TC-HC-ARF (Fig. 1(a)) at the operating wavelength of 1.06 µm to justify the numerical accuracy with respect to the PML thickness and meshing. We have used the maximum mesh element size as λ/6 m for silica, and λ/4 m for the air regions, respectively, where m is a mesh size parameter and λ displays the working wavelength in our case. It is noted that the minimum mesh element size is 1.68 nm here, and actual meshing will depend on the maximum to minimum element size limit, the curvature factor, the element growth rate, etc. We have now varied m and PML thickness to see the leakage loss stability only (Figs. 2(a) and 2(b)) because LL is a vital fiber’s performance parameter and more sensitive than the others. After initial oscillations, it is seen that a constant loss is observed beyond m ≥ 0.8; hence, m = 1 is used for further investigation to save computational time without losing computational accuracy. Similarly, Fig. 2(b) shows the LL execution in relation to the thickness of the PML. It can be observed that beyond a thickness of greater than 5 µm, PML consistently provides a stable response (nearly constant loss) for the designed fiber. This is the reason why a 10 µm PML thickness was employed for this work.
Fig. 2. The convergence experiment: leakage loss analysis of our selected fiber (8 tube non-rotated geometry shown in Fig. 1(a)) at the wavelength of 1.06 µm for (a) utilizing the maximum mesh size parameter (m) with a value of λ/6 m for the silica region and λ/4 m for the air region, and (b) considering a PML thickness range of up to 10 µm as chosen for this study.
In addition, for the justification of numerical study, we reproduced a result (red curve with DR-NCF marked) from a related double cladding structure [36] and found good agreement over the whole wavelength of interest as shown in Figs. 3(a) (the result of the Ref. paper [36] along with inset structure) and 3(b) (our regenerated result of the Ref. [36]). We focused primarily on the wavelength of 1.06 µm since fiber lasers with high-power are widely accessible here, and are chosen as our operating wavelength. As a results, most of the results are optimized at 1.06 µm (can be seen in Figs. 2(a), 2(b), and Fig. 4 as few examples).
Fig. 3. Justification of numerical accuracy by comparing our simulation results with the results obtained in a related existing double cladding structure [36]: (a) The confinement loss in dB/m (also known as leakage loss) of the Ref. paper [36] where the red color curve represents their DR-NCF (structure is inset that we considered), although other curves are for their remaining studied structures [36], (b) The reproduced confinement loss of Ref. [36] vs. wavelength where the regenerated electric field surface of DR-ARF (in our COMSOL environment) is inset in the plot. The frame color is correlated with the curve color.
Fig. 4. The optimization process of cladding tubes diameters of our proposed structure (in Fig. 1(a)) by taking into consideration the leakage loss, at 1.06 µm, with respect to the (a) d1/Dc for first layer cladding, (b) d2/Dc for second layer cladding, and (c) d3/Dc for third layer cladding.
3.1. Analysis of the optimization of the structures
In our research, we have tried to optimize our structures first to achieve the minimum leakage loss at 1.06 µm of wavelength. The process of structure optimization is similar for the four considered fiber geometries, and one structure (shown in Fig. 1(a)) is analysed here to clarify the steps. Our first target is to fine-tune the value of d1 (tube diameter of the nearest ring around the core), and the corresponding structure is inserted in Fig. 4(a). As a result, the fundamental mode (FM) leakage loss is depicted in Fig. 4(a) as a function of d1/Dc, which ranges from 0.3 to 0.6. When the d1/Dc ratio rises, the loss begins to fall, and it stays practically constant across a large range as 0.45 < d1/Dc <0.58. The ARTs intersect with one another at d1/Dc = 0.60, and loss increases due to the creation of additional nodes. As a result, the value of d1/Dc cannot be raised further, and the minimum leakage loss is attained at d1/Dc = 0.57.
We then proceeded to introduce the second ring ARTs in the structure (inset of Fig. 4(b)) with a diameter of d2 after setting d1/Dc = 0.57. Figure 4(b) shows the leakage loss with regard to d2/Dc, the loss reduces as the d2/Dc ratio rises, and the leakage loss is nearly constant from d2/Dc = 0.65 to d2/Dc = 0.72. The leakage loss is decreased by three orders of magnitude (at 1.06 µm) due to the addition of second ring as seen in Fig. 4(b). At about d2/Dc = 0.70, the loss is settled at its lowest level; thereafter, it steadily rises as d2/Dc grows in its value. In a similar way, we added a third layer of ARTs by keeping the already optimized diameters of d2/Dc at 0.70 and d1/Dc = 0.57 (the corresponding geometry can be seen inset of Fig. 4(c)). According to Fig. 4(c), the leakage loss decreases quite sharply with the raises of d3/Dc up to its value of 0.29, and then the loss raises for the further increment of d3/Dc. As a result, the minimum loss is further lowered by three orders of magnitude (at 1.06 µm) which is 5.82 × 10−8 dB/m and the optimized diameter ratio of the third layer of ARTs is selected at around d3/Dc = 0.29. A summary of the optimized structural parameters can be seen in Table 1. It is noted that LL is considered in dB/m (instead of dB/km) in Fig. 4 which is because of the clear understanding of the low loss level during the optimization process.
3.2. Analysis of leakage loss
For simplicity of analysis, the leakage loss performance is calculated first and analysed for the four considered fibers. Figure 5 shows the LL spectra for the studied structures within the wavelength range of 0.90 µm to 1.60 µm. Among those structures, the eight tubes unrotated fiber has the lowest LL because of the additional number of layers (negative curvatures) and limited nodes, which leads to a better anti-resonant reflection. In the lower wavelength range, each of these fibers offer a low loss level, i.e., 5.82 × 10−5 dB/km at the operating wavelength of 1.06 µm, 3.28 × 10−4 dB/km at ~1 µm, 7.86 × 10−4 dB/km at 1.06 µm, and 5.14 × 10−4 dB/km at ~1 µm, respectively, for the structure having 8 tubes, 8 tubes 45° rotated, 6 tubes, and 6 tubes 45° rotated cladding arrangement in the third ring of the geometry.
Fig. 5. Comparison of leakage loss performance among four studied structures within a range of wavelengths, although our focusing point is at 1.06 µm. All the structures feature an identical core radius (Rc = Dc/2 = 15 µm) and a strut thickness (t) of 0.42 µm. The red, blue, black and green color curves correspond to the fiber structures having eight tube non-rotated, eight tube rotated, six tube non-rotated, and six tube rotated cladding arrangement, respectively.
Figure 5 displays a spectrum of leakage loss for the 8 tube nonrotated three layered cladding components of the best TC-AR-HCF along with the other three counter configurations. Due to the close proximity of the core and the outer capillary layer in the cladding, the 6-tube rotating ARF recorded the greatest LL of all those structures, which is 1.55 × 10−3 dB/km (green color dotted indicated) at 1.06 µm of wavelength. Then, within the wavelength of interest (Fig. 5), the 8-tube rotated structure reported a second reduced LL (blue color dotted) compared to the prior one (6 tube rotated one). The loss performance improved, in eight tube rotated fiber’s structure, due to the increased number of negative curvatures in the cladding, but the number of nodes creates limitation to achieve the best performance. Besides that, the absence of node between the outer and second circular capillaries in the 6-tube non-rotated structure improves the loss performance of the fiber and leads a comparatively third lower LL of 7.86 × 10−4 dB/km at 1.06 µm (black color solid line). The above limitations have been improved in the 8-tube non-rotated configuration due to the increased number of cladding tubes in the third ring along with less number of nodes creation, which offers the lowest LL (5.82 × 10−5 dB/km, red color solid line) among the others. To have a better visibility of the structural insight, the side panel of Fig. 5 illustrates the four studied structure’s constructions with indicated dimensions where the box colour correlates with the line color of the leakage loss spectra.
The performances based on LL at 1.06 µm among the four investigated structures are tabulated in Table 2. Therefore, among all of the investigated structures, the proposed 8-tube non-rotated TC-ARF (Fig. 1(a)) offers the minimal LL (red color solid line): the combination of three circular tube rings results in the lowest loss because they offer more antiresonance strength by using more negative curvatures. The best structure (shown in Fig. 1(a)) offers a LL of 5.82 × 10−5 dB/km at a wavelength of 1.06 µm. Besides that, a LL of <∼ 0.08 dB/km and <10 dB/km are obtained across a spectral width of 250 nm (from 0.95 µm to 1.06 µm) and 400 nm (from 0.90 µm to 1.30 µm), respectively, in our best optimized arrangement.
Table 2. Leakage Loss of the Compared Fiber Structures at 1.06 µm
3.3. Analysis of bending loss
A fiber should possess a natural resistance to the effects available in real-world applications. Due to structural distortion and the coupling effect, the bending-induced loss in the HC-ARF emerges. The subsequent mathematical expression is known as the equivalent refractive index model and is applied to determine fiber bending-induced loss [35,36,39] along the x direction as
where nb implies the equivalent RI after bending, nm is the material refractive index of the undistorted fiber. Moreover, Rb represents the bending radius (distance between fiber center to the outer capillary under bending).The bending-induced loss relative to the curved bend radius for the studied structures is shown in Fig. 6(a) at 1.06 µm of wavelength. It is evident that as the curved bending radius increases, the bending loss decreases, which holds true for all fiber types [5,20,26,36,38–41]. As a result of the phenomenon known as the anti-crossing effect [6,26,35,36], it is shown that the 6-tube rotated (45°) configuration has the highest BL (green color dotted line) among all. The maximum BL was recorded at a curved bend radius of 4 cm because of the tendency for coupling between this structure's core mode and cladding modes under bending state. The 6-tube’s (without rotation) structure thus offers comparatively better BL (black colour solid line) than the 6-tube turned (45°) structure, but it is still quite high. Better BL than the previous two constructions is provided by the 8-tube rotated structure (blue colour dotted line curve) and 8-tube non-rotated cladding arrangements (red colour solid line), although both suffer from anti-crossing effects at 3 cm (only 8-tube non-rotated one), 6 cm, and 9 cm of bend radius. Although the 8-tube rotated one provides better BL in the higher bending regions (bend radius of less than 14 cm), eventually, the suggested fiber (red color solid line) showed the best BL among the evaluated fiber architectures, thanks to a limited air zone in the cladding and inhibited coupling propensity between core mode and cladding modes.
Fig. 6. (a) Comparison of the bend radius-related bending loss performance of various constructions studied in this research. The same strut thickness, t = 0.42 µm and core radius, Rc = 0.15 µm, are employed. The corresponding field profiles are depicted in right side panel for some specific bend radius of (b) 2 cm, (c) 4 cm, (d) 6 cm, and (e) 8 cm, where field profile’s box color is matched with line color of the BL curve of the optimized structure only (red color).
The bending loss curve exhibits multiple peaks at different bending radii before reaching a bend radius value of 10 cm. This behaviour is attributed to the influence of the anti-crossing effect [24]. Notably, at a bend radius of 14 cm, the bending loss measures approximately 9 × 10−4 dB/km and remains less than 9 × 10−2 dB/km and 6 × 10−3 dB/km of loss while the bend radius exceeds 7 cm and 11 cm, respectively. Moreover, with a curved bend radius of 20 cm, a BL of 0.000272 dB/km is attained. As a result of the debilitated propensity of coupling between the central (core) mode and surrounding (cladding) modes, it exhibits three increasing peaks at bend radii of 3 cm, 6 cm, and 9 cm because of the structural distortion that occurs due to too much bending. It is noted that a smaller bend radius indicates larger fiber bending. However, the loss reduces monotonically as the bend radius grows (for example, a decreasing loss tendency can be seen after 9 cm of bend radius in Fig. 6(a)). Hence, the fiber with eight tube non-rotated structure performs better than the remainder equivalent. So, for the remaining discussion, we will focus on the eight tubes’ non-rotated construction only. In the right-side panel, Figs. 6(b)–6(e) shows the corresponding electric field profiles of our finalized structure at the bending radius of 2 cm, 4 cm, 6 cm, and 8 cm, respectively, to clearly understand the bending loss behaviour of the best performed structure (red colour marked). It is seen that field profile distorted much (core region of Fig. 6(b)) because of the too much bending radius of 2 cm which is expected. The distortion in field profile reduces as the bending radius increases further (4 cm to 8 cm) as can be seen in Figs. 6(c) to 6(e).
It is also crucial to examine the bending-induced loss behaviour of our proposed best structure (eight tubes non-rotated structure) in relation to the relevant wavelength. Figure 7 displays the variation in bending loss as a function of wavelength for different values of Rb (bending radius). The bending-induced loss is illustrated in this study with a given curved bend radius of 14 cm. It is chosen as 14 cm because the bending loss decreases after 9 cm bend radius and becomes stable in 12 cm, which provide stable loss up to 20 cm. To be more specific, it is an arbitrary bend radius chosen just for discussion, we can choose any bend radius from the range of 2 cm to 20 cm (the similar range can be found in the literature [6,26,32,36]). The lowest loss (< ~ 10−3 dB/km) is obtained at the wavelength of 1.06 µm as expected. The loss is still less than 0.087 dB/km between wavelengths of 1.00 µm and 1.22 µm. The presence of the silica probe connection (the connection between two silica tube layers, i.e., the junction between one-layer tubes to other layer tubes) results in Fano-resonance, leading to the specific oscillations observed in the bending loss spectra (Fig. 7) [8,39]. There is some abrupt change in the BL curve, especially at the wavelengths of around 1.14 µm, 1.20 µm, 1.25 µm, and 1.35 µm which is because of structural distortion due to anticrossing effect [24,35,36] happened in the numerical simulation at some particular critical point.
Fig. 7. The behaviour of bending-induced loss of the best designed structure in relation to the wavelength. In this analysis, a constant curved bend radius of Rb = 14 cm is employed for our chosen best fiber structure (actual schematic is in Fig. 1(a)).
3.4. Analysis of single mode performance
The ratio between the minimal higher order modes (HOMs) loss and the FM loss is known as HOMER, which stands for single mode properties of a fiber [32]. The fiber can effectively operate as a single mode if HOM losses are sufficiently greater than the basic mode (FM) loss. In our fiber, FM is HE11 and HOMs are considered as TM01, HE21, TE01, HE31, and EH11 (modes can be differentiated with the help of different color’s legend). According to Fig. 8(a), FM (HE11) has the lowest loss level, while the TE01 mode exhibits the least level of loss among all the HOMs. It is noted that the above explanation regarding the lowest loss level of FM and HOMs is valid over the whole wavelength of interest although our focusing point specially is around 1.06 µm due to the high-power laser delivery. As a result, the wavelength range that is being studied is restricted to 1.00 µm to 1.30 µm. The corresponding electric field patterns of HOMs and FM are presented at the apex of Fig. 8, where the box color of field profile corresponds with the line color of the loss spectra. Figure 8(b) displays the nature of HOMER variation for the change in wavelength. As the wavelength increases, it is seen that the value of HOMER keeps its high value (> ~ 103) until it reaches its maximal level (8590) at around 1.06 µm. After that, the HOMER maintains much better than the well-known single mode standard (HOMER = 10 [6,8,36]). The aforementioned explanation leads to the conclusion that the provided device can function as a top-notch single mode fiber. The other three studied structures also show good HOMER performance, but the selected one provides the best performance by considering other loss properties.
Fig. 8. (a) Spectra regarding leakage loss of HOMs and FM showcasing dependency on wavelength variation, and (b) HOMER versus wavelength, specifically focusing on the FM of HE11 and TE01 mode due to its minimal loss compared to other HOMs. The top section showcases the field profiles of HOMs and FM, visually represented with matching colors.
3.5. Comparative analysis of our achievements
Table 3 displays a comparative behavioral analysis of our proposed fiber with relevant and current research on the platform of HC-ARF. One such example is the solitary ring, eight-tube AR-HC fiber reported in [33], which exhibits a two orders higher fiber bending-induced loss (compared to our case) of 3 × 10−2 dB/turn at Rb (bend radius) of 15 cm and a considerable higher loss of 7.70 dB/km in the wavelength area of 0.75 µm.
Table 3. Comparative Summary of our Fiber Performances with the Existing Related and Recent Literatures
Moreover, Chen and colleagues [41] reported a double negative curvature AR-HCF at 1.35 µm and improved the level to 0.05 dB/km (still far away from the current reported loss level) with superior bandwidth of 400 nm by maintaining a loss level of < 1.0 dB/km. In 2020 [36], a remarkable HOMER of 103 was discovered, which is lower than the reported HOMER here by one orders of magnitude, while Wang's and co-authors demonstrated a significant reduction in leakage loss, achieving an impressive value of 0.01 dB/km (which is much higher compared to the current value) at the corresponding wavelength of 1.06 µm. Importantly, nearly two orders of magnitude higher LL and bending losses are observed in very recent research outcomes [42,43]. There are more recent and related fibers [2,30,34,35] in the literature (not summarized in Table 3) that have attempted to improve leakage loss, bending loss, and single mode properties. For instance, in [35], an enhanced performance is seen in terms of higher loss (10−3 dB/km) with a similar HOMER of 103. Therefore, it is clear from the above summary that the suggested fiber may be able to perform significantly better than the reported fibers due to its minimal leakage loss (5.82 × 10−5 dB/km), high HOMER (~104), and better bending-induced loss (0.0009 dB/km).
3.6. Analysis of fabrication feasibility
From a manufacturing perspective, it is crucial to assess the variation in structural parameters to ensure the perspective of the achieved results throughout the fabrication process. The presented fiber is made with three layers of cladding circular tubes, and it is necessary to consider the overlapping of the tubes at the junction points. We are considering this overlapping or penetration as an ingression length (p) in percent. The ingression of the tubes is happened between two successive layers i.e., rings. We have increased this length from ideally optimized (t/10) to 10% of its ideal value. The corresponding geometry of every considered ingression length is depicted in the right panel of Fig. 9 and can be identified by color matching between box (right side) and line curve. It is noted that we have considered ingression in both layer’s node uniformly which can be visualized from two geometries located in each row. For example, two geometries marked as black color (top one) represent zoom view of nodes created in between first (around the core) to second (middle) ring and second (middle) to the third (close to the outer capillary) ring of our optimized structure with initial ingression (t/10), respectively. The following black, green, blue color box are the corresponding geometries for the ingression length (p) of 4%, 6%, and 10%, respectively.
Fig. 9. Leakage loss curve for the fabrication test with respect to wavelength where the error is shown in two layers tube ingression with the ideal one. Here, p is ingression length in percent due to ingression of tubes between two consecutive rings.
Figure 9 depicts the leakage loss as a function of ingression length variation with respect to wavelength. From Fig. 9, it is perceived that the LL is elevated with the increment of ingression length over the wavelength, thus the edge length has a negative impact on the fiber’s performance. Due to the increase of ingression length (p) from its optimum value, the LL increases gradually. This happens because increasing ingression results in a wider nodes area, and those nodes lead to light leakage through the cladding, which results in high leakage loss. However, up to 10% of ingression of the tubes, the LL is maintaining less than ~0.001 dB/km which is still a significantly lower loss than the existing reported loss [22,33,41]. Hence, it is concluded that the fiber can maintain the lower loss performance after suffering enough ingression tolerance. This tolerance level may be useful if the ingression is created from cladding tube pressure as well as pull and feed speeds during the drawing process of fabrication [36].
At the time of fabrication, the thickness of the structure might be deviated. So, by increasing and decreasing the values of the thickness, t, we can evaluate the performance of the selected structure. By comparing the LL spectra of ideal (optimized) tube thickness with −2% to +2% of the ideal tube thickness, the tolerance of tube thickness, t is observed thoroughly as shown in Fig. 10(a). When there is an increase of 2% in the tube thickness, the LL initially increases due to the change in resonance wavelength because resonance wavelength is highly sensitive to the tube thickness [6,35,36]. From Fig. 10(a), it is noticed that a relatively limited oscillation in the loss curve is observed for the optimized t and for its variation from −2% to +2%: the pattern looks almost the same, and in higher wavelength regions, the loss variation is nearly the same. The LL spectra are suffering from oscillation due to Fano resonance [35,36] that occurs at the node between ARTs. Therefore, it is concluded that, after the postprocessing, the fiber can obtain its desired performance.
Fig. 10. (a) Leakage loss variation for the tube thickness (t) variation of +2% to −2% for finding the effect on real time application with respect to wavelength comparing the results with optimized tube thickness. (b) Leakage loss performance with respect to wavelength while the core diameter (Dc) is varied from + 2% to −2% along with its optimized core diameter.
At the end, from the real point of view of fabrication, we go through the analysis of tolerance for the fiber core diameter (Dc). We vary the core diameter from −2% to +2% of its optimized value and summarized the effects in terms of LL over the specified wavelength range (Fig. 10(b)). It is seen that a bit of oscillation is observed in the LL spectra, and the amount of loss variation is within a tolerated level. Because, the oscillation originally observed in the loss curves of every multi-layered structure, as explained earlier.
Moreover, one pioneering work which is based on second cladding layer is successfully fabricated by Huang and co-workers [44]. Another related structure namely split cladding ARF having triple cladding has already been fabricated in previous days [45]. On the other hand, conjoined tube based antiresonant fiber was found 0.8 dB/km as simulated loss, and 2 dB/km loss was found after fabrication at 1.55 µm [34]. Thus, we have chosen a tolerance level of ±2% by following previous literature [5,34,44,45] and found negligible difference with the optimized one. This means that the structure could tolerate more. It is noted that we have also discussed overlapping or penetration as an ingression length (p) in percent which may be helpful regarding the fabrication challenge. Therefore, we hope that the proposed structure may maintain its numerical achievements in its fabrication stages along with few postprocessing.
4. Conclusions
In order to reveal the physical insight of multilayered cladding in ARF, the design of a few new multilayer cladding based AR-HCFs are studied, analysed, and the best proposal is obtained through the finite element numerical method. The effect of nodes and the number of layers in the cladding are clearly investigated and as a result, the leakage loss reduces significantly by a few orders of magnitude. Numerical result shows that the leakage loss in the presented fiber is reduced by two and three orders of magnitude, respectively, compared to the double-layered cladding nested and double-layered negative curvature AR-HCFs (can be seen in Table 3). Additionally, a better bending-induced loss and excellent single mode performance (HOMER = 104) is obtained. We believe that the proposed low losses multilayered cladding based single mode fiber hold enough potential for high power fiber laser systems.
Funding
Department of Research & Extension, Rajshahi University of Engineering & Technology (RUET) through the University Grant Commission (UGC), Bangladesh (DRE/7/RUET/640(53)/PRO/2023-24/14).
Acknowledgments
The authors acknowledged the computational and other logistic support provided by the Department of Electrical & Electronic Engineering (EEE), Rajshahi University of Engineering & Technology (RUET), Bangladesh. We also want to thank Md. Sarwar Hosen (EEE, RUET) for his suggestions during the period of this research. Dr. Abdul Khaleque wants to acknowledge the financial support (DRE/7/RUET/640(53)/PRO/2023-24/14) provided by Research & Extension of RUET through the University Grant Commission (UGC) of Bangladesh. Moreover, Kumary Sumi Rani Shaha wants to acknowledged the support provided by the Department of Electrical, Electronic and Communication Engineering (EECE), Pabna University of Science and Technology (PUST), Pabna-6600, Bangladesh.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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