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Nodeless antiresonant hollow core fiber for low loss flatband THz guidance

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Abstract

This paper reveals a THz leading nodeless antiresonant slotted hollow core fiber (NARS-HCF) with low transmission loss and broad band flat near zero dispersion. We have achieved better results in a simpler structure as far as we know: a minimal confinement loss in the order of around 10−4 dBm-1 and a very low effective material loss of 0.0248 dBm-1, resulting in a lowest total transmission loss of 0.0254 dBm-1 at 1.27 THz and offering a 0.88 THz (0.8 THz – 1.68 THz) low loss transmission bandwidth with the loss of less than 0.0811 dBm-1. Additionally, we achieved a 0.0614 ± 0.0468 ps/THz/cm near zero flat dispersion over the widest bandwidth of 1.02 THz (0.80 THz to 1.82 THz). Moreover, our proposed structure can also effectively perform as single mode fiber with excellent bending loss performance, hence, can be useful for efficient THz transmission systems.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Terahertz (THz) waves are useful electromagnetic wave between the radio (microwave) and optical (infrared) regimes with the operating frequency ranging from 0.10 THz to 10 THz [1]. They are playing a gigantic part in the advancement of technology for its excellent interconnection with matters, hence, millions of people are enjoying its benefits in the field of spectroscopy [2], sensing [3], medical diagnosis and imaging [4], DNA and RNA mutations and characterization [5], very fast and short distance communication [6], security [7]. Although the effective THz sources and detectors are commercially accessible, THz transmission is quite difficult through conventional waveguides because of their excessive loss parameters [8], therefore the researchers are still facing a significant hurdle to implement efficient THz guiding medium. In the modern world, optical fiber is a better medium for high-quality THz transmission due to its extraordinary performances. Recently, different fibers have been designed and proposed to overcome these problems and up to now, hollow core fiber (HCF) provides the best solutions where light can confine in air core and travel faster than a solid core fiber (SCF) [9,10]. Both types of HCF such as photonic bandgap (PBG) fiber and anti-resonant fiber (ARF) have been able to overcome few issues partially but still struggling to achieve low loss, low dispersion, broad bandwidth simultaneously in a simpler fiber structure. For example, PBG fiber offers lowest loss among HCFs along with the bandwidth limitations which can be solved by ARFs [912]. However, anti-resonant hollow core fiber (AR-HCF) is in front line due to the low losses, wide bandwidth due to the inhibited coupling between the core and cladding modes [9]. Various forms of cladding structures are available in AR-HCFs [1121], including circular tubes with [1315] or without nested [16] patterns, ice cone shape tubes [17], nested [18] or non-nested [19] with elliptical or semi elliptical [20] tubes, half circular and half elliptical [21] tubes. Among them, negative curvature cladding tubes are mostly observed for its better performances. In addition, a modest separation between adjacent cladding tubes, responsible for nodeless structure, able to reduce losses by avoiding node resonance [12]. The loss can be further reduced by adding nested tubes [22].

In 2018, Hasanuzzaman et al. [23] introduced an AR-HCF having six circular tubes and six nested tubes in the cladding and offered 0.05 dBm-1 effective material loss (EML) at 1 THz and near zero flat dispersion of < 0.11599 ps/THz/cm over 0.8 THz to 1.4 THz of frequency. In the same year, Yan et al. [24] proposed a complex ARF structure having ten circular cladding tubes where two of them contained nested arrangements and attained higher transmission loss of 2.1 dBm-1 at 1.2 THz. The following year, Zhu and his colleagues suggested a more complex HCF in which cladding was consisted of nine circular tubes and nine nested elliptical tubes, yielding unappealing performances: EML of 0.019 cm-1 (8.25 dBm-1), confinement loss (CL) of 0.29 cm-1 (125.95 dBm-1) from 0.9 THz to 1.5 THz, and a flat dispersion of ±0.029 ps/THz/cm over the frequency of 0.6 THz – 1.5 THz [25]. In 2020, another related but comparatively complex geometry having five conjoined (half circle and half elliptical) tubes is presented and claimed a minimum loss of 0.034 dBm-1 at 1 THz frequency and a flat near zero dispersion of 0.1068 ± 0.0760 ps/THz/cm from the frequency range of 0.7–1.4 THz [21]. Very recently in 2021 [26], a relatively complicated fiber structure, constructed with eight unequal circular and two semi elliptical nested tubes, was proposed and reported a higher CL of 0.231 dBm-1 and limited dispersion of ±0.188 ps/THz/cm over the flat dispersion bandwidth of 0.475 THz. Therefore, based on the recent and related literature, it is concluded that the fiber performance parameters (as mentioned above) in THz regime need to be improved in a simpler geometry.

The motivation of our presented manuscript is to introduce a simpler slotted structured optical fiber with the lowest transmission loss (combination of CL and EML), broad bandwidth with low transmission loss, the wider flat band near zero dispersion, which can be operated as effectively single mode fiber (ESMF). In this study, a non-nested, node free and five tubes cladding based simpler slotted HCF is presented able to show an extremely low transmission loss, flat near zero dispersion over a wide frequency range and acceptable bending loss as well as effective single mode performance. Although we didn’t fabricate the proposed fiber yet, according to the theoretical background and analysis it is observed that our fiber construction seems to be quite simpler due to the use of only five circular tubes each having one rectangular slot inside. In addition, the appropriate optimization and slot location lead to achieve the above expected goals, overall, the presented work offers the best result in a simpler structure, to the best of our knowledge.

The reminder of this study is arranged as: section 2 describes the fiber design, section 3 includes the results analysis, section 4 depicts the fabrication feasibility, and section 5 concludes the article.

2. Fiber design and theory

The proposed simpler fiber construction is shown in Fig. 1. There are five cladding tubes in this construction, and each tube has a rectangular slot within it. These slots are positioned to prevent the leaking of light from core to the cladding. The optimized core diameter of DC is 3 mm while circular cladding tubes diameter of D0 is chosen as 0.86 times of DC. The rectangular slot position DS is selected from the pick position of negative curvature connected with DC and chosen as DS = 0.7 DC. We choose a uniform thickness, t = 0.07 mm for both the cladding tubes and slots. The overall fiber diameter is 8.4386 mm. The settings of all parameters have been chosen to provide the best performance with the least amount of total transmission loss and the optimized parameters are tabulated in Table 1. A perfectly matched layer (PML) is utilized to absorb the radiated energy, leading to better confinement of light to the core. For this structure, background material is TOPAS (black region in Fig. 1) with the refractive index of 1.5258 [23]. We have selected TOPAS rather than other materials because it has a constant refractive index over a wide frequency range (0.1 to $\sim$1.7 THz) and lower bulk material loss than polymethyl methacrylate (PMMA) between 0.2 THz to 1.6 THz [27].

 figure: Fig. 1.

Fig. 1. Proposed cross-sectional view of the fiber with hollow core diameter of Dc = 3 mm, anti-resonant tubes diameter of D0 = 0.86 Dc, rectangular slots position from the core side of Ds= 0.7 D0 and thickness of t = 0.07 mm. Black and aqua regions stand for TOPAS and air, respectively.

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Tables Icon

Table 1. Optimized structural parameters

Our goal is to achieve the lowest transmission loss within a wide frequency range by adjusting the structural parameters DC, D0, DS, and t for THz guidance. Here, CL and EML are two dominant loss parameters: when THz waves are transmitted through the fiber core, some light waves are leaked through the cladding zone which results in CL [22], and EML happens when rays are absorbed by surrounding fiber materials [23]. The CL of the fiber can be calculated by the following equation as [22]

$$CL = 8.686 \times 2\pi \times \left( {\frac{c}{f}} \right) \times {I_m}({{n_{eff}}} )\;\; \mathrm{dBm}^{-1}$$
here, Im(neff) is the imaginary component of the fundamental mode's effective refractive index, f is the operating frequency, and c is the free space light velocity, which is 3 × 10−8 ms-1. Another significant fiber loss in THz regime is EML can be expressed as [23]
$${\rm{EML}} = \sqrt {\frac{{{{\rm{\varepsilon }}_0}}}{{{{\rm{\mu }}_0}}}} \;\frac{{{\smallint _{{{\rm{A}}_{{\rm{mat}}}}{\rm{\;\;}}}}{\rm{n}}{{\rm{\alpha }}_{{\rm{mat}}}}{\rm{\;\;}}{{\left| {\rm{E}} \right|}^2}{\rm{\;dA}}}}{{2{\rm{\;}}{\smallint _{{\rm{All}}}}{{\rm{S}}_{\rm{Z}}}{\rm{\;dA}}}}\;\;{\mathrm{dBm}^{- 1}}$$

In this case, $\epsilon_0$, $\mu_0$ are the vacuum permittivity, permeability, respectively, Sz is the pointing vector along propagation direction, n denotes the refractive index of the background material, and αmat is the bulk material loss which is 1 dBcm-1 [23]. It is noted that Amat and All represent the integration limit for solid material region and entire fiber region respectively. Therefore, the total loss (TL) can be calculated here by adding both CL and EML and can be written as

$$TL = CL + EML\;\; \mathrm{dBm}^{-1}$$

3. Results and discussion

The finite element method (FEM) based mode solver is used to calculate and analyze the fiber performances. To check the accuracy of our numerical calculation, we have simulated a few recent analogous structures from the literature and obtained excellent agreements. By following previous studies [9,21,22,23], accuracy is assessed using a convergence experiment to determine a PML thickness accurately along with mesh sizes. We have chosen an incredibly tiny mesh size of λ/8 for air area as well as λ/16 for the fiber material (TOPAS), respectively, to increase the computational accuracy, where λ (c/f) represents the operating wavelength and f denotes the operating frequency in THz.

To justify our numerical accuracy, we have also simulated a basic finding of two recent and related works [11,23] and results are compared as shown in Figs. 2(a) and (b). In Fig. 2(a), we have calculated the CL, EML, and TL with respect to the frequency (f) for the similar structure as presented in Ref. [11] and found good agreement which can be justified by comparing simulated results with the snapshot (inset). In the same way, another existing and related fiber [23] has been regenerated in terms of TL for the optimized thickness of 0.09 mm only and found excellent agreement as can be seen in Fig. 2(b).

 figure: Fig. 2.

Fig. 2. Regenerated loss analysis as a function of frequency (f) for the literature (a) Ref. [11], and (b) Ref. [23]. Three losses (CL, EML and TL) are considered for Ref. [11] and only TL is considered for Ref. [23] with optimized thickness of 0.09 mm.

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As a part of our optimization process, at first, we have optimized the structural parameters of DC and D0, respectively, by analyzing the three significant loss parameters (CL, EML, and TL) for our suggested structure, as shown in Figs. 3(a) and 3(b). It is noted that scaling of left and right y axis is different, hence, CL is plotted along the left y axis while EML and TL are plotted along right y axis in order to summarize all the loss parameters in one graph. The CL, EML, and TL are discussed initially by varying DC from 2.4 mm to 3.6 mm while D0= 0.86DC and DS/D0 = 0.7, hence, the results are summarized in Fig. 3(a): both losses are in decreasing trend with the increment of DC, causing the decrement of overall TL.

 figure: Fig. 3.

Fig. 3. Loss performance of the proposed structure with the variation of (a) core diameter, Dc where D0= 0.86DC and Ds/D0 = 0.7, (b) tubes diameter, D0 where DC = 3 mm and Ds/D0 = 0.7, and (c) slot position (Ds/D0) where DC = 3 mm and D0= 0.86DC. The diamond, circle and star type markers, respectively, are used to differentiate the three loss components. For (a) and (b), three losses (CL, EML and TL) are plotted in the same x axis scale and two (left and right) different y axis scales.

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We have finalized the value of DC at the midpoint as 3 mm which offers the CL in the order of 10−4 and well enough for terahertz guidance [23]. In the same way, CL, EML, and TL are discussed with the variation of D0 as depicted in Fig. 3(b), where DC is set at 3 mm and DS = 0.7D0. In this case, both losses are decreasing in nature when D0 is varied from 2 mm to 2.8 mm but the change of EML is flat in nature which is happening due to the wide y axis scaling used for TL (inset shows the small variation of EML). Basically, larger diameter results in the lower losses but responsible for increased critical bend radius and fiber overall diameter which is not expected because fiber should be as thin as possible [23]. However, we have selected the optimum tube diameter of D0 = 0.86DC = 2.58 mm as same way as the core diameter selection. Therefore, for the optimum core and tube diameters, the CL and EML are 4.64×10−4 dBm-1, and 0.025 dBm-1, respectively.

After optimizing core and tube diameter, we have positioned the slot in different locations and observed it’s influences on the loss parameters (CL, EML, and TL). By adjusting the value of slot position (DS/D0 changes from 0.1 to 1.0), the characteristics of CL, EML, and TL are summarized in Fig. 3(c): CL decreases as slot position (DS/D0) changes from 0.1 to 0.7, then rises again as slot position increases till 1.0, and the lowest CL is obtained at 0.55 of the slot position. Similarly, for the slot position (DS/D0) variation up to 0.3, EML decreases, and then it stays steady having the lowest EML at DS/D0 = 0.7. Based on the optimized CL and EML, the lowest TL of 0.025 dBm-1 is observed at DS/D0 = 0.7, indicating the optimal slot location. For better comprehension, field profiles with two distinct slot positions are inset in Fig. 3(c).

Actually, CL value is comparatively lower than the EML and found fluctuating in nature as expected which is due to the Fano-resonance [28] created by the node between tubes and rectangular bars. On the other hand, EML is mostly related to the background material, limited in this type of ARF structure because of the high air filling fraction, used in a fiber having light-matter interaction.

After fixing the slot location, we have investigated the losses (CL, EML, and TL) by tuning the tube thickness (t) from 0.03 mm to 0.08 mm (Fig. 4(a)). In this figure, CL decreases and fluctuates over the entire thickness variation whereas EML increases slightly with the increase of the tube thickness and the lowest TL is noticed at t = 0.05 mm. But we have chosen optimum thickness of 0.07 mm by considering overall fiber performances especially the wide low loss bandwidth and effective single mode operation (detail discussion is included in the rest of the parts).

 figure: Fig. 4.

Fig. 4. Loss performance of the proposed structure (a) CL, EML, and TL as a function of thickness t, and (b) TL as a function of frequency f for different tube thicknesses t. In this case, the core diameter Dc = 3 mm, tube diameter D0 = 0.86DC, and slot position Ds/D0 =0.7.

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The TL performance is also observed with respect to the frequency (f) from 0.8 THz to 1.6 THz for five different thicknesses (t = 0.06 mm, 0.065 mm, 0.07 mm, 0.075 mm, and 0.08 mm) as can be seen in Fig. 4(b). TL is evaluated in five different thicknesses in order to optimize the tubes thickness of our fiber structure over the frequency of interest especially around 1.0 THz. In addition, it can be seen from the Fig. 4(b) that TL increases significantly beyond this mentioned thickness range of 0.06-0.08 mm. It is also noted that Fig. 4(b) is specially provided to see how loss increases with frequency for five different tube thicknesses. The losses for different thicknesses are differentiated by using different colors and markers. It is seen that the loss increases with the increase of t and this effect is highly observed for the higher frequency region starting from around 1.1 THz (Fig. 4(b)). It is also noticed that, lower loss is reported around the lower frequency regions (0.8 to 1 THz) for the higher value of t, compared to our optimized thickness of 0.07 mm, but we have chosen t = 0.07 mm as the optimum thickness by considering the low TL over the entire frequency of interest.

Since all the structural parameters have been optimized, now the effects of including slot in each tube is summarized by considering the CL and TL as a function of frequency (f) as can be seen Fig. 5. The CL performance for our NARS-HCF structure is analyzed for with slot and without slot conditions (Fig. 5(a)). It is observed that the CL is improved significantly (nearly two orders) by adding slots. The lowest CL of 4.65×10−4 dBm-1 is found at 1.27 THz for the slotted structure while CL = 1.84×10−2 dBm-1 is achieved when the slot is not inserted in the cladding tubes. But there is no substantial difference in EML for the addition of slot. Hence, it is noticed from Fig. 5(b) that the minimum TL of 0.02542 dBm-1 and 0.04364 dBm-1 are found, respectively, for with and without slotted conditions at the frequency of 1.27 THz. Therefore, a significant improvement of TL is investigated due to the slot inserted in each cladding tubes. Figure 5(c) represents the contour plot of slotted tube geometry and slot-free tube structure and it is seen that contour lines are not spreading to the outer region of tubes because of having slot, meaning that slot has significant impact to well confine the light in the core. As a result, the optimally designed parameters of the suggested fiber deliver the lowest loss performance over the frequency of interest including the optimized frequency of 1.27 THz.

 figure: Fig. 5.

Fig. 5. The effects of including slots on the loss parameters over a band of frequency (f): (a) CL, (b) TL, and (c) the contour plot at 1.27 THz with slotted tubes (red border) and without slotted tubes (black border) in the structure. Optimized structural parameters are considered here as shown in Table 1.

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Concerning the above loss performances, we have obtained a very low TL of 0.02542 dBm-1 at f =1.27 THz, and in the next step, additional fiber performance factors like dispersion, higher order mode extinction ratio (HOMER), and bending loss are discussed with proper analysis.

Dispersion is an essential parameter for our proposed structure, which describes how an input signal spreads out as it travels down to the fiber. Therefore, dispersion (D) is calculated by following the equation as [23]

$$D = \frac{{2{\rm{\;}}}}{c}\frac{{d{n_{eff}}}}{{d\omega }} + {\rm{\;}}\frac{{{d^2}{n_{eff}}}}{{d{\omega ^2}}}$$
where angular frequency, ω = 2πf and c is the light velocity in free space.

Figure 6(a) shows the dispersion curve as the function of frequency ranging from 0.69 THz to 1.84 THz. It is highly expected to achieve near zero dispersion over a broad bandwidth and from this figure it is seen that, a flat near zero dispersion of 0.0614 ± 0.0468 ps/THz/cm is achieved over a broad frequency band of 1.02 THz (0.8 THz to 1.82 THz). This is the best near zero dispersion over a wide bandwidth up to now, to the best of our knowledge, and preferable for efficient THz guidance.

 figure: Fig. 6.

Fig. 6. (a) Dispersion, (b) HOMER, and (c) TL of FM (LP01) and HOMs (LP11 and LP21) as the function of frequency for our presented fiber where core diameter DC = 3 mm, tube diameter D0 = 0.86 DC, slot position DS = 0.7D0, and t = 0.07 mm. Field profiles for FM and HOMs are located at right panel where line color matched with the box color.

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Another performance indicator for a fiber structure is HOMER which refers to the ratio of the lowest loss of higher-order modes (LP11 in our case) to the fundamental mode (LP01) loss [9,1214]. However, the HOMER is calculated with respect to frequency and summarized in Fig. 6(b): it varies from 6 to 21 over a given frequency range and maximum value of 36 is obtained at 1.1 THz. For better understanding, TL of FM and HOMs are included over the frequency of interest as shown in Fig. 6(c) where corresponding field profiles are given in right side panel having box color similar as line color. It is well known that a fiber having HOMER value of around 10 or above can be consider as a single mode fiber [22], therefore, our designed fiber is well enough for performing as a single-mode fiber due to having maximum HOMER value of 36, and around the frequency range of interest, the HOMER value is nearly 10. It is also noted that higher HOMER can lead the fiber to operate as more ESMF but it is hard to achieve in THz region (literatures and comparison Table 2). Importantly in our case, HOMER is calculated based on the total loss (TL) compared to the few literatures considered CL only [21].

Tables Icon

Table 2. Performance study of recent and related HC-ARFs in THz regime

It is obvious that fiber could be bent in real-life applications, hence, it is essential to calculate the bending loss of our presented fiber. This loss is actually happened due to the light leaking from the core to the cladding region under the bending of a fiber. In our case, it is calculated by considering the modified refractive index of the background fiber materials along x-direction as [9,22,29]

$${n_{tm}} = n\left( {1 + \frac{x}{{{R_b}}}} \right)$$
where, ntm is the modified refractive index due to the bend of fiber, n is the original refractive index of TOPAS and air, Rb denotes the bending radius in cm along the x-direction. In Fig. 7, a decreasing tendency of bending loss is observed with the change of bend radius from 5 cm to 120 cm. From 5 to 25 cm, the bending loss is relatively higher (63 dBm-1 to 6 dBm-1) which is expected and after that, the value is decreasing in trend. The lowest bending loss of 0.053 dBm-1 and 0.0173 dBm-1 are noticed at 45 cm and 70 cm, respectively. Bending loss is increasing after the bend radius of 85 cm which is not expected and happening due to the creation of anti-crossing effect for geometrical deformation (coupling between air core and slotted tubes) [9,22,29]. For better understanding, the three field profiles responsible for three bend radius (25 cm, 40 cm, and 70 cm) are included inside the plot and it is clearly seen that higher loss is happening due to the decrease of bend radius and vice-versa.

 figure: Fig. 7.

Fig. 7. Bending loss measurement with respect to the bending radius where the fiber core diameter Dc = 3 mm, tube diameter D0= 0.86 DC, slot position Ds =0.7D0, and thickness t = 0.07 mm at 1.27 THz frequency.

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We have changed the number of cladding tubes in our proposed structure and observed the overall transmission loss as a function of frequency (f) as shown in Fig. 8. In this case, the proposed structure is modified from five tubes structure to the usually available six tubes structure and nearly similar loss is observed over higher frequency ranges from 1.1 THz to 1.7 THz but higher loss is observed around the lower frequency region (0.8 to 1.05 THz). On the other hand, in our five tubes structure, loss is minimum over the whole frequency range of interest. Within the frequency range, we have obtained a minimum loss of 0.0254 dBm-1 at 1.27 THz frequency and a maximum loss of 0.0812 dBm-1 at 0.8 THz for the five-tubes arrangement. Furthermore, the least loss in a six-tubes construction is 0.0258 dBm-1 at f = 1.3 THz, whereas the highest loss is 0.18996 dBm-1 at the frequency of 0.8 THz. Therefore, in order to achieve low loss performance over broad bandwidth, five tubes structure shows better performances than six tubes structure in our case.

 figure: Fig. 8.

Fig. 8. The comparative TL performance for five and six tubes structures as a function of f (frequency) where core diameter Dc = 3 mm, tube diameter D0 = 0.86Dc, slot position Ds =0.7D0, and thickness t = 0.07 mm.

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In Table 2, the summary of the constructional simplicity and performance parameters of recent related fibers are tabulated. Here, we have focused on structural geometry, CL, EML, TL performance, low loss transmission bandwidth, and wideband near zero flat dispersion. A complex HC-ARF structure is presented by Yan et al. [24] by using eight uneven tubes, including two nested tubes cladding that delivers TL of 1.68 dBm-1 at 2.34 THz, hence, the propagation loss is quite higher than our proposed result. In addition, literature [23] represents six nested circular tubes cladding in a HC-ARF having 0.05 dBm-1 effective material loss at 1 THz, TL of 0.095 dBm-1, with bandwidth of 0.4 THz, dispersion of 0.0983 ± 0.01767 ps/THz/cm over 0.6 THz flat band and our structure is delivering better results in all related aspects. Besides, third one [30] in the comparison table speaks for a pentagram HC-ARF with 0.025 cm-1 (i.e., 10.85 dBm-1) TL at 1.94 THz and in the next year [32] they resubmitted a double pentagram HC structure with a modified lower TL of 0.012 cm-1 (or 5.2 dBm-1) at 0.992 THz. Their TL is comparatively higher and low loss bandwidth is comparatively lower than ours and other parameters like HOMER and dispersion are not discussed. Furthermore, Sultana et al. [31] discussed five circular tubes cladding HC-ARF and mentioned the TL of 0.10 dBm-1 at 0.43 THz which is larger than our TL findings (0.025 dBm-1). In addition, their low loss bandwidth is comparatively narrow and didn’t discuss the dispersion properties.

Another tough geometry, having nine circular tubes with nine elliptical nested tubes, is demonstrated [25] with the EML, CL and dispersion of < 0.019 cm-1 (i.e., < 8.25 dBm-1), < 0.29 cm-1 (i.e., < 125.95 dBm-1), ± 0.029 ps/THz/cm, respectively, without mentioning the dispersion bandwidth and single mode operation. Besides, a complex structure having HC-six non-circular tubes were represented at 1.89 THz with > 0.4 dBm-1 TL which is comparatively greater than our findings [33] and they didn’t discuss one of the dominant loss namely EML. Additionally, a more complex structure is proposed by conjoining six circular and elliptical tubes in the cladding [21] and showed relatively higher TL of 0.034 dBm-1 at 1.0 THz, narrower low loss transmission bandwidth of 0.5 THz (0.78–1.28 THz), and flat near-zero dispersion of 0.1068 ± 0.076 ps/THz/cm with shorter bandwidth of around 0.7 THz. Recently in 2021, another complicated design is proposed having eight non uniform circular tubes and two semi elliptical nested tubes in the cladding of the fiber [26] and achieved ±0.188 ps/THz/cm flat dispersion over 0.475 THz bandwidth, the lowest CL of 0.231 dBm-1 at 2.575 THz with only CL bandwidth of 0.825 THz without discussing TL and EML.

According to the above assessments, the suggested fiber shows the lowest TL of 0.025 dBm-1 at 1.27 THz with wider low loss bandwidth of 0.88 THz by keeping the value of less than 0.0811 dBm-1, and the lowest EML of 0.0248 dBm-1. Additionally, the fiber reveals near zero flat dispersion as 0.0614 ± 0.0468 ps/THz/cm over the 1.02 THz which is the widest bandwidth till now. Moreover, our structure exhibits better single mode performance with low bending loss compared to the literature available in Table 2.

4. Fabrication feasibility

Fabrication feasibility is a critical and important aspect of real-world application, and 3D printing, extrusion, stack and draw methods are commonly used for both millimeter and micrometer ranging fiber fabrication. The stack and draw method have been used to manufacture the structure with HC single tube cladding [34], nested tube cladding [35], non-circular shaped cladding and so on. However, in recent years, 3D printing has become the most preferred method for fabricating numerous complicated, multilayered structures at a low cost [36]. This fabrication technique can minimize terahertz waveguides losses; moreover, most complex geometries are now becoming simpler. In addition, it offers design flexibility through 3D CAD modeling, tiny metallic waste and the ability to employ fabrications through different types of commercial printers [36].

Since 2011, HC photonic crystal fiber (PCF) [37], HC-PBG fiber [38], and HC-ARF [39] were manufactured by the 3D printing method. Although ice cone structure is highly challenging to fabricate, a THz guidance with NC-HC-AR ice cone shape fiber is fabricated by fused decomposition modeling (FDM) of 3D printing method in 2015 [40]. Besides that, Yang et al. [38] designed and fabricated a complex THz dominating HC kagome PCF by 3D printing process. Additionally, in Ref. [36], authors described THz sensing on various complex structures (porous polymer, HC-PCF, HC-ARF and various HC bragg fibers) which were successfully fabricated in 3D printing process. FDM 3D printer is used to manufacture a TOPAS based THz guidance suspended-core microstructured polymer optical fiber (SC-MPOF) in 2020 with overall fiber diameter of 1600 µm [41]. In the same year, another two comparatively complex structures such as HC half circular and half elliptical asymmetrical conjoined tube anti resonant (HC-ACTAR) fiber [21] and a porous core PCF with hexagonal and trapezium type asymmetric air hole’s structure [42] are reported by two different research groups and they claimed that their structures can be fabricated successfully by 3D printing technique. Furthermore, in 2021, Talataisong and his colleagues [43] proposed a relatively complex THz transparent hollow core anti resonant polymer optical fiber (HC-ARPF), which is fabricated by a single stepped FDM 3D printer. With the fabrication by a photosensitive resin 3D printer, another difficult semi-elliptical eight tubes cladding structure is proposed in 2021 [20]. Lastly, it is claimed now-a-days that 3D printing with extrusion is capable of fabricating any type of complex structure (circular, elliptical, square, rectangular) having symmetry or asymmetry in the cladding arrangement [4244], hence, straight bar in the current circular tubes structure should be alright to realize.

Therefore, our proposed structure is comparatively simpler, has only five circular tubes with rectangular slotted cladding, and dimensions are in the similar range of the above compared structures, hence, we recommend 3D printing for fabricating our proposed fiber construction.

5. Conclusion

In summary, we proposed a simpler NARS-HCF construction and analyzed the performance parameters such as EML, CL, TL, low loss bandwidth, near zero dispersion with flat bandwidth, bending loss, and single mode characteristics. The numerical calculations show the lowest EML of 0.0248 dBm-1 and the lowest CL of 4.65 ×10−4 dBm-1 lead the lowest transmission loss of 0.0254 dBm-1 at 1.27 THz frequency. In addition, low transmission loss bandwidth of 0.88 THz (0.80 -1.68 THz) maintains the loss lower than 0.08 dBm-1. Furthermore, we have obtained best results in terms of flat dispersion of 0.0614 ± 0.0468 ps/THz/cm across a wide frequency band (0.80 THz to 1.82 THz). Moreover, we reached maximum HOMER of around 36 at 1.1 THz frequency and the value can sustain over 10 covering the frequency of interest. A considerable low bending loss of 0.0173 dBm-1 at 70 cm bend radius is also noticed, therefore, our suggested structure may be employed for low cost, low loss efficient THz transmission system. In addition to low loss, flat near zero dispersion is preferable for efficient THz transmission which could be further applied to the area of THz sensing, detection as well as THz communication.

Funding

Dept. of EEE and research and extension of RUET, Bangladesh ((DRE/7/RUET/528(39)/PRO/2021-22/17)).

Acknowledgments

This work has been supported by the Dept. of EEE and research and extension (DRE/7/RUET/528(39)/PRO/2021-22/17) of RUET, 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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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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Figures (8)

Fig. 1.
Fig. 1. Proposed cross-sectional view of the fiber with hollow core diameter of Dc = 3 mm, anti-resonant tubes diameter of D0 = 0.86 Dc, rectangular slots position from the core side of Ds= 0.7 D0 and thickness of t = 0.07 mm. Black and aqua regions stand for TOPAS and air, respectively.
Fig. 2.
Fig. 2. Regenerated loss analysis as a function of frequency (f) for the literature (a) Ref. [11], and (b) Ref. [23]. Three losses (CL, EML and TL) are considered for Ref. [11] and only TL is considered for Ref. [23] with optimized thickness of 0.09 mm.
Fig. 3.
Fig. 3. Loss performance of the proposed structure with the variation of (a) core diameter, Dc where D0= 0.86DC and Ds/D0 = 0.7, (b) tubes diameter, D0 where DC = 3 mm and Ds/D0 = 0.7, and (c) slot position (Ds/D0) where DC = 3 mm and D0= 0.86DC. The diamond, circle and star type markers, respectively, are used to differentiate the three loss components. For (a) and (b), three losses (CL, EML and TL) are plotted in the same x axis scale and two (left and right) different y axis scales.
Fig. 4.
Fig. 4. Loss performance of the proposed structure (a) CL, EML, and TL as a function of thickness t, and (b) TL as a function of frequency f for different tube thicknesses t. In this case, the core diameter Dc = 3 mm, tube diameter D0 = 0.86DC, and slot position Ds/D0 =0.7.
Fig. 5.
Fig. 5. The effects of including slots on the loss parameters over a band of frequency (f): (a) CL, (b) TL, and (c) the contour plot at 1.27 THz with slotted tubes (red border) and without slotted tubes (black border) in the structure. Optimized structural parameters are considered here as shown in Table 1.
Fig. 6.
Fig. 6. (a) Dispersion, (b) HOMER, and (c) TL of FM (LP01) and HOMs (LP11 and LP21) as the function of frequency for our presented fiber where core diameter DC = 3 mm, tube diameter D0 = 0.86 DC, slot position DS = 0.7D0, and t = 0.07 mm. Field profiles for FM and HOMs are located at right panel where line color matched with the box color.
Fig. 7.
Fig. 7. Bending loss measurement with respect to the bending radius where the fiber core diameter Dc = 3 mm, tube diameter D0= 0.86 DC, slot position Ds =0.7D0, and thickness t = 0.07 mm at 1.27 THz frequency.
Fig. 8.
Fig. 8. The comparative TL performance for five and six tubes structures as a function of f (frequency) where core diameter Dc = 3 mm, tube diameter D0 = 0.86Dc, slot position Ds =0.7D0, and thickness t = 0.07 mm.

Tables (2)

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Table 1. Optimized structural parameters

Tables Icon

Table 2. Performance study of recent and related HC-ARFs in THz regime

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

C L = 8.686 × 2 π × ( c f ) × I m ( n e f f ) d B m 1
E M L = ε 0 μ 0 A m a t n α m a t | E | 2 d A 2 A l l S Z d A d B m 1
T L = C L + E M L d B m 1
D = 2 c d n e f f d ω + d 2 n e f f d ω 2
n t m = n ( 1 + x R b )
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