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Abstract
We report a novel hollow-core asymmetric conjoined-tube anti-resonant (HC-ACTAR) fiber for efficient and low-loss THz wave guidance. The cladding tubes of the proposed HC-ACTAR fiber is formed by conjoining a half circle and a half elliptical tube and is placed in the radial direction. We observe that the proposed fiber is superior in terms of achieving low-loss and low dispersion in a wide range of frequencies than the previously reported designs. We show that our proposed HC-ACTAR fiber ensures lowest loss of 0.034 dB/m at 1 THz and marinates a low-loss window of 0.5 THz. Moreover, the proposed fiber has promising optical properties in the THz regime such as low bending loss, broadband flattened dispersion, and effective single-mode guidance, which are essential for efficient THz wave guidance.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The terahertz (THz) radiation is one of the significant parts of the electromagnetic spectrum, which is located between millimeter wave and infrared frequencies and is roughly defined to lie between $0.1$-$10$ THz or 3 mm to 30 $\mu$m in wavelengths [1]. Over the last few decades, THz spectrum have attracted a great deal of attentions in the scientific community and is actively being researched for biomedical imaging to security applications [1]. So far, remarkable progress has been attained in designing effective THz detectors and sources. Despite long-standing efforts in design and fabrication of THz waveguides, it is still an ongoing challenge for the researchers to design compact, efficient and low-loss THz waveguides. To date, a range of THz waveguides with different configurations have been demonstrated for efficient transmission of THz waves [2–4]. One of the simplest form of THz waveguides is the metallic wired configuration, but such waveguides are heavily affected by the radiation losses. Unlike the metallic waveguides, parallel plate waveguides have almost no pulse broadening, i.e., zero dispersion and have low attenuation losses [5]. However, the main loss mechanism of such waveguides are the ohmic losses arsing from the finite conductivity of the plates and divergence losses, which is due to the beam spreading in the unguided directions [5].
To overcome those problems, a different class of fibers, including Bragg fiber, plastic fiber, and solid core photonic crystal fibers (PCFs) have been proposed by the researchers [6]. However, such fibers are severely affected by the material absorption loss, which is known as effective material loss (EML) [3]. Over the years, researchers have been used porous-core PCF, an alternative solution to guide the THz wave with acceptable loss limit. In contrast of solid-core PCF, the core of the porous core fiber is filled with the micro-structured air-holes, which reduces the area of the solid material, and hence the effective material loss [3,7]. Another promising approach to reduce the transmission loss is to use hollow-core PCF, in which light is trapped inside the air-core, an entirely unconventional light guiding mechanism [8]. Depending on the light guiding mechanism, hollow-core PCF can be classified into two types: photonic band gap (PBG) fiber and inhibited-coupling hollow-core fiber or hollow-core anti-resonant (HC-AR) fiber [8]. In PBG fiber, light propagates through the air-core by the photonic band gap effect, whereas in HC-AR fiber, light is trapped inside to core of the fiber by the inhibited-coupling between the core and the cladding modes and anti-resonant effect [8,9].
Recently, HC-AR fibers have drawn enormous attentions because of their unique and excellent transmission properties, such as very low transmission loss, low bending loss, low dispersion and larger bandwidth [8–12]. In 2018, a HC-AR fiber was proposed with loss of 0.095 dB/m in the THz regime in between 0.8-1.2 THz [13]. In the same year, S. Yan et al. proposed a HC-AR fiber, where the cladding elements are touching each other [2], leading to a higher attenuation loss even without considering EML. To reduce the transmission loss, node-free HC-AR fiber designs have been proposed [14,15]. Later on, H. Xiao et al. proposed a HC-AR fiber with four half-elliptical cladding elements [16], which is difficult to fabricate as well as the fiber loss is also high as 10 dB/m in the operating window. More recently, HC-AR THz fiber with metamaterial cladding has been demonstrated to reduce losses [4]. However, the inclusion of metal into the cladding requires additional step in the fabrication process, thus increasing fabrication complexity. HC-AR fiber with asymmetric cladding structure has also been demonstrated for polarization filter realization in [17].
In this paper, we propose a novel HC-AR fiber referred to as hollow-core asymmetric conjoined-tube anti-resonant (HC-ACTAR) fiber to obtain a wider low-loss band centered at 1 THz. The fiber consists of six conjoined anti-resonant (AR) tubes with a negative-curvature core. Each cladding tube is designed by connecting a half circle and a half elliptical tube. Therefore, the multiple interfaces of the cladding elements provide efficient confinement of THz wave. The modal properties of the fiber such as confinement loss, EML loss, dispersion, and bending loss are investigated by the finite element method. We further explore the impact of core and cladding diameter on the loss characteristics. Moreover, we observe that the proposed HC-ACTAR fiber offers a wide low-loss band than both elliptical tube nested and conjoined tube (two D-shaped) structure of the same core and cladding size [18,19].
2. Design and fabrication possibility of the proposed HC-ACTAR fiber
HC-AR fiber having hybrid cladding tubes [20], anisotropic anti-resonant tubes [14], and conjoined-tubes [19] are superior to obtain ultra low loss and better single mode characteristics over simple tube lattice fiber. In the present study, we propose a HC-ACTAR fiber which is illustrated in Fig. 1. It contains of six conjoined anti-resonant tubes having the same tube thickness, and is symbolized by $g$. Each cladding tube is created by conjoining two (half circle and half elliptical) cladding elements. We designed the fiber cladding structure in such way that the THz wave can not leak out by the five successive layers (marked in green) i.e. negative–curvature polymer layer having thickness of $g$, the half circle air hole with radius $r$ , the straight bar with the thickness of $g$, the half elliptical air hole with major and minor axis of $r_e$ and $r$, respectively, and positive-curvature polymer layer having thickness of $g$. The diameter of the core ($R$) is kept of 3 mm. In the THz regime, a range of polymer materials, e.g., Teflon, PMMA, Topas and Zeonex are commonly used as bulk material to design THz waveguides [6]. In our study, we use Zeonex as the host material as it offers low material absorption loss in the THz spectrum [21]. In our simulations, the refractive index (RI) of Zeonex is considered to be 1.53 and kept constant over the frequency band considered [21].
Fig. 1. Geometrical structure of the proposed HC-ACTAR fiber having core diameter $R$ = 3 mm., cladding tube length $D$ = 3 mm ( half circle radius $r$ = 1 mm, half elliptical major and minor axis are $r_e$ = 2 mm and $r$ = 1 mm, respectively), and tube thickness g = 0.09 mm.
To date, the most frequent used techniques to fabricate negative curvature hollow core fiber are 3D printing [22–24], extrusion [25] and stack and draw [26–28]. The 3D printing and extrusion fabrication technology are potentially able to fabricate any types of asymmetrical structure. However, researchers in [19] fabricated and experimentally realized a conjoined-tube negative curvature hollow core fiber using stack and draw method. Thus, the proposed HC-ACTAR is feasible to fabricate by employing the existing PCF fabrication technologies.
3. Results and discussion
In HC-AR fiber, the phase matching between the core and cladding modes occurs at a specific frequency, known as resonant frequency, where maximum transmission loss occurs. In contrast, at anti-resonant frequencies, light is strongly confined in the core, leading to a low transmission loss. The resonant frequencies of the HC-AR fiber can be calculated as [13]
where $m$ is an integer, $c$, $n_{zeonex}$, and $n_{air}$ indicate velocity of light in vacuum, RI of Zeonex and RI of air, respectively.3.1 Propagation loss
A finite-element method based COMSOL software (version 5.4) has been used for our numerical simulations. A perfectly matched layer was used outside the fiber domain to calculate the loss of the fiber. We optimized the mesh size of the fiber domain and PML parameters according to [9]. We first calculate the resonance frequencies for different tube thickness and is computed using Eq. (1). For tube thickness of $g$ = 0.08, 0.09, 0.10 and 0.11 mm, we found resonance frequencies of 1.62, 1.44, 1.30, and 1.18 THz, respectively. We then calculate the leakage loss or confinement loss (CL), which can be expressed as [2]
where $Im(n_{eff})$ is the imaginary effective refractive index, $k_0$ is the free space wave vector, $k_0~=~2\pi /\lambda$. The CL profile obtained from simulation is shown in Fig. 2(a). It can be seen from Fig. 2(a) that for tube thickness of 0.09, 0.10 and 0.11 mm, the resonance frequencies can be found nearly at 1.44, 1.30 and 1.18 THz (marked in vertical dotted lines), respectively, and the results are in good agreement with the analytical results.Fig. 2. (a) Confinement loss, CL, (b) Effective material loss, EML, and (c) Total loss of the proposed HC-ACTAR fiber with different tube thickness. The doted lines indicate the resonance frequency for corresponding tube thickness.
As mentioned, in THz fibers another significant propagation loss arises from the material absorption (EML loss), which can be expressed as [3]
We now calculate the total loss, which can be calculated by combining CL and EML, and is plotted as a function of frequency with different tube thickness, which is shown in Fig. 2(c). We show that for tube thickness of 0.11 mm, the maximum loss occurs around 1 THz, then the resonance frequency is shifted to the longer frequency with the increasing of tube thickness. In contrast, the anti-resonant (low-loss) frequency is found around 1 THz for relatively lower tube thickness i.e. 0.08 mm, and 0.09 mm. At 1 THz, the minimum total loss of 0.029 dB/m is achieved for $g$ = 0.08 mm. However, the tube thickness is selected to 0.09 mm because it ensures a low-loss bandwidth of 0.5 THz (from 0.78 to 1.28 THz) centered at 1 THz with losses lower than 0.1 dB/m.
3.2 Dispersion
Dispersion is one of the important parameters that affects the THz wave communication through pulse broadening. Low and flat dispersion profile is thus always desirable that makes the fiber suitable for long distance communication. Since the RI of the Zeonex is constant, the contribution of the material dispersion on the chromatic dispersion can be neglected. So, the total dispersion of the proposed HC-ACTAR fiber will be only the group velocity dispersion ($\beta _2$), and can be expressed as [13]
where $n_{eff}$ and $c$ is the effective refractive index and light speed, respectively, and $\omega$ is the angular frequency. The dispersion profile as a function of frequency is shown in Fig. 3. From figure, it can be seen that the proposed HC-ACTAR fiber offers very low and flat $\beta _2$ of 0.1068$\pm$0.0760 ps/THz/cm in between 0.70-1.40 THz.3.3 Bending loss
The bending loss of a fiber is another significant parameters, which needs to be considered. Using conformal transformation method, an equivalent refractive index is used to replace the straight fiber with a bend one, and can be expressed as [16]
where $n(x,y)$ and $n^{'}$ are the RI of straight fiber and after bending, respectively, $s$ is the direction of bending ($x$ or $y$) and $R$ is the bending radius. Figure 4(a) shows the bending loss in the $x$ direction with bending radius from 5 to 70 cm. As expected, bending loss is decreasing with increasing bending radius, a loss peak is observed at $R$ = 52 cm (critical bending radius), similar phenomena of loss profile has already been observed in [29]. However, the bending loss is less than 1 dB/m for the $R$ more than 25 cm.Fig. 4. (a) Bending loss as a function of bending radius. The inset shows field distribution for bending radius 15 cm, 30 cm, 45 cm and 60 cm, and corresponding losses are indicated by black, red, green and yellow dots, respectively, (b) HOMER as a function of frequency for $TM_{01}$, $TE_{01}$, and $HE_{21}$ modes. Field distributions are shown in the inset by same frame colour.
3.4 Higher order mode extinction ratio (HOMER)
A fiber is suitable or not for single mode propagation can be decided by the higher order mode extinction ratio (HOMER), which is defined as the ratio between the loss of higher order modes having the lowest transmission loss and the transmission loss of the fundamental mode [9]. The HOMER of the proposed HC-ACTAR fiber in the low-loss frequency range is calculated for $TM_{01}$, $TE_{01}$, and $HE_{21}$ with respect to the transmission loss of the fundamental mode. Figure 4(b) shows that the maximum value of HOMER for $TM_{01}$, $TE_{01}$, and $HE_{21}$ are 46, 76 and 96 which are found at 1.14, 1.00 and 102 THz, respectively. Hence, the proposed HC-ACTAR fiber can be used for efficient single mode propagation.
3.5 Effect of geometrical parameter on total loss
The effect of $R$ and $D$ of the proposed HC-ACTAR fiber on the losses is investigated. Figure 5(a) and (b) show lower loss can be obtain with larger $R$ and $D$. However, larger core and fiber diameter hampers the fiber flexibility. Hence, the $R$ and $D$ both are selected as 3 mm where the total loss is ${3.4\times 10^{-2}}$ dB/m at 1 THz. Total loss variation with the ratio $r$ and $r_e$ is also investigated. When the value of $r$/$r_e$ is 1, two adjacent conjoined structures touch each other. Hence, to obtain the node-less structure the value of $r$/$r_e$ must be less than 1 and from Fig. 5(c), it is seen that lowest loss is obtained for $r$/$r_e$ = 0.5.
4. Performance comparison with existing HC-AR fiber
To date, a variety of HC-AR fiber with circular tube [14] elliptical tube [14], circular tube nested [30], elliptical tube nested [18], and conjoined tube [19] have been demonstrated. Existing numerical demonstrations reveal that HC-AR fiber with elliptical element offers better low-loss characteristics than the circular element HC-AR fiber [14,18]. A comparison of loss characteristics of the proposed HC-ACTAR fiber with elliptical tube nested, and conjoined tube HC-AR fiber is carried out, which is shown in Fig. 6. According to the figure, although 0.1 dB/m low-loss bandwidth of conjoined tube fiber (0.84 to 1.24 THz) and elliptical tube fiber (0.94 and 1.32 THz) is nearly equal, the elliptical tube fiber shows ${1.9\times 10^{-2}}$ dB/m lower loss than the conjoined tube fiber at 1 THz. However, the proposed HC-ACTAR fiber offers comparatively wider low-loss bandwidth of 0.5 THz (0.78 to 1.28 THz) and total loss as low as 0.034 dB/m at 1 THz.
Fig. 6. Loss comparison of the proposed fiber with two existing structure having same core and cladding diameter. Field distributions are shown in the inset by same frame colour.
5. Conclusion
We proposed a promising HC-ACTAR fiber for THz wave transmission that offers lowest loss of ${3.4\times 10^{-2}}$ dB/m at 1 THz, low-loss bandwidth of 0.5 THz that ranging from 0.78 THz to 1.25 THz with losses lower than 0.1 dB/m, very low and flat dispersion in the wider spectral range, and effective single mode characteristics. Such outstanding performance indicates that the proposed HC-ACTAR fiber has immense potential to achieve the goal of ultra low-loss transmission of THz waves.
Disclosures
The authors declare no conflicts of interest.
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