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Abstract
A novel highly birefringent and low transmission loss hollow-core anti-resonant (HC-AR) fiber with a central strut is proposed for terahertz waveguiding. To the best of our knowledge, it is the first time that a design of a highly birefringent terahertz fiber based on the hybrid guidance mechanism of the anti-resonant mechanism and the total internal reflection mechanism is provided. Several HC-AR fibers with both ultra-low transmission loss and ultra-low birefringence have been achieved in the near-infrared optical communication band. We propose a HC-AR fiber design in terahertz band by introducing a microstructure in the fiber core which leads to tremendous improvement in birefringence. Calculated results indicate that the proposed HC-AR fiber achieves a birefringence higher than 10−2 in a wide wavelength range. In addition, low relative absorption loss of 0.8% (8.6%) and negligible confinement loss of 1.69×10−4 dB/cm (9.14×10−3 dB/cm) for x-polarization (y-polarization) mode at 1THz are obtained. Furthermore, the main parameters of the fiber structure are evaluated and discussed, proving that the HC-AR fiber possesses great design and fabrication tolerance. Further investigation of the proposed HC-AR fiber also suggests a good balance between birefringence and transmission loss which can be achieved by changing strut thickness to cater numerous applications ideally.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In the last decades, terahertz band ranging from 0.1 to 10 THz has attracted considerable attention due to its extensive applications in various fields including sensing [1,2], imaging [3,4], biotechnology [5–7], spectroscopy [8,9], security [10] and communications [11–13]. Up to now, appreciable improvements have been achieved in generation [14–16] and detection [17,18] of terahertz wave. However, flexible and commercially available high-performance low-loss terahertz waveguides are still absent. Under such circumstances, most commercial THz systems still employ free space as medium for terahertz wave propagation owing to the non-absorbable property of dry air [19]. But when the air is mixed with dust and vapor, unavoidable and uncertain loss will be caused in signal coupling and transporting process. Aiming at these issues, various terahertz waveguides have been reported, which can be generally divided into two categories by material, namely metallic waveguides and dielectric waveguides [20]. However, metallic waveguides tend to have high intrinsic Ohmic loss [21], which results in unavoidable dissipated heat and increasing transmission loss. By contrast, dielectric waveguides including photonic crystal fibers (PCFs) [22–24] and hollow-core anti-resonant (HC-AR) [25,26] fibers have received ever-increasing attention in recent years, due to the evident superiority in transmission loss.
For terahertz fibers applied in THz communications, filtering and sensing, birefringence is another noteworthy property. Introducing asymmetrical structures to fiber cores or fiber cladding to obtain birefringence is a recognized way for PCFs. However, PCFs designed to achieve high birefringence tend to suffer from high material loss at the same time. Authors in Ref [27,28]. obtained ultra-high birefringence up to the order of 10−1 through a suspended elliptical core with slotted air hole structures. However, high effective material loss restricted the practical applications of the proposed fibers. Moreover, numerous efforts have been devoted in reducing the absorption loss while keeping high birefringence [29–32]. Nevertheless, the effective material loss is still not significantly reduced.
HC-AR fibers have attracted great interest due to their ultra-low transmission loss [33]. As early as in 2015, a silica fiber with adjacent nested anti-resonant tubes was proposed in Ref [34]., where the transmission loss achieved the order of 10−3 dB/m in the wavelength ranging from 2.7µm to 3.6µm. The property of low transmission loss is benefited from the core modes not coupling with cladding modes and the light restricted in the central air area, where the absorption loss is much lower than in dielectrics. In 2018, Hasanuzzaman et al. reported a hollow-core fiber with nested anti-resonant tubes realizing the effective material loss of 0.05 dB/m at 1THz [35], which proved the low loss HC-AR fiber working well in terahertz band with the same theory. However, it is difficult for HC-AR fibers to achieve high birefringence like PCFs. Significant progress has been made to enhance the birefringence of HC-AR fibers through the introduction of asymmetric cladding [36–38]. However, the enhanced birefringence still fails to break through 10−3. It is worth noting that on the other hand HC-AR fibers are indeed promising to act as a platform to support nonlinear optics [39]. For example, by focusing on the point of high laser damage threshold of HC-AR fibers, researchers in Ref [40]. have made great developments in a novel gas-filled HC-AR fiber laser with supercontinuum in ultraviolet.
In this paper, we present modeling and simulation results of a novel eight-ring HC-AR terahertz fiber with a center slender strut in the fiber core connected with the two polymer tubes along y-direction. Different from other existing works, we innovate with a simple microstructure in the fiber core instead of that in the fiber cladding to obtain superior characteristics including the ultrahigh birefringence and low transmission loss. The well-designed structure introduces prominent structural asymmetry, which results in considerable birefringence. In the meantime, the transmission loss of this HC-AR fiber, including relative absorption loss and confinement loss, still exhibits relatively low level in contrast to that of other PCFs or HC-AR fibers owing comparable high birefringence. Thus, our proposal demonstrates a flexible balance between transmission loss and birefringence of the HC-AR fiber, making it of vital and various applicability. In addition, the high birefringence and low transmission loss characteristics of this design are insensitive to structure parameter variations, indicating appreciable manufacturing compatibility.
2. Geometry of fiber structure
Figure 1 shows the cross-section of the proposed HC-AR fiber with the enlarged view of the central strut. Compared with normal eight-capillary cladding-based HC-AR fibers, the reported fiber benefits from the strut structure to introduce strong structural asymmetry which ensures great potential to achieve high birefringence. The thickness of the central strut is represented by h. The eight polymer capillaries have the same radius Rn and thickness g. The radius of the inner core is denoted by Rs. To explore the properties of the proposed HC-AR fiber, the finite element method has been used to perform the simulations. A perfectly matched layer (PML) is also applied outside the fiber cladding to calculate the confinement loss. Optical thick perfect match layer is set in the model boundary of which the thickness is 800µm. To guarantee the accuracy of the simulation results, we set the biggest mesh smaller than 30µm in the fiber cladding area and 6µm in the central strut area. Thus, the total mesh elements of the model reach 147080 and the rate of the effective refractive index change in more dense mesh set is negligible 0%.
Fig. 1. Schematic diagram of the hollow-core anti-resonant fiber cross section. The inset is the enlarged view of the introduced strut.
Resonant frequencies of HC-AR fibers, leading to the coupling between core modes and cladding modes, can be expressed as [41]:
where m is any positive integer, c is the velocity of light in vacuum, g is the tube thickness, nmat and nair are the refractive index of fiber material and air, respectively. In the process of numerical simulation, we set g with fixed value of 70µm of which the corresponding resonant frequency is 1.92THz as m = 1. To balance the high birefringence and low transmission loss, h is selected as 15µm. To confine the mode field distribution in the fiber core region, the radius of cladding tubes Rn is set as 700µm and the radius of fiber core Rs is set as 2460µm.Cyclic olefin copolymer, named TOPAS in commerce is adopted as the fiber material in our design. TOPAS shows highly constant refractive index of 1.5258 over 0.1THz to 2THz. Moreover, it has plenty of advantages including low bulk material absorption loss and low water absorption [42], making it preferred in fiber design and fabrication.
3. Simulation results and discussion
Figure 2 shows the power flow distributions of the orthogonal fundamental modes with different h at 1THz. Both x-polarization and y-polarization modes are well confined in the fiber core, especially localized around the designed strut structure. In addition, the mode field distribution is effectively restricted in a smaller scale on the x-axis when the struct thickness is getting larger.
Fig. 2. Power flow distributions of (a-c) x-polarization modes and (d-f) y-polarization modes at 1THz when (a, d) h = 10µm, (b, e) h = 15µm and (c, f) h = 20µm, respectively. The red arrows indicate the corresponding polarization directions.
As depicted in Fig. 3(a), the pure HC-AR fiber can restrict the light in the hollow core part because of the anti-resonant reflection mechanism which can ensure a low transmission loss but together with ultra-low birefringence characteristic. Instead, the central strut will break the symmetry. Obviously, from Fig. 3(b), we can realize that the strut not only creates the asymmetry, but also acts as a waveguide. It can be observed more precisely in Fig. 3(d), the normalized electric field intensity of the proposed fiber is significantly sharpened in the fiber core. Thus, it can be alleged that the fundamental modes of proposed fiber are based on the hybrid guidance mechanism of the anti-resonant mechanism and the total internal reflection mechanism. For this reason, as show in Fig. 3(c), the electric field is more tightly restricted around the central struct.
Fig. 3. Normalized modulus of electric field intensity at different positions of the horizontal diameter of (a) the proposed fiber but removed the strut, (b) the proposed fiber but removed the tubes cladding and (c) the proposed fiber.
The calculated effective refractive index for the x- and y-polarization modes as a function of frequency is shown in Fig. 4(a). According to the calculated results, it is obvious that y-polarization mode owns a higher effective refractive index than x-polarization mode because of the more concentrated electric field along the strut and less leakage into the air area of the hollow-core. Furthermore, for both x- and y- polarization modes, the effective refractive index presents the same trend as the frequency changes, because the higher frequency light interacts with the fiber material stronger. The increase for the polarization parallel with the strut length direction is more prominent. That is to say, the effective refractive index of the y-polarization mode occupies a sharper rise compared to that of the x-polarization mode when enlarging the frequency.
Fig. 4. (a)Effective refractive index and (b)birefringence versus frequency between 0.7THz and 2.05THz with the optimum parameters.
Birefringence caused by the deviation of the effective refractive index between x- and y- polarization modes can be defined as:
where B stands for birefringence, nx and ny are the effective refractive index of x- and y-polarization respectively. It can be found in Fig. 4(b) that there exists a concise positive correlation between birefringence and light frequency. This phenomenon comes from the asymmetric slender strut in the y direction making it easier for y-polarization mode rather than x-polarization mode to penetrate into the strut and interact with it. Thus, the gradient of the effective refractive index of the y-polarization mode is higher than that of the x-polarization mode, leading to the higher birefringence under higher light frequency. The birefringence of the proposed HC-AR fiber breaks through the order of 10−2 covering the main simulated terahertz region. More specifically, the birefringence reaches 0.0102, 0.0506 at 0.83THz, 2.05THz respectively and maintains an upward trend in a wavelength band as wide as 1.22THzFor HC-AR fibers, confinement loss is the major loss in light transmission. Confinement loss is considered as the energy loss when light escapes form the core and leaks into the fiber cladding [43], which can be estimated by the following equation [44]:
Fig. 5. Confinement loss versus frequency for x- and y-polarization modes with the optimum parameters
Furthermore, because of the introduction of the central strut, both the orthogonal fundamental modes suffer from the absorption loss induced by the dielectric material inevitably. Note that the absorption loss of air is ultra-low and is therefore neglected in following simulations. Thus, we only take the absorption caused by TOPAS into account. According to a perturbation theory [45], relative absorption loss has been used to characterize absorption loss of the fundamental mode, which can be calculated by
Finally, we evaluate the influence of three main parameters on the birefringence and transmission loss properties to figure out the fabrication flexibility and compatibility of the proposed HC-AR fiber. It can be seen from Fig. 7(a) that when the h changes from 10µm to 20µm, the birefringence achieves a nearly fourfold increase. Figure 7(b) shows that increasing h results in higher relative absorption loss and confinement loss for both orthometric fundamental modes. As shown in Fig. 2, the fundamental modes are restricted tighter with thicker h, which can intensify the difference of refractive indices between x- and y- polarization modes magnifying both the relative absorption loss and confinement loss accordingly. It is worthwhile that the relative absorption loss for y-polarization is more sensitive to the change of h but still within the change rate of 0.011/µm. Figure 7(c) shows the birefringence as a function of the cladding tube radius Rn. The birefringence maintains extreme stability and there only exists a difference less than 10−5 in the full calculated Rn region from 580µm to 820µm. The relative absorption loss and confinement loss with different Rn is showed in Fig. 7(d), where all these curves keep stable. The last parameter discussed is the radius of the fiber core. It is seen from Fig. 7(e) and Fig. 7(f), birefringence and relative absorption loss exhibit the similar constant characteristics as Fig. 7(c) and Fig. 7(d) respectively. Moreover, the confinement loss indicates only a tiny declining at a slow rate covering the whole Rs span between 2160µm and 2760µm. It is understood that the lager fiber core makes it more difficult for the light to escape into the cladding area resulting in the reduce of the confinement loss. Based on the above discussion, the performance of the proposed HC-AR fiber is insensitive to the cladding tube radius and the fiber core radius, which brings the HC-AR fiber enormous potential in fabrication. In 2021, Talataisiong et al. reported a novel method combined with traditional extrusion technique and 3D printing technique of a fused deposition modeling which succeeded in extruding TOPAS-based HC-AR fiber directly in a single step [46]. This technology tends to be an optimum choice for the fabrication of the proposed fiber. In addition, required performances of fibers in different practical applications are varied. Thus, flexibly controlling the strut thickness can be the effective method to make a balance between birefringence and transmission loss.
Fig. 7. Birefringence as a function of (a)strut thickness h, (c)cladding ring radius Rn and (e)fiber core radius Rs at 1THz. Relative absorption loss and confinement loss [black (red) curves for x-polarization (y-polarization)] as functions of (b)strut thickness h, (d)cladding ring radius Rn and (f)fiber core radius Rs at 1THz. Fiber parameters except the abscissa variables are fixed as g = 70µm, h = 15µm, Rn = 700µm, Rs = 2460µm.
4. Conclusion
In summary, we have proposed a novel HC-AR terahertz fiber with high birefringence and low transmission loss. Because of the introduction of the central strut, the reported design achieves flexible and adjustable performances including birefringence and transmission loss for different applications through changing vital parameters. Our results confirm that an ultra-high birefringence up to the order of 10−2 is realized in a wide terahertz region ranging from 0.83THz to 2.05THz. Besides, the relative absorption loss is less than 30% for y-polarization mode and 5% for x-polarization in the entire simulation region. Moreover, the confinement loss is negligibly low within 0.99–1.99THz. The impact of structure parameters to the HC-AR fiber optical performance has also been investigated, which indicates that the proposed design has excellent tolerance for the core and cladding dimensions. What’s more, a quite sensible balance between high birefringence and low transmission loss can be made by regulating strut thickness. Therefore, our results demonstrate remarkable potential and appreciable manufacturing compatibility in various applications.
Funding
Natural Science Foundation of Zhejiang Province (LQ22F050007); Science and Technology Department of Zhejiang Province (2022C03066, 2022C03084).
Acknowledgments
We acknowledge the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ22F050007, and the “Pioneer” and “Leading Goose” R&D Program of Zhejiang (No. 2022C03084 and 2022C03066).
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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