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Abstract
A simple polymer twin-tube terahertz (THz) fiber that can be used as a polarization filter is proposed and investigated using the finite element method in this paper. The twin-tube THz fiber consists of two closely spaced identical tubes located symmetrically inside the protecting jacket. The simulation results show that the y-polarization fundamental mode (YPFM) can be well confined between the two tube walls near the fiber center, while the x-polarization fundamental mode (XPFM) has a huge confinement loss due to the coupling with the tube mode. For the fundamental mode (FM), a polarization extinction ratio (PER) of 30 dB can be realized after a 1.3 cm length of the fiber, and the insertion loss of the YPFM is less than 0.5 dB at 1 THz. In addition, higher order modes (HOMs) can be effectively suppressed by further increasing the fiber length. Simulation results indicate that all HOMs have powers being 30 dB lower than that of the supported YPFM after a 7.44 cm length of the fiber, and the insertion loss of the YPFM is less than 2.7 dB at 1 THz. Furthermore, the effects of fiber structure parameters on the loss properties are investigated, proving that the proposed fiber has a good fabrication tolerance. Owing to the simple structure, the proposed fiber polarization filter is easy to be fabricated and low-cost, which makes it a potential application in commercial THz systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past decades, THz wave has attracted great interests due to its applications in various fields including spectroscopy [1], imaging [2], security [3], sensing [4], communications [5], etc. In most cases, linearly polarized THz wave is more preferred, thus polarization filter is an important component in THz systems. Various THz polarization filters based on different materials have been proposed [6], such as liquid crystals [7], metal wire grid [8], carbon nanotubes [9], and silicon wafers [10], however, most of which are designed for free space transmission or reflection mode. There are few reports about fiber-based polarization filter [11,12], which has the advantages of wave confinement and compact size. Although THz polarization beam splitter (PBS) based on the mode-coupling between the dual-core of microstructure fibers can be used as a polarization filter on some occasions, high PER and broad bandwidth can’t be fulfilled simultaneously [13,14].
Actually, single polarization single mode (SPSM) THz fiber is the good choice for polarization filter. To design a SPSM fiber, one of the two orthogonal FMs and all of the HOMs should be prohibited [15–17] or experience much higher propagation loss compared with the supported polarization FM so that SPSM can be realized after some propagation distance [18]. In this situation, large loss difference (LD) between the supported polarization FM and all the other (unwanted) modes is required. However, large LD is not easy to be realized in THz range because the material absorption loss is the dominant factor in most situations. As a consequence, only very few works have been reported to achieve THz SPSM fiber [19–21]. The THz SPSM photonic crystal fiber (PCF) presented in Ref. [19] has a rectangular array of micro-holes in the core, which make the cut-off frequencies of the two orthogonal FMs be different. As a result, only the higher index mode for the range between the two cut-off frequencies will be supported in the fiber core. This fiber is suitable for polarization filter application, but the fine structure requirement of the fiber core results to a huge challenge for fabrication. The THz SPSM PCF presented in Ref. [20] employs the index-matched cladding defects to achieve the LD of the two orthogonal FMs but the LD is only 0.036 dB/cm, which means 8.33 m fiber is needed to obtain a 30 dB PER. Recently, Yang et al. proposed a THz SPSM PCF using low loss high resistivity silicon as the background material [21]. Epsilon-near-zero (ENZ) material is introduced into the air holes near the fiber core to enhance the attenuation of the unwanted modes, while gain material is introduced in the fiber core to amplify the supported polarization FM. In this way, the LD is significantly improved with value greater than 9.4 dB/cm, which is better than their previous published work (8 dB/cm) based on the similar method [22]. Although the result is exciting, the special assumed materials and rather complicated structure make this kind of fibers very difficult to be fabricated under present conditions.
Besides the THz SPSM PCFs mentioned above, a suspended core THz fiber also has been proposed for polarization filter [11]. The struts of this fiber are made of high-loss polyethylene terephthalate (PET), while the fiber core is made of low-loss cyclic olefin copolymer (named Topas in commerce). The YPFM that partly distributes in the fiber struts suffers higher loss compared with the XPFM that mainly distributes in the air and fiber core region. A PER of 30 dB is realized with an insertion loss less than 4 dB. Hollow-core anti-resonant fiber, which has attracted much attention in recent years, also has been demonstrated for polarization filter [12], however with a relatively low PER of 10 dB.
In this paper, we propose a novel simple polymer twin-tube THz fiber which can be used as a polarization filter. The fiber consists of only two closely spaced twin tubes that are located symmetrically inside the protecting jacket. Simulation results indicate that all of the unwanted modes have powers being 30 dB lower than that of the supported YPFM after a 7.44 cm length of fiber, and the insertion loss of the YPFM is less than 2.7 dB at 1 THz. The effects of fiber diameter, tube separation distance, tube thickness, tube position deviation and different-sized tubes set have been numerically studied, proving that the proposed fiber has a good fabrication tolerance. Owing to the simple structure, the proposed fiber is easy to be fabricated and low-cost, which make it has a potential application in commercial THz systems.
2. Fiber structure and mode characteristics
The cross section of the proposed THz fiber structure is shown in Fig. 1(a). The two closely spaced twin tubes are symmetrically located inside the protecting jacket and both of them are fixed to the jacket inner wall. The inner radius of the jacket is defined as the fiber radius, and is represented by R. The twin tubes have the same outer radius r and thickness t. The separation distance of the two tubes is denoted by s. It is clearly that the r, R and s satisfy the relationship r = R/2-s/4. The protecting jacket has a thickness of 100 µm. A perfect matching layer with thickness of 200 µm is set outside the fiber region. Topas is selected as the fiber material because it has a highly constant refractive index of 1.53 and a relatively low bulk material absorption loss of 0.2 cm −1 (i.e. 0.868 dB/cm) around 1 THz [23]. The finite element method has been used to perform the numerical calculations. To ensure the accuracy of the simulation results, we create mesh smaller than 4 µm in the twin tubes area and smaller than 30 µm in the air area. The total mesh elements of the model reach 592433 when R = 740 µm, s = 100 µm, t = 28 µm and the variation of the effective refractive index with more dense mesh set is nearly zero.
Fig. 1. (a) Cross section of the proposed THz fiber and the electric field distribution of (b) YPFM, (c) XPFM and (d) the LL-HOM at 1 THz when R = 740 µm, s = 100 µm, t = 28 µm.
As mentioned earlier, to design a fiber for a polarization filter, the LD between the supported polarization FM and unwanted modes should be large enough. The total loss (TL) of a fiber mode is generally composed of the confinement loss (CL) and the effective material absorption loss (EML). For the proposed THz fiber, it is difficult to get a large LD by manipulating the EML of different modes. Thus, the fiber structure parameters are adjusted to increase the CL difference. As an example, Fig. 1(b)-(d) show the electric field distributions of the YPFM, the XPFM and the lowest loss HOM (LL-HOM, i.e. the HOM with the lowest loss) at 1 THz when R = 740 µm, s = 100 µm, t = 28 µm. It is clearly observed that the YPFM can be well confined between the two tube walls near the fiber center. As a contrast, the XPFM couples with the tube mode, which definitely leads to a high CL. The CL value can be calculated by the following equation [24]:
3. Loss properties analyzation
For a polymer THz fiber device, insertion loss is always a major concern. In the following paragraphs, the effects of the three structure parameters (R, s, t) on the loss properties will be investigated at 1THz. First, the effect of fiber radius R is studied with fixed s = 100 µm, t =28 µm. As shown in Fig. 2(a) and Fig. 2(b), the CL of YPFM, XPFM and the LL-HOM all decrease obviously with the increasing R, while both the EML increment of YPFM and the LL-HOM are very limited. The EML of XPFM decreases slightly with the increasing R and it can be neglected since it is much lower than the XPFM CL. For YPFM, the EML is the major part of TL in the simulated R range, while the CL is the dominant factor of the LL-HOM TL. The LD between the YPFM and the LL-HOM decreases as R increases, which is shown in Fig. 2(c). Figure 2(d) shows the needed fiber length and the corresponding insertion loss when the LL-HOM is required to be 30 dB lower than the YPFM after the fiber polarization filter. The fiber length increases as R increases, which is contrary to the LD tendency. The insertion loss reaches the minimum value of 2.66 dB with the corresponding fiber length of 7.44 cm when R = 740 µm.
Fig. 2. The loss properties versus fiber radius R with fixed s = 100 µm, t =28 µm at 1THz. (a) The CL, EML, and TL of the YPFM, and the CL and EML of the XPFM. (b) The CL, EML, and TL of the LL-HOM, (c) The LD between the YPFM and the LL-HOM. (d) The needed fiber length and the corresponding insertion loss when the LL-HOM is required to be 30 dB lower than the YPFM.
Next, the effect of tube separation distance s is studied with fixed R = 740 µm, t =28 µm. Since the XPFM has a much higher loss than the LL-HOM, to suppress unwanted modes, the LL-HOM is the only concern. Thus, the XPFM will not be discussed below. As shown in Fig. 3(a), both the CL of YPFM and the LL-HOM increase with the increasing s. The EML of YPFM slightly decreases as s increases. Note that the EML of the LL-HOM hasn’t been independently displayed in Fig. 3(a) to simplify the illustration, but its value still can be estimated from the distance between the TL and CL. The LD has the similar tendency with the HOM TL. To meet the requirement of 30 dB suppression of unwanted modes, the needed fiber length and the corresponding insertion loss are shown in Fig. 3(b). The insertion loss reaches the minimum value when s = 100 µm.
Fig. 3. The loss properties versus tube separation distance s with fixed R = 740 µm, t =28 µm at 1THz. (a) The CL, EML, and TL of the YPFM, the CL and TL of the LL-HOM, and the LD between the YPFM and the LL-HOM. (b) The needed fiber length and the corresponding insertion loss when the LL-HOM is required to be 30 dB lower than the YPFM.
At last, the effect of tube thickness t is studied with fixed R = 740 µm, s =100 µm. As shown in Fig. 4(a), the CL of YPFM and the LL-HOM have opposite tendencies. On the other hand, both the EML of YPFM and the LL-HOM increase with the increasing t. The LD between the YPFM and the LL-HOM increases as t increases. Similarly, the needed fiber length and the corresponding insertion loss are shown in Fig. 4(b). The insertion loss reaches the minimum value of 2.6 dB when t = 31 µm.
Fig. 4. The loss properties versus tube thickness t with fixed R = 740 µm, s = 100 µm at 1THz. (a) The CL, EML, and TL of the YPFM, the CL and TL of the LL-HOM, and the LD between the YPFM and the LL-HOM. (b) The needed fiber length and the corresponding insertion loss when the LL-HOM is required to be 30 dB lower than the YPFM.
Based on the above investigation, we can see that there are optimal parameter values to get the minimum insertion loss. However, it also can be found that the insertion loss value is quite insensitive to the parameter variation around the minimum position. More precisely, the insertion loss value can be kept lower than 2.7 dB at 1THz in these situations: (1) R in the range from 710 to 770 µm with fixed s =100 µm, t = 28 µm. (2) s in the range from 85 to 115 µm with fixed R = 740 µm, t = 28 µm. (3) t in the range from 27 to 37 µm with fixed R = 740 µm, s =100 µm. If we use <3 dB as the acceptable insertion loss limit, then the requirement of the structure parameters will become much looser, which is favorable for fiber fabrication.
To test the working bandwidth of the fiber polarization filter, the loss property at different frequency has been simulated when R = 740 µm, s =100 µm, t = 28 µm. As shown in Fig. 5(a), the CL of YPFM decreases with the increasing frequency, while the EML has an opposite tendency due to more power confined in the polymer material. The CL of the LL-HOM also decrease with the increasing frequency, and the gradient becomes steeper when the frequency larger than 1.22 THz. The needed fiber length and the corresponding insertion loss for 30 dB suppression of unwanted modes are shown in Fig. 5(b). The insertion loss reaches the minimum value of 2.57 dB with the corresponding fiber length of 7.65 cm at 1.06 THz. The region A labeled in the Fig. 5(b) represents the frequency span (0.94 THz∼1.24 THz) whose insertion loss is less than 3 dB. In practical application, a fixed fiber length is usually adopted. Here, the insertion loss of an 8-cm-long fiber is also depicted in the Fig. 5(b). The frequency span (0.98 THz∼1.18 THz), as labeled region B, can satisfy both the conditions that the length requirement < 8 cm and the insertion loss <3 dB.
Fig. 5. The loss properties versus frequency when R = 740 µm, s = 100 µm, t = 28 µm. (a) The CL, EML, and TL of the YPFM, the CL and TL of the LL-HOM, and the LD between the YPFM and the LL-HOM. (b) The needed fiber length and the corresponding insertion loss when the LL-HOM is required to be 30 dB lower than the YPFM, and the insertion loss of an 8-cm-long fiber.
4. Fabrication discussion
Owing to the simple structure, the fabrication of our proposed fiber can be quite easy by using the stack-and-draw technique [26,27] or 3D printing technique [28]. Here, the possible fabrication process by using the stack-and-draw technique is discussed. To obtain the desired fiber preform, we firstly fabricate an auxiliary preform to make the twin tubes adhere to the inner surface of the jacket tube and locate symmetrically with the designed spacing distance. The cross section of the auxiliary preform is shown in Fig. 6(a). An assisting rod and two identical assisting tubes are introduced to keep the twin tubes in place. The diameter of the assisting rod equals to the spacing distance between the twin tubes, while the outer diameter of the assisting tube is designed to make it tangent to the twin tubes and the jacket tube. In the first step of fabrication, the twin tubes, assisting tubes, and assisting rods are stacked. Note that the assisting components are only used at the two end positions as shown in Fig. 6(b). Next, the stacked components are placed inside the jacket tube. After drawing process, the auxiliary preform will be obtained. Now, the twin tubes have been firmly adhered to the jacket tube and the auxiliary preform can be used for drawing fiber to finally obtain the proposed THz fiber. Note that during the second drawing process, the two end parts of the auxiliary preform are discarded and only the middle part are used.
Fig. 6. (a) Cross section of the auxiliary preform. (b) The schematic diagram of the fiber fabrication process.
During the fabrication process, the twin tubes may be slightly deviated from the perfect symmetrical position. Figure 7(a) shows the situation that the left tube has a 5° in-plane rotation with respect to the fiber center. Compared with the perfect symmetrical structure, the 5° deviation only causes a slight insertion loss increment (<0.05 dB), as shown in the Fig. 7(b). The inset shows the electric field distribution of the YPFM at 1THz when the left tube has a 5° deviation. The result indicates that the property of our proposed fiber polarization filter is quite stable even with small tube deviation.
Fig. 7. (a) Cross section of the proposed THz fiber when the left tube has a 5° in-plane rotation with respect to the fiber center. (b) The insertion loss of the proposed fiber with 5° tube deviation when the LL-HOM is required to be 30 dB lower than the YPFM. The insertion loss of the proposed fiber with no deviation is depicted here for comparation. The inset shows the electric field distribution of the YPFM at 1THz when the left tube has a 5° deviation.
The two tubes may not be kept the same size during the fabrication process. Figure 8(a) shows the situation that the left tube has a radius of r1 = 350 µm, while the right tube has a radius of r2 = 345 µm. The two tubes have the thickness of 28 µm, and the fiber radius R is 740 µm. The corresponding insertion loss property is shown in Fig. 8(b). Compared with the fiber with the same-sized tubes, this situation with different-sized tubes causes a slight insertion loss increment (<0.08 dB) when the frequency is larger than 0.98 THz. The inset shows the electric field distribution of the YPFM at 1THz when the fiber has the different-sized tubes. The result indicates that the property of our proposed fiber polarization filter is relatively stable when the two tubes have a small difference in radius.
Fig. 8. (a) Cross section of the proposed THz fiber when the left tube has a radius of r1 = 350 µm, while the right tube has a radius of r2 = 345 µm. (b) The insertion loss of the proposed fiber with different-sized tubes when the LL-HOM is required to be 30 dB lower than the YPFM. The insertion loss of the proposed fiber with the same-sized tubes is depicted here for comparation. The inset shows the electric field distribution of the YPFM at 1THz when the fiber has the different-sized tubes.
5. Conclusion
In summary, a novel simple polymer twin-tube THz fiber has been proposed for a polarization filter, which only the YPFM can be supported with relatively low loss. For the fiber with R = 740 µm, s =100 µm, t = 28 µm, simulation results indicate that all of the unwanted modes have powers being 30 dB lower than that of the supported YPFM after a 7.44 cm length of fiber, and the insertion loss of the YPFM is less than 2.7 dB at 1THz. Besides, the insertion loss is kept less than 3 dB in the frequency range from 0.94 to 1.24 THz. The effects of the structure parameters on the loss properties have been investigated, which demonstrate the insertion loss value is quite insensitive to the parameter variation around the minimum position. The insertion loss value can be kept lower than 2.7 dB at 1THz in these situations: (1) R in the range from 710 to 770 µm with fixed s =100 µm, t = 28 µm. (2) s in the range from 85 to 115 µm with fixed R = 740 µm, t = 28 µm. (3) t in the range from 27 to 37 µm with fixed R = 740 µm, s =100 µm. The fabrication process by using the stack-and-draw technique has been discussed. In addition, the effects of 5° tube rotation and different-sized tubes set (r1 = 350 µm, r2 = 345 µm) have been discussed, which only cause a slight insertion loss increment of <0.05 dB and <0.08 dB, respectively. Owing to the simple structure and good fabrication tolerance, the proposed fiber is easy to be fabricated and low-cost, which make it has a potential application in commercial THz systems.
Funding
NingboTech University (20201203Z0189); Natural Science Foundation of Zhejiang Province (LQ22F050007); Science and Technology Department of Zhejiang Province (2022C03066, 2022C03084); Huangshan University (2020xkjq015).
Disclosures
The authors declare no conflicts of interest.
Data availability
Date 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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