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We report on the fabrication and characterization of an elliptical hollow fiber inner coated with a silver layer and a dielectric layer for polarization maintaining and low loss transmission of terahertz (THz) radiation. The primary purpose of adding the dielectric layer is to prevent the silver layer from oxidation. The thickness of the dielectric layer is non-uniform owing to the surface tension of the coating, which was initially applied as a liquid. Transmission loss and polarization maintenance are experimentally characterized. Effects of the dielectric layer on transmission properties are analyzed by comparing the fiber to Ag-only fiber. Results show that a dielectric layer with thickness less than λ/10 can effectively decreases the power distributed on the metal surface and thus can practically reduce loss resulting from roughness of the silver layer. Bending effects on transmission loss and polarization maintenance are also investigated.
© 2015 Optical Society of America
1. Introduction
Metallic or dielectric/metallic hollow waveguides have been extensively studied in the microwave, infrared, and optical regimes, after pioneering work in the millimeter-wave spectrum in 1960s [1], including a theoretical study published in 1964 [2]. The study of this fiber type for infrared transmission began in the mid-1970s [3] and since then this type of fibers have found applications in high power and ultra-short pulse laser light delivery [4], gas sensing [5], Raman detection [6], and wide band spectroscopy [7].
In recent years, this kind of fiber also received attention for its use at terahertz (THz) frequencies. Since a dominant part of the power is transmitted through the air core, the effect of Ohmic losses on metallic surfaces and absorption inside dielectrics, which are the two main challenges for low-loss THz waveguides, can be reduced. Early studies of their applications for THz radiation focused on hollow fibers with metal coatings, known as metallic hollow fibers (MHFs). A loss of 3.9 dB/m was obtained for a 3 mm bore hollow fiber with an internal Cu coating at wavelengths of 158.51 μm. It was shown that the single mode of a laser was preserved for smaller bore fibers [8]. Hollow glass fibers internally coated with silver were developed and the measured losses were 7.5–8 dB/m at wavelengths from 190 to 250 μm for fibers with an inner diameter of 1 mm and the bending losses were low [9].
Subsequently, MHFs were improved by including a dielectric layer over the metal layer, known as dielectric-coated metallic hollow fibers (DMHFs). This technique has proven effective in reducing the transmission loss of the fibers in the MIR. The main concerns in adapting this technique to THz frequencies are the thickness of the dielectric layer and the absorption of the dielectrics. The thickness of the dielectric layer in THz hollow fibers should be tens to hundreds of times larger than that in the MIR, as the optimum dielectric layer thickness is proportional to the wavelength. The thickness of the dielectric layer is required to be approximately 1/7th of the wavelength, for a refractive index of 1.5, giving an optimal thickness of approximately 40 μm for 1 THz [10].
The dielectric coatings may be applied to the MHFs using liquid-flow coating methods. The method parameters such as solution concentration and flow speed should be carefully controlled to obtain the correct thickness with reasonable uniformity. An 8.2 μm thick polystyrene (PS) film was deposited inside a 2 mm bore silver-coated glass tube, achieving a loss of 0.95 dB/m at a wavelength of 119 μm (2.5 THz) [11]. An improvement in the dielectric coating process was later reported in [12], using a vacuum pump instead of a peristaltic pump to push the dielectric solution through the Ag-coated tube. A cyclo-olefin polymer (COP) layer with a thickness larger than 40 μm was reported in [13]. The loss was 1.5 dB/m for the 3 mm diameter fiber. In the same reference, the authors fabricated dielectric-metallic hollow fibers by inserting a polyethylene (PE) film coated with silver on one side into flexible plastic tubing. The losses were lower than 3 dB/m in the wavelength region from 150 μm to >250 μm. However transmission properties were affected by structural irregularities of the inserted film, and this technique is not appropriate for fabricating thin fibers. Other dielectric material such as AgI, fabricated by converting metal to dielectric using iodination process, has also been attempted [14]. However, these materials are very lossy in the THz region and the coating thickness is limited to 1-2 μm. A promising way to fabricate terahertz DMHFs with a desirable dielectric layer thickness is by metallizing the outer surface of polymer tubes. A quasi-single-mode (HE11) DMHF was fabricated by coating 1-mm diameter 38-μm-thick polytetrafluoroethylene tubes with silver [15].
Metallic hollow fibers with multiple dielectric layers have also been studied, in order to reduce the transmission and bending loss through increased reflection from a multi-layer structure [16–19 ]. However, the fabrication of multi-layer DMHF is a big challenge owing to difficulties in achieving a reasonable index difference between the dielectric layers (preferably > 0.5) and obtaining the desirable layer thickness (around λ/5) [17]. Elliptical or rectangular cross section fibers [20, 21 ] were also considered, to achieve specific properties such as high birefringence and higher flexibility.
Highly birefringent (HB) fibers, in which strong birefringence is deliberately introduced, have been widely studied and have found many applications in optical communication systems, devices and fiber sensors operating in the infrared. With the rapid development of THz science and technology, HB fibers for THz radiation will ultimately find their application in the context of polarization-sensitive imaging and THz communications. Various kinds of HB THz fibers, based on plastic photonic crystal fibers [22, 23 ], air-core band-gap fibers [24], porous fiber [25, 26 ], and polymer tubes [27, 28 ], have been proposed. High birefringence is achieved by introducing asymmetry in the geometry (form birefringence), for example, through an asymmetric refractive index defect in a plastic photonic crystal fiber [22] or the use of rectangular holes in porous fibers [26].In a previous paper, elliptical polycarbonate (PC) hollow fibers with an inner silver coating were reported [29]. A significant improvement in polarization maintenance was observed in the fiber compared to ones with a circular cross section. However, the silver layer could oxidize in air, which will greatly reduce the reflectivity of the silver layer and hence increase the transmission loss. Furthermore, the fiber length was limited and the shape of the cross section was not precisely controlled as the elliptical tubes were fabricated by heating and compressing circular tubes between two glass plates.
In this paper, elliptical tubes several meters in length are fabricated by drawing techniques. These are internally coated with silver, and additionally a COP layer is added over the silver coating to protect the silver layer from oxidation. The thickness of the COP layer was observed to be non-uniform around the cross section of each tube owing to the surface tension of the coating. The transmission loss and polarization-maintaining properties of these fibers are numerically and experimentally studied from 0.75 to 1.1 THz, mainly focusing on 0.87 THz due to lower absorption by air. The effects of the dielectric layer on the transmission properties are analyzed by comparing the fiber to Ag-only fiber. Experimental and simulation results show that a dielectric layer with thickness less than λ/10 can effectively decreases the power distributed on the metal surface and thus can practically reduce loss resulting from roughness of the silver layer. Effects of bending on the transmission loss and polarization maintenance are also investigated.
2. Fiber design and structure
The structure of the fiber considered in this work is illustrated in Fig. 1 . The fiber consists of a reflective metallic layer and a reflection-enhancing dielectric layer deposited on the inner wall of a hollow tube. In order to make the fiber polarization maintaining, the cross section of the tube is elliptical. In the fabricated fibers the thickness of the dielectric layer produced using a liquid-flow coating process was found to be non-uniform, due to the surface tension of the liquid, resulting in d2 being smaller than d1, as the inner surface of the liquid attempts to become circular. The parameters characterizing the fiber structure are the inner major and minor radii a and b, the thickness of the metallic layer s, and the major and minor thickness of the dielectric layer d1 and d2.
Fig. 1 Cross section of the elliptical dielectric-coated metallic hollow fiber. a = 1.4 mm, b = 0.5 mm, d1 = 15 μm, d2 = 1 μm, s = 1 μm
The fiber is multi-mode when λ/a <1.89 [30]. In DMHFs, the field distribution of the eigenmodes is frequency dependent, particularly near the cut-off frequencies or the Fabry-Perot resonances [15, 31, 32 ]. We numerically examined the field properties of the eigenmodes of the fiber from 0.7 to 1.1 THz, covering the frequency range used in the experimental work. Field distribution changes little over this frequency region. Therefore, we only show the results at 0.87 THz here. Figure 2 shows the electric field direction and power distribution for some of the low order eigenmodes supported by such elliptical DMHF at 0.87 THz, calculated using a commercial finite element solver (COMSOL). The fiber parameters used in simulation were set as: a = 1.4 mm, b = 0.5 mm, d1 = 15 mm, d2 = 1 µm, and s = 1 µm, which is much larger than the skin depth in the frequency region of interest, and hence the silver layer thickness has no effect on the transmission properties of the fiber. The refractive index of COP layer was 1.51 and the absorption coefficient was 0.3 cm−1 [33]. The air was assumed to be lossless with refractive index of 1, and the refractive index of silver was taken to be 687-844i using a Drude model [34].
Fig. 2 Low-order eigenmodes of the fiber at 0.87 THz. The electric vector is indicated by the arrows and the power distribution is indicated by the color scale.
The fiber supports hybrid EH and HE modes in which both transverse E and H fields are non-zero. The modes are denoted as HE or EH depending on whether the components of H or E make the larger contribution to the transverse field. The mode designations are consistent with the definitions of odd (x-polarization) and even (y-polarization) hybrid modes adopted for elliptical waveguides [35]. Mode correspondence between HE/EH and TE/TM modes can be found in Table 1 in [35].
Table 1. Simulated mode effective indices and losses of the highest-coupled modes at 0.87 THz
Figure 3 shows the coupling efficiencies for a Gaussian beam incident on the fiber end-face for the three highest-coupled modes at 0.87 THz, as a function of the Gaussian width normalized to the radii of the fiber. The Gaussian beam has a beam-waist diameter of 2w and is linearly polarized along the x-axis (x-polarization, Fig. 3(a)) or y-axis (y-polarization, Fig. 3(b)). For these elliptical fibers, the HE11 x, EH11 x, and HE12 x modes have the highest coupling efficiency when the incident radiation is x-polarized. In the case of y-polarization, the HE11 y, EH11 y, and HE31 y have highest coupling efficiency. It is noted that the fiber is expected to have higher coupling efficiency when the incoming radiation is y-polarized. In the work presented here, w/a = 0.7 and w/b = 2, indicated by dashed lines in Fig. 3. It is seen that more power can be coupled to the fundamental mode when y-polarization is launched. It is worth mentioning that the coupling efficiency is highly frequency dependent. For example, the HE11 x mode has a maximum coupling efficiency of 0.48 at 0.87 THz while this value increases to 0.82 at 3 THz.
Fig. 3 Coupling efficiency between a Gaussian beam and the three highest-coupled modes at 0.87 THz for (a) x-polarization and (b) y-polarization, with w the beam waist of the Gaussian, a = 1.4 mm, b = 0.5 mm. The experimental parameters w/a = 0.7 and w/b = 2 are indicated.
The dielectric film thickness can have a significant effect on the fiber’s transmission characteristics. The dielectric film thickness in a DMHF can be optimized to obtain a low loss for the HE11 mode [10]. However, there are no results reported that can be used to optimize the thickness of a non-uniform dielectric layer. We investigated the relationship between the thickness of the dielectric layer and the transmission loss at 0.87 THz using COMSOL 4.4, for the same parameters as in Fig. 2 except that the thickness of the COP layer was varied. Figures 4(a) and 4(b) show the transmission loss of the HE11 x and HE11 y mode as a function of d1 at the frequency of 0.87 THz. The maximum thickness considered was d1 = 75 µm since in practice it is difficult for the thickness of the dielectric layer obtained by the liquid-flow method to exceed this value. Transmission loss varies with the change of thickness due to the Fabry-Perot resonances of the dielectric layer. This can be seen from the power distributions at different dielectric layer thicknesses, as shown in Fig. 4(c). In Fig. 4(c), (A), (D), (E), and (G) are at anti-resonant frequencies when the field is largely confined in the air core, while (B), (C), (F), and (H) are at resonant frequencies when the field concentration increases in the dielectric layer. Concentration of field in the dielectric layer results in high loss.
Fig. 4 Simulated loss as a function of dielectric layer thickness d1 with various values of d2, and power distribution for selected cases, for 0.87 THz. (a) Loss for the HE11 x mode. (b) Loss for HE11 y mode. Loss of metallic hollow fiber is shown for comparison in both, and d2 was fixed for each curve. (c) Power distribution of the HE11 x or HE11 y mode for various dielectric layer thicknesses. Positions for (A)-(H) are indicated in Figs. 4(a) and 4(b).
The transmission loss of the Ag-only fiber is also shown for comparison. It is found that at 0.87 THz, the dielectric layer can hardly lower the transmission loss. This is because the dielectric layer thickness required to effectively lower losses at the lower frequency is larger, making the dielectric absorption more significant. This also happens in the fiber with a uniform dielectric layer [36]. For example, the required thickness of dielectric layer for operating wavelength of 0.87 THz and 3 THz is 47 μm and 13.6 μm, respectively.
In addition to transmission loss, adding the dielectric layer may also affect the polarization maintenance. Birefringence is an important parameter characterizing a fiber’s ability to maintain polarization - a fiber with a higher birefringence has a stronger ability to maintain polarizations corresponding to the birefringence axes. Birefringence is defined as B = |neffx – neffy|, where neffx and neffy are the effective refractive indices of the x-polarization and y-polarization modes, respectively. To investigate how the dielectric layer affects the polarization maintaining ability of the fiber, we studied the relationship between the dielectric thickness and birefringence at 0.87 THz. The simulation results are shown in Fig. 5 . Dielectric thickness d2 was kept constant at 5 µm in the simulations. The birefringence of MHF, which is indicated by the solid line in Fig. 5, is added for comparison. It is seen that the dielectric thickness can have a significant influence on birefringence. Transmission loss (shown in Fig. 4(a)) is added to Fig. 5 toF show its variation with birefringence. The results also show that there should be a trade-off between transmission loss and birefringence. The peaks of birefringence and transmission loss are fairly correlated, meaning that certain dielectric thicknesses will increase the birefringence, but also introduce high transmission loss. The peaks of birefringence are also due to the Fabry-Perot resonances of the dielectric layer.
Fig. 5 Relationship between birefringence and dielectric layer thickness d1 at 0.87 THz, d2 = 5 μm. Transmission loss shown in Fig. 4(a) is added to show variation relationship between birefringence and loss. The birefringence of MHF, which is indicated by the solid line, is added for comparison.
Although the addition of a dielectric layer hardly reduces the transmission loss at 0.87 THz according to Fig. 4, it is very important in terms of preventing the silver layer from oxidation. The dielectric layer can significantly affect transmission loss and polarization maintenance and there is a trade-off between the two, however the dielectric layer will not weaken a fiber’s ability to maintain the polarization at 0.87 THz, as seen in Fig. 5. Therefore, priority is given to transmission loss in this paper and the dielectric layer thickness needs to be carefully considered to obtain low loss. In Fig. 4 the thicknesses considered were (d1 = 10 µm, d2 = 1 µm), (d1 = 60 µm, d2 = 5 µm), (d1 = 30 µm, d2 = 10 µm), (d1 = 40-60 µm, d2 = 10 µm), and (d1 = 75 µm, d2 = 10 µm). However, according to [15] and our experience in COP deposition, a smooth dielectric layer thicker than 30 µm would be very difficult to form during the liquid phase deposition (see next section). Therefore, (d1 = 10 µm, d2 = 1 µm) was chosen as the target structure.
3. Fabrication
The fabrication process of the fiber includes two steps: a silver layer was deposited on the inside of the base tube using a mirror plating method detailed in [37], and a dielectric layer was coated over the silver layer using a liquid-flow deposition method.
The base tube used is normally a glass tube with a smooth inner surface which is important for the quality of the inner coatings. However, owing to the longer wavelength in the THz region, the dimension of DMHF for THz radiation is much larger than for the MIR. A glass tube of large dimensions becomes inflexible, hence a polymer tube with good flexibility is used. However, its inner surface is usually less smooth than for glass. Adhesion of the silver to the base tube is another factor that needs to be taken into consideration, e.g. silver has poor adhesion to polytetrafluoroethylene (PTFE) and PE. In this paper, we used PC capillaries as the base tubes. In previous work, elliptical PC tubes were fabricated by reshaping in a furnace [29].To overcome the length limitation caused by the size of the furnace (10s of cm), fiber drawing was used in this work to obtain longer PC tubes (several meters). An ellipticity around 3 is desirable both for low transmission loss and high birefringence [21]; the PC tubes used here have an ellipticity of 2.8 (1.4 mm major radius and 0.5 mm minor radius).
Liquid-flow coating was used to add the dielectric layer, in which the dielectric solution was forced to flow through the silvered tube by a peristaltic pump, leaving a coating of dielectric solution on the inside of the tube. The tube is kept vertical to maintain a good symmetry of the coating: During the deposition stage, the viscous COP solution is slowly pulled down by gravity, limiting the achievable thickness of COP. The tube was then cured in an electronic furnace while nitrogen flowed through the tube for faster evaporation of the solvent. PS and COP are commonly used materials for the dielectric layer in a DMHF for THz transmission since both have low absorption [11, 33 ]. The advantage of PS over COP is that the concentration of PS solution (maximum concentration around 30 wt %) can be higher than that of COP solution (maximum concentration around 20 wt %). However, during the fabrication the solvent for PS (toluene) penetrated the silver layer deforming the PC base tube. Therefore, COP was used.
COP pellets were dissolved in cyclohexane to form solutions. The property of the COP film is dependent on the concentration and flow speed of the solutions and temperature of the drying process. The higher the concentration of the COP solution or the flow speed, the thicker the COP film. The highest concentration obtained at a temperature of 30 °C was 20 wt %. However, the liquid-phase COP film was observed to have large roughness when the concentration exceeded 20 wt% or the flow speed exceeded 5 cm/min, hence a concentration of 15% and a flow speed of 3 cm/min were chosen. One of the difficulties in the process of COP coating is that the film in the more curved side of the elliptical tube tends to have larger roughness owning to the thicker liquid layer coating the walls of the tube. Therefore the dry-curing process must be designed carefully and the process must be well controlled in order to efficiently evaporate the solvent.
The optical micrograph of the fabricated fiber is shown in Fig. 6 (a) . The COP layer at various positions is shown in Figs. 6(b)-6(d). Note that the COP layer has been detached from the inner wall in order to give a clear indication of its thickness. It is obvious that the layer is thicker towards the side with higher curvature. This is due to the surface tension of the COP solution used for coating, which results in non-uniform thickness along the inner wall of the base tube.
4. Experiment characterization
The transmission loss and polarization-maintaining ability of the fiber was characterized with a linearly polarized THz source. Figure 7 shows the schematic setup. A microwave synthesizer with its multipliers (Virginia Diodes) was used as the THz source. The frequency of the source is tunable and the frequency band used in the measurements is from 0.75 to 1.1 THz. Since the horn (shown in Fig. 7) used in front of the source has a diameter of 2 mm, which is well matched with the size of the fiber, the THz wave was directly launched into the coupling fiber without using lenses. A short tip, 10 cm length of fiber was used as a coupling waveguide so as to eliminate lossy modes. A pair of methylpentene polymer lenses with a focal length of 5 cm was used to focus the beam into a power meter. A wire-grid polarizer was used to detect the power at various polarization angles. The transmission loss was obtained by comparing the intensity transmitted with the fiber in place, and without the fiber and the lenses shifted by the length of the fiber.
4.1 Transmission loss
Fibers of various lengths were characterized at 0.87 THz and the results are shown in Fig. 8 . Figure 8(a) is the transmission loss for the x-polarization (parallel to the long axis of the cross-section) and Fig. 8(b) is the transmission loss for the y-polarization (parallel to the short axis). From the lines of best fit, the transmission losses for the x-polarization and y-polarization are estimated at 3.8 dB/m and 6.2 dB/m, respectively. The coupling loss between the test fiber and the coupling fiber should be zero, however any misalignment and imperfect cleaving will result in coupling loss. It is noted that there is an oscillation in the transmission loss for both polarizations, which may be beating between residual higher order modes. Table 1 presents the transmission loss and mode effective index (n eff) of the highest-coupled modes for both polarizations. The resulting beat lengths between these, defined as λ/∆n eff, are on the scale of millimeters. Therefore, the mode beating could affect the output of the fibers which are centimeters long.
We estimated d1 as 15 μm and d2 as 1 μm, as shown in Fig. 6. A thickness error of 20% was taken into consideration to investigate how the thickness error could affect the transmission loss. Table 2 shows the simulation results for the fiber with various values of thickness at 0.87 THz. It is seen that within the thickness range considered, the average of the loss is around 3 dB/m for the x-polarization and around 6 dB/m for the y-polarization, indicating that the experimental results match well with the simulations.
Table 2. Simulated transmission losses of HE11 mode for various dielectric layer thicknesses at 0.87 THz
The transmission loss spectrum of the fiber was also investigated and was compared to that of a MHF. For a fair comparison, the two fibers (DMHF and MHF) under investigation were cut from the same MHF, with one further coated to become the DMHF. Both were 90 cm long and the losses presented include the coupling losses between the coupling fiber and the test fibers. The results are shown in Fig. 9 . The loss peak at 0.98 THz arises from absorption of the air. Contrary to the simulation results, we found that the transmission loss had been reduced by adding the COP layer. One reason for this discrepancy may be the oxidation of the silver layer in MHF, however no oxidation could be observed by the naked eye. Another reason may be the surface roughness of the silver layer, which was not considered in the earlier simulations. The surface roughness of the silver layer in a polymer-based hollow fiber is much larger than in a glass-based hollow fiber, because the glass tube has a smoother inner wall. The COP layer greatly reduces the power distribution on the metal, and hence reduces the transmission loss resulting both from the finite conductivity of the metal and surface roughness.
Fig. 9 Loss spectrum for elliptical DMHF and MHF. The length of the fibers is 90 cm. The loss shown includes the coupling loss between the test fiber and the coupling fiber.
To confirm the fact that COP layer can reduce the power at the metal surface, we investigated the electric field distribution in the fiber through numerical simulations as shown in Fig. 10 . Figures 10(a) and 10(b) present the electric field norm of the x-polarization along the line (x = 0.8 mm) indicated by the dotted line. The value was normalized to the maximum electric field norm at the centre of the fiber (x = 0, y = 0). It is seen that in the MHF, the field has a large value (~45% of maximum) at the silver surface, while in the DMHF the field at the silver surface is greatly reduced by the COP layer (<15% of maximum). Here x = −0.8 mm was chosen as an example, and other positions also show that the COP layer reduces the field at the metallic surface. This also holds true in the case of y-polarization.
Fig. 10 Electric field profile of x-polarization at x = −0.8 mm in (a) MHF (b) DMHF. f = 0.87 THz. The electric field norm is normalized to the maximum value at the center of the fiber. Electric field profile of DMHF at the boundary (air/COP/Ag) is magnified.
To investigate the effect of silver layer roughness on the transmission loss, longitudinally invariant roughness which was periodically distributed on the silver surface was considered in 2-Dimensional simulation as shown in Fig. 11(b) . Figure 11(a) shows the loss as a function of roughness amplitude for MHFs and DMHFs. The area indicated by the rectangle in Fig. 11(b) is magnified to show the layers more clearly. It is seen that silver layer roughness has less influence on DMHFs than MHFs, as again the field at the metal is decreased by the dielectric layer. The silver layer roughness has less influence on the x-polarization, as the y-polarization has more power distributed on the metal surface (see Fig. 2). Although these results only take longitudinally invariant roughness into consideration without considering the roughness along the fiber, they indicate the different effect of silver layer roughness on MHFs and DMHFs, which explains why a thin dielectric layer practically reduces the transmission loss.
Fig. 11 Additional loss due to silver layer roughness and rough layer structure used for simulations at 0.87 THz. (a) Additional loss as a function of roughness. (b) Rough layer structure used in simulations for MHF and DMHF. The roughness amplitude is 500 nm. Field distribution of the TE11x mode is shown in the upper panel. The lower panel shows the HE11x mode of the DMHF.
4.2 Polarization maintenance
It has already been shown that circular hollow fibers cannot preserve the polarization of the propagating light, whilst elliptical MHF fibers can [29]. To investigate the present fiber’s ability to maintain polarization, a linearly polarized THz beam was launched into the fiber and the output was analyzed by placing a wire grid polarizer in front of the power meter as in Fig. 7. The fiber length tested was 90 cm and measurements were taken by rotating the polarizer by increments of 10°. The measured results for elliptical DMHF and MHF are shown in Fig. 12 , with the angle defined as that between the output and input polarizations, and x-polarization is taken to be parallel to the long axis, y-polarization parallel to the short axis. For comparison, an elliptical MHF with a length of 90 cm was also characterized.
Fig. 12 Measured power at various polarization angles at 0.87 THz for DMHF and MHF. (a) and (c): The incoming light is parallel to the long axis in DMHF and MHF, respectively. (b) and (d): The incoming light is parallel to the short axis in DMHF and MHF, respectively.
4.3 Bending effect on transmission loss and polarization maintenance
In many applications, such a flexible fiber may be required to bend, e.g. if the fiber is used as the arm of an endoscope. Therefore, it is important to study the bending properties of the fiber. To measure the effect of bending on loss, we bent the center part of 90 cm long fibers, leaving 5 cm lengths at both ends fixed straight; an example is shown in the inset to Fig. 13(a) . Figure 13 shows measured additional loss in the fiber after bending as a function of the bending angle at 0.87 THz. The error bars were estimated by aligning and measuring the same fiber five times. Four conditions, combining two polarizations and two bending directions (parallel or perpendicular to the long axis), were considered. Note that when bending plane is parallel to the long axis, the fiber is relatively rigid and the maximum bending angle is around 45°. Bend-induced losses arise due to coupling to the higher order modes which have higher transmission loss compared to the HE11 mode. It was also observed that the loss increases for the x-polarization with the bending plane parallel to the long axis (defined as Condition A in Fig. 13) was larger than for the other three combinations of bending and polarization. This behavior is similar to MHFs.
Fig. 13 Bending loss as function of bending angle for 0.87 THz. The experimental setup is shown in the inset in (a). (a) Both incoming polarization and bending plane are parallel to the long axis, (b) both incoming polarization and bending plane are parallel to the short axis, (c) incoming polarization is parallel to the long axis and bending plane is parallel to the short axis, and (d) incoming polarization is parallel to the short axis and bending plane is parallel to the long axis.
To investigate this, we compared the diameter of the bent fiber to that of the straight fiber. For example, at the middle point of the fiber, the outer diameter along the short axis is 1.53 mm in a straight fiber while it is 1.48 mm when the fiber is bent in 360° as in Condition B. It indicated that the cross section of the fiber is deformed during the bending. In Condition B and C, bending causes less deformation than in A and D. The increased deformation increases the coupling of HE11 mode to higher order modes which have more energy distributed at the sides of the cross section. For the x-polarization, the HE11 x mode (loss of 3 dB/m) may couple to the HE21 x (6.1 dB/m) or the HE31 x (8.2 dB/m). For the y-polarization, the HE11 y mode (5.8 dB/m) may couple to the HE21 y (7 dB/m) or the HE31 y (7.7 dB/m). The loss difference between the HE11 x and the higher order modes likely to be coupled to is larger than that for the y-polarization, explaining the larger additional loss. Another contributing factor may be that more power is coupled to the fundamental mode in the case of the y-polarization as shown in Fig. 3.
Figure 14 is the polarization ratio as a function of the bending angle. The ability to maintain a polarization tends to decrease as the bending angle increases. That is because the high order modes, which can be excited during the bending, are not linearly polarized. The trend is particularly obvious in Condition A, in which the fundamental mode is more likely to couple to higher order mode as explained above.
Fig. 14 Polarization ratio as a function of bending angle at 0.87 THz. Four conditions combing two polarizations and two bending directions are considered.
It worth mentioning that bending conditions B and C are much more likely to occur in practical use than A and D. The advantage for practical use is that conditions B and C have low additional loss due to bending (< 2 dB). We also note that in these two cases the polarization ratio remains higher than 0.85 for bending angles < 100°.
5. Discussion and conclusion
To fabricate a low-loss elliptical DMHFs, thinner dielectric layers are preferable for two reasons. Firstly to avoid transmission peaks resulting from dielectric resonances; for the thicker layers, the dielectric layer thickness would need to be well controlled which is hard to achieve in an elliptical tube, whilst thinner layers have fewer resonances. Secondly, a thin layer effectively decreases the power distributed on the metal surface and thus can practically reduce loss resulting from roughness of the silver layer.
By using the liquid-flow method, the thickness of the dielectric layer inner coated in an elliptical tube was not uniform due to the surface tension of the coating, which was initially applied as a liquid. However elliptical DMHFs having uniform dielectric layers could be fabricated by using other methods, e.g. by inserting metallic-coated dielectric layer into a tube [13] or by coating a metallic layer outside a dielectric tube [15]. Another potential route is applying fiber drawing techniques. A macroscopic preform with internal structure similar to Fig. 1 but with a uniform dielectric layer, could be heated in a furnace and drawn down into a fiber. The dielectric layer thickness can be controlled by the drawing conditions such as draw speed and feed speed. This fabrication method will be pursued in future work.
In conclusion, an elliptical silver hollow fiber inner coated with a non-uniform COP layer was fabricated and characterized. The inner major and minor radii of the fiber were 1.4 mm and 0.5 mm respectively and the length was 90 cm. The COP layer was added to protect the silver layer from oxidation. The effect of the COP layer on the transmission loss and polarization maintenance was numerically and experimentally studied. The measured loss of the x-polarization and y-polarization were 3.8 dB/m and 6.2 dB/m at 0.87 THz, respectively. The fiber can maintain the linear polarization of the incoming light. The polarization ratio for the x-polarization and y-polarization are 95.4% and 96.7% respectively for a straight 90-cm long fiber when a Gaussian beam was launched. Bending effects on transmission loss and polarization maintenance were investigated. Experiment results showed that under certain bending conditions, the additional loss due to bending is low. Bending had a detrimental effect on the fiber’s ability to maintain the polarization when the bending angle is large. The fibers investigated showed a good compromise between loss, flexibility, and ability to maintain the polarization. Whilst it is difficult to reduce the transmission loss of elliptical DMHFs to that of circular DMHFs due to the difficulties in the dielectric coating of an elliptical tube, compared to the circular DMHFs the elliptical fibers do have advantages of better flexibility and the ability to maintain the polarization. As such, elliptical DMHFs have promising applications for THz technology.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants 61201062 and 11173015, Postdoctoral International Exchange Program jointly sponsored by China Postdoctoral Science Foundation and The University of Sydney, and theNational Basic Research Program of China (“973” Program) (No. 2014CB339800).
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