Design and optimization of low-loss high-birefringence hollow fiber at terahertz frequency

Xiao-Li Tang; Bang-Shan Sun; Yi-Wei Shi

doi:10.1364/OE.19.024967

1. Introduction

Polarization maintenance is one of the most crucial issues in terahertz (THz) polarization-sensitive systems, e.g. polarization-sensitive THz time-domain spectroscopy [1, 2]. High-birefringence fiber delivers the x-polarized mode and the y-polarized mode with different propagation constants, thus maintaining the polarization of the incoming light [3]. Up to now, there are a few reports on high-birefringence THz fibers, such as plastic photonic crystal fiber [4], air-core band-gap fiber [5], porous fiber [6–9], and polymer tube [10, 11]. Non-circular cross section is normally introduced in the fibers to achieve high birefringence. Cho et al. [4] demonstrated a modal birefringence of ~2.1×10⁻² for a plastic solid-core photonic crystal fiber. However the propagation loss was as high as 400dB/m at 1THz because a large part of power was transmitted in the absorbing solid core. To avoid the high material absorption in the solid core, Ren et al. [5] proposed an air-core polarization maintaining THz fiber. The band-gap effect repels the modal power from the absorbing polymers, resulting in a significant suppression of the material absorption. Nevertheless, the modal birefringence was relatively low in the order of 10⁻³. Recently, porous fiber was suggested as a novel THz fiber by two research groups [12, 13]. Porous fibers with rectangular air holes [6, 7], elliptical air holes [8], and super-cell structures [9] have been designed to achieve high birefringence. It was demonstrated that the fabrication techniques for these fibers were complicated and transmission losses were still high due to the material absorption. More recently, Chen et al. [10] and Wang et al. [11] reported a high-birefringence THz fiber of simple structure, a polymer tube with an elliptical cross section. A low absorption loss was achieved since a large part of the power was guided in the air. Nevertheless, the fiber is weak to the environmental disturbance because modes coupled strongly to the cladding environment.

Dielectric-coated metallic hollow fiber (DMHF) is one of the most attractive means of delivering terahertz waves [14–16]. This type of fiber usually has a metallic film of silver (Ag) and a single dielectric film of polystyrene (PS), cyclic olefin polymer (COP), or polyethylene (PE) on the inner wall. A low loss of 0.95 dB/m at the wavelength of 119 μm (2.5 THz) was obtained for the 2 mm bore 90-cm-long polystyrene (PS)-coated silver hollow glass fiber [15]. Circular cross sectional DMHF is the most common configuration used to date. However, circular cross sectional hollow fibers do not preserve polarization to any appreciable degree [17, 18]. By going to square and rectangular cross section fibers, Gibson and Harrington [19] showed that the fiber obtained the ability to preserve the polarization of a polarized CO₂ laser light. However, there are few reports on the polarization-preservation ability of DMHF in THz region.

In this paper, an elliptical cross section is introduced into the design of DMHF to attain modal birefringence up to the order of 10⁻². The elliptical cross section is chosen since the fabrication is expected to be easier than the rectangular ones, whose corners are very difficult to maintain during the fabrication [7, 19]. We first present the structure of an elliptical DMHF and investigate the transmission characteristics, including the attenuation, modal birefringence, and the modal confinement in the air core. We then study the optimization of the fiber geometry to reduce the attenuation and to increase the modal birefringence. Numerical results predict that modal birefringence of 3.3×10⁻² and simultaneously attenuation of 2.4 dB/m can be achieved with a 1.8 mm × 0.6 mm elliptical DMHF at 1 THz.

2. Fiber structure

A DMHF typically consists of a reflective metallic layer and a reflection-enhancing dielectric layer deposited on the inner wall of a hollow substrate, as shown in Fig. 1 . Elliptical cross section is designed to attain high modal birefringence B, where B = |n_effx-n_effy|. n_effx and n_effy are the effective refractive indices of the x- and y-polarized HE₁₁ modes, respectively. The main parameters to characterize the fiber structure are the inner major radius a, the inner minor radius b, the thickness of the dielectric layer d, and the thickness of the metallic layer s. Low-loss property can be attained at a target wavelength λ by an optimized dielectric film thickness d given by [20]:

d = \frac{λ}{2 π \sqrt{n^{2} - 1}} \arctan (\frac{n}{\sqrt[4]{n^{2} - 1}}),

where n is the reflective index of the dielectric layer. In Eq. (1) the dielectric layer is assumed to be free of absorption. We have reported that the optimum dielectric layer thickness becomes smaller with the presence of the dielectric absorption [21]. Throughout the paper, n is chosen to be 1.5, which is a typical value for most polymers in the THz region. The air is assumed to be lossless with refractive index of 1. The metallic layer is Ag, which is often used in the fabrication of DMHF. s is chosen to be 1 μm because the thickness is experimentally attainable by wet chemistry [15] and it is much thicker than the skin depth in the frequency region [22]. Optical constants of silver are obtained from the literature [22]. A full-vector finite-element method (FEM) is employed to conduct the calculations.

Fig. 1 Schematic cross section of an elliptical

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Single-mode DMHF with small diameter has high attenuation. Large-bore hollow fiber has low attenuation. However, it results in multi-mode propagation. The power coupling efficiency of the incident beam to the m-th mode of the fiber can be expressed by [23]:

η_{m} = \frac{{| \int_{S} E^{i} \times H_{m}^{*} \cdot \hat{z} d S |}^{2}}{\int_{S} E_{m} \times H_{m}^{*} \cdot \hat{z} d S \cdot \int_{S_{\infty}} E^{i} \times H^{i} \cdot \hat{z} d S},

where Eⁱ and Hⁱ are the electric field and the magnetic field of the incident beam. E_m and H_m are the electric field and the magnetic field of the m-th mode. S and S_∞ denote the integration over the air-core region and the infinite plane transverse to the fiber axis z. Most of the coherent THz sources emit a linearly polarized Gaussian beam. A Gaussian beam focused to a 1/e² waist ω₀ and linearly polarized along the x-axis can be expressed by:

E^{i} (x, y) = E_{0} e^{- \frac{x^{2} + y^{2}}{ω_{0}^{2}}} \hat{x},

Figure 2 shows the calculation results of power coupling efficiencies for the first few modes in an elliptical DMHF at 1THz. The structural parameters of the fiber considered are a=800 μm, b=400 μm, and d=39 μm. It is seen that the HE_11X mode and the HE_11Y mode have much higher coupling efficiency than the other modes. The highest coupling efficiency for the HE_11X mode and the HE_11Y mode are 93% and 92.7% when $ω_{0} / \sqrt{a b} = 0.65$ . Single-mode propagation is possible in a large-diameter fiber if the input field is properly launched [24].

Fig. 2 Power coupling efficiencies for the first few modes in an elliptical DMHF at 1THz as a function of the spot size to core size ratio $ω_{0} / \sqrt{a b}$ .

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Analogous to the pipe waveguides [25], an elliptical DMHF has two types of confined modes: the cladding modes and the core modes. Figure 3 shows the normalized z-component power flow and the electric field vector distributions for the cladding HE₁₁ mode and the core HE₁₁ mode. Figure 3(a) and Fig. 3(b) are the cladding modes, whose power is largely located inside the cladding region. The cladding modes attenuate rapidly due to the high material absorption. These modes are guided by total internal reflection, with the fiber itself acting as a high index core and the surrounding air behaving as the low index cladding. Figure 3(c) and Fig. 3(d) are the core modes. Since the power is mainly confined inside the air core, the core modes have less material absorption losses than the cladding modes. The guiding mechanism is similar to that of the antiresonant reflecting optical waveguide (ARROW) [26]. Core modes are leaky because the refractive index of the core is less than that of the cladding. In this work, only the characteristics of the fundamental core modes (the HE_11X mode and the HE_11Y mode) are investigated.

Fig. 3 Normalized z-component power flow and electric field vector distribution for (a) the cladding HE_11X mode at 1.88 THz, (b) the cladding HE_11Y mode at 0.69 THz, (c) the core HE_11X mode at 2 THz, and (d) the core HE_11Y mode at 2 THz. The power flow is presented by the colors and the electric field is presented by the arrows.

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3. Transmission characteristics

Structural parameters of the fiber considered in this section are a=800 μm, b=400 μm, and d=39 μm. Attenuation of the HE_11X mode and the HE_11Y mode from 0.8 to 4 THz are shown in Fig. 4(a) . In Fig. 4(a), the dielectric is assumed to have a frequency-independent absorption with an extinction coefficient of 4.8×10⁻⁴ throughout the frequency region. The two polarized modes have different attenuation valleys but almost the same attenuation peaks. The attenuation spectrum of the elliptical DMHF is periodic owing to the dielectric layer, which can be viewed as a Fabry-perot etalon [25–27]. The wave enters the dielectric layer and undergoes multiple reflections. When the reflected beams are in phase, constructive interference occurs. This causes the core modes to appear with the waves bouncing back and forth inside the core region. On the other hand, if the reflected beams are out of phase, destructive interference occurs. This case corresponds to the attenuation peaks in Fig. 4(a), when fields could hardly exist inside the core region. Although the results are not shown in this paper, we examined DMHFs of different core sizes and different ellipticities (a/b=1, 2, 3, and 4) but with the same dielectric layer thickness. We found that the fibers have the same resonant frequencies. The resonant frequencies, which can be used to locate the transmission windows, depend on the layer thickness d and the dielectric reflective index n [27, 28]. It was demonstrated that the material absorption does not affect the positions of the resonant frequencies [27]. However, the material absorption brings additional loss. The absorption values of polymers differ due to the variability of polymer chain length and cross-linking. Taking High Density Polyethylene (HDPE) for an example, it values ranging from ~0.15 cm⁻¹ [29] to ~2.0 cm⁻¹ [30] at 1THz. Figure 4(b) shows the attenuation constants of the two polarizations in DMHF as a function of the absorption coefficient at 1THz. The attenuation curves for an Ag-only coated hollow fiber are also shown for comparison. The inner major radius and the inner minor radius of the Ag-only coated hollow fiber are 839 μm and 439 μm, respectively. Although the dielectric layer can effectively enhance the reflectivity, it brings additional loss due to its absorption. The attenuations increase as the absorption coefficient becomes larger. The attenuation of the DMHF is equal to that of the Ag-only coated hollow fiber when the dielectric absorption coefficient is 0.6 cm⁻¹ and 0.3 cm⁻¹ for the x- and the y-polarization, respectively. It means that polymers with absorption coefficient larger than 0.6 cm⁻¹ is not suitable for inner coating in the case considered in Fig. 4. The absorption tolerance for the polymer is dependent on the dielectric refractive index and the core size of the hollow fiber. Increased core size makes a larger absorption tolerance for the polymers [21].

Fig. 4 (a) Attenuation spectra for the HE_11X mode and the HE_11Y mode from 0.8 to 4 THz. (b) Attenuation constant of a DMHF as a function of the absorption coefficient at 1THz. Attenuation of an Ag-only coated hollow fiber is shown for comparison.

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Effective refractive indices of the HE_11X mode and the HE_11Y mode are shown in Fig. 5(a) . The frequency region from 1.5 to 4 THz is enlarged in the inset to clearly show the values in the resonant regions. The refractive indices for the two polarizations are less than 1 and tend to increase with the frequency except in the resonant regions. The group velocity is important for the propagation of electromagnetic pulses that are often used in the THz region. The group velocity can be expressed as:

v_{g} = \frac{C}{n_{n e f f} + ω \frac{\partial n_{n e f f}}{\partial ω}},

where C, n_eff, and ω are light velocity in vacuum, effective refractive index, and angle frequency, respectively. Figure 5(b) shows the group velocities of the two polarizations as a function of the frequency. The shadows in Fig. 5(b) indicate the frequency regions where the HE_11X attenuation is smaller than 2dB/m. It shows that small group velocity dispersion can be achieved in the low-loss transmission windows.

Fig. 5 (a) Effective refractive indices and (b) group velocities of the HE_11X mode and the HE_11Y mode.

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The modal birefringence of the fiber can be explained by the electric field boundary conditions. The difference of the electric field distributions between the two polarized modes can be seen in Fig. 3. The electric field of the HE_11X mode is normal to the boundaries at the left and right sides of the air core. According to the electric field boundary conditions, the electric field in the air core at those boundaries is prominently reduced by the refractive index contrast between the air and the dielectric. Similarly, the electric field of the HE_11Y mode in the air core is suppressed at the top and bottom boundaries. The intensity disparity around the interface is more significant for the HE_11Y mode due to the longer effective boundary and thus results in the difference of the effective refractive indices between the two polarizations. Figure 6 presents the modal birefringence as a function of the frequency. The peaks of the modal birefringence occur at the resonant frequencies. By comparing Fig. 6 with Fig. 4(a), it is seen that the fiber tends to have higher birefringence but also higher attenuation at lower frequencies. The shadows in Fig. 6 indicate the frequency regions where the HE_11X attenuation is smaller than 2dB/m. The proposed fiber shows a great promise to achieve high birefringence and low attenuation simultaneously over a wide frequency region. At 1THz particularly, the modal birefringence is 1.36×10⁻² and the attenuation is as low as 1.5dB/m.

Fig. 6 Modal birefringence of the hollow fiber as a function of the frequency. The core-size of the fiber is a=800 μm and b=400 μm.

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To avoid the influence of the highly absorbing materials in the THz region, an effective fiber design should maximize the guided power fraction in the air, because dry air is nearly lossless for THz wave propagation. Figure 7 shows the power ratio of the HE_11X mode in the air core. The power fraction in the air core is obtained according to the equation:

η = \frac{\int_{c o r e} S_{z} d A}{\int_{t o t a l} S_{z} d A},

where “core” and “total” indicate integration over the air-core region and the entire fiber cross section. S_z is the time-averaged z-component Poynting-vector. In the most part of the frequency region, the HE_11X mode has a very high power ratio (up to 99.9%) in the air core due to the high reflectivity of the metal layer. The ratio is much higher than that of the other high-birefringence THz fibers, such as elliptical-hole terahertz fibers (~50%) [8], super-cell structure fibers (~35%) [9], and the polymer tubes (~30%) [11]. The tightly confined light in the hollow core not only ensures the low-loss propagation but also greatly enhances the ability to resist environmental disturbance.

Fig. 7 Power ratio in the air core of the HE_11X mode.

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4. Optimization of the fiber geometry

Optimization of the fiber geometry is investigated considering both birefringence and attenuation properties. The HE_11X mode is analyzed in this section because the attenuation for the HE_11X mode is smaller than that of the HE_11Y mode. In this section, d is taken to be 39 μm at the wavelength of 300 μm. The extinction coefficient of the dielectric layer is assumed to be 4.8×10⁻⁴. Firstly, optimization in terms of the air-core ellipticity (a/b) is investigated. a/b from 1 to 9 is considered. Note that the disadvantage of any elliptical fiber with a large ellipticity is that it can be bent only along a preferred axis. Figure 8(a) is the modal birefringence as a function of the ellipticity with various values of b. All curves exhibit maximum value around a/b=3, and larger-bore fiber has smaller birefringence. Figure 8(b) is the attenuation for the HE_11X mode as a function of the ellipticity with various values of b. The attenuation decreases rapidly with the increase of the ellipticity in the region of a/b<3 while it remains almost constant in the region of a/b>3. It can be concluded that a desirable value of a/b is around 3, both for high modal birefringence and low attenuation. It is also shown that small bore fiber has strong birefringence but high attenuation.

Fig. 8 (a) Modal birefringence and (b) attenuation for the HE_11X mode as a function of a/b.

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To study the mechanism for Fig. 8, we examine the power distribution for the HE_11X mode and the HE_11Y mode with various ellipticity. The case of b=300 μm is considered and the power distributions are presented in Fig. 9 . Since b is fixed at 300 μm, the power distributions along the y-axis are almost the same for various ellipticities, as shown in Fig. 9(a) and Fig. 9(b). On the other hand, the power distribution along the x-axis extends with the increase of the ellipticity, as shown in Fig. 9(c) and Fig. 9(d). Hence the mode areas for both of the two polarizations change from near-round shape to near-elliptical shape as the ellipticity increases. The variation of the mode area together with the change of the fiber cross section results in the change of the effective boundaries. For the HE_11X mode, the effective boundaries (at the left and the right sides of the air core) decrease with the increase of the ellipticity. While for the HE_11Y mode, the effective boundaries (at the top and the bottom sides of the air core) increase as the ellipticity increases. We note that the influence of the ellipticity on the mode area becomes weak with the increase of the ellipticity, as shown in Fig. 9(c) and Fig. 9(d). The boundary conditions become less influential on modal birefringence with the increase of the ellipticity because less energy is distributed along the boundaries. This explains the maximum value for the modal birefringence around a/b=3. The power distributions also explain the attenuation properties in Fig. 8(b). A larger part of the power propagates in the metallic and the dielectric layers in the fiber with a smaller ellipticity, which causes a higher attenuation. As the power ratio in the cladding layer becomes smaller and stable with the increase of the ellipticity, the attenuation becomes stable. Figure 9 also shows that the HE_11X mode and the HE_11Y mode exhibit near-Gaussian field shape at the air-core region. It indicates that the HE_11X mode and the HE_11Y mode have potentially high couple efficiencies with a Gaussian beam.

Fig. 9 Distributions of the normalized power flow along x-axis and y-axis for various ellipticities. (a) HE_11Y mode along y-axis, (b) HE_11X mode along y-axis, (c) HE_11Y mode along x-axis, and (d) HE_11X mode along x-axis. The dotted lines indicate the positions of the air/dielectric boundaries. In Fig. 9(c) and Fig. 9(d), the dotted lines from the left to right correspond to the cases of a/b = 1, 2, 3, 4, 5, 6, 7, 8, and 9. The polarizations and the investigation positions are also shown at the top right corner. λ is 300 μm.

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The dependence of the modal birefringence and the attenuation on the fiber core size is investigated and presented in Fig. 10 . The core size, which is characterized by $\sqrt{a b}$ , is normalized at different wavelengths by $\sqrt{a b} / λ$ . The dotted data are the numerical results and the expressions for the curves are given in the figure. It is observed that both the attenuation and the modal birefringence decrease with the increase of the core size. The structure parameters should be carefully selected for fiber with both low attenuation and high birefringence. The curve fitting in Fig. 10 shows that both birefringence and attenuation are proportional to ${(\sqrt{a b})}^{- 3}$ . The ${(\sqrt{a b})}^{- 3}$ effect of the attenuation is analogue to the well known A∝r⁻³ property of the circular DMHF, where A is the attenuation and r is the inner radius [20]. We have shown the dependence of attenuation and modal birefringence on the wavelength for a non-scaled DMHF in Fig. 4(a) and Fig. 6. Here, we examine the wavelength dependence for DMHF with core size scaled according to the wavelength. Note that different values of d are used in the simulations at different wavelengths according to the Eq. (1). Inset in Fig. 10(a) is the modal birefringence as a function of the wavelength for $\sqrt{a b} / λ = 2 \sqrt{3}$ and $\sqrt{a b} / λ = 3 \sqrt{3}$ . It is interesting to find that the modal birefringence is not dependent on the wavelength when $\sqrt{a b} / λ$ is a constant. However the attenuation shows dependence on wavelength as seen in Fig. 10(b). For the case of $\sqrt{a b} / λ = 2 \sqrt{3}$ , the attenuation is 0.73 dB/m and 0.39 dB/m at the wavelength of 100 μm and 300 μm, respectively. This phenomenon is consistent with the attenuation property of the circular DMHF, whose losses are inversely proportional to the wavelength at a certain r/λ [20].

Fig. 10 (a) Modal birefringence and (b) attenuation for the HE_11X mode as a function of the normalized core size ( $\sqrt{a b} / λ$ ). The dotted data are the numerical results and the expressions for the curves are given in the figure. The inset in Fig. 10(a) is the modal birefringence as a function of the wavelength. a/b = 3.

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At last, elliptical DMHF with multiple dielectric layers is numerically investigated. Refractive index profile of a five-layer elliptical hollow fiber is shown in Fig. 11 . n₁ and n₂ are the low and high refractive indices of the dielectrics. Larger contrast for n₁ and n₂ is preferable to reduce attenuation [20]. d₁ and d₂ are the thickness of the low-index and high-index dielectrics. It has been well proved both theoretically and experimentally that multiple dielectric layers can greatly enhance the reflectively thus reducing the attenuation [31, 32]. Figure 12 shows the attenuation and modal birefringence as a function of the layer number for elliptical DMHF with inner major radius of 900 μm and inner minor radius of 300 μm. n₁ and n₂ are 1.5 and 3, respectively. Although pure polymers seldom have THz refractive indices above ~2, higher refractive index can be achieved in polymer compounds [33, 34].To attain low attenuation, the thickness of dielectric layer adjacent to the air core is designed according to Eq. (6) and the other layer thicknesses satisfy the Eq. (7) [20].

Fig. 11 Refractive index profile of a five-layer elliptical DMHF along x-axis.

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Fig. 12 (a) Attenuation and (b) modal birefringence for multilayer elliptical DMHF as a function of the number of the dielectric layers. The attenuation and modal birefringence of the Ag-only coated hollow fiber are shown for comparison.

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d = \frac{λ}{2 π \sqrt{n_{1}^{2} - 1}} \arctan [\frac{n_{1}}{\sqrt[4]{n_{1}^{2} - 1}} {(\frac{n_{1}}{n_{2}})}^{m_{p}} {(\frac{n_{1}^{2} - 1}{n_{2}^{2} - 1})}^{- m_{p} / 2}], (m_{p} = 0, 1, \dots, 7) .

d_{i} = \frac{λ}{4 {(n_{i}^{2} - 1)}^{1 / 2}}, (i = 1, 2) .

Here m_p is an expression for the total number of the dielectric layers, which is given by l=2m_p+1. The attenuation and modal birefringence of the Ag-only coated hollow fiber are also shown in Fig. 12 for comparison. The core size of the Ag-only coated hollow fiber is equal to the distance of the metal layer in the corresponding multilayer DMHF, which means that the core size of the Ag-only coated hollow fiber increases with the increasing total thickness of the dielectric layers. It is seen that a significant reduction of the attention can be achieved by coating multiple dielectric layers. Attenuations for the HE_11X mode and the HE_11Y mode decrease exponentially with the increase of the layer number. At the same time, only a small change of the modal birefringence in the DMFH is observed when the layer number increases as shown in Fig. 12(b). The modal birefringence of the DMHF is much higher than that of the corresponding Ag-only coated hollow fiber. It indicates that the multilayer structure is a promising way to low-loss and high-birefringence fibers. However, the result is based on the assumption that the dielectrics are free from absorption. Practically, the incorporation of additives in order to increase the dielectric refractive index normally significantly increases the absorption loss [33, 34]. For a three-layer DMHF considered in Fig. 12, the absorption tolerance for the higher-index dielectric is ~0.5 cm⁻¹ when the absorption coefficient of the lower-index dielectric is 0.2 cm⁻¹. Same as the case of single-layer DMHF, the absorption tolerance is dependent on the dielectric refractive index and the core size.

5. Conclusion

In conclusion, elliptical DMHF is studied for low-loss and high-birefringence properties at THz frequencies. The transmission spectrum of the elliptical DMHF is periodic owing to the dielectric layer which can be viewed as a Fabry-perot etalon. The birefringence of the fiber is attributed to the different lengths of the effective boundaries between the two polarized modes. The fiber exhibits a nearly perfect power confinement (up to 99.9%) in the air core because of the high reflectivity of the inner coatings. Optimization of the fiber geometry is also investigated. A desirable ellipticity of the air core is found to be around 3, both for the high birefringence and the low attenuation. Numerical results predict that modal birefringence of 3.3×10⁻² and simultaneously attenuation of 2.4 dB/m can be achieved with a 1.8 mm × 0.6 mm elliptical DMHF at 1 THz. Calculated results show that both the modal birefringence and the attenuation are proportional to ${(\sqrt{a b})}^{- 3}$ . With regard to the wavelength dependence, the modal birefringence is constant at different wavelengths for the fiber with a constant normalized core size $\sqrt{a b} / λ$ . While the attenuation is lower at a longer wavelength. Increasing the number of the dielectric layers effectively reduces the attenuation with little influence on the modal birefringence. Although material absorption has obvious influence on the fiber attenuation, it does not affect the modal birefringence. Like other fibers with air cores, the elliptical DMHF is promising in their spectroscopic and sensor applications. The hollow core offers the possibility of putting an analyte directly into the fiber, thus dramatically increasing the sensitivity. Elliptical DMHF has potential applications including polarization-maintaining THz fiber, THz sensor, and THz filter.

We are also preparing to fabricate an elliptical DMHF. Polycarbonate (PC) capillary was chosen as the supporting tube, because PC capillary demands lower temperature to be reshaped. A 1.5-mm-bore circular PC capillary was sandwiched in between two glass plates. The distance between the plates was adjustable according to the desired ellipticity. The PC capillary together with the glass plates were heated to the temperature of 192°C when the PC capillary was soften and reshaped. Silver and dielectric layers are inner-coated by using liquid-phase coating techniques. There are several challenges to fabricating DMHF for the THz wave transmission, such as much thicker silver and dielectric layers comparing to the MIR DMHF, uniform elliptical cross-section, and longer hollow fiber. Thicker inner layers introduce larger surface roughness. Nevertheless the surface roughness has less effect on the attenuation at THz frequencies because of the longer wavelengths. Perturbations to the ellipse cause coupling of the HE_11X mode to the higher loss HE_11Y mode. It is also possible to form an elliptical PC preform by using the extrusion method [7, 35]. Then glass-draw method can be used to fabricate longer elliptical capillary. It is still a challenge to control the ellipticity during the drawing process.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (60971014) and Talented Graduate Student Foundation of Fudan University.

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Design and optimization of low-loss high-birefringence hollow fiber at terahertz frequency

Abstract

Corrections

1. Introduction

2. Fiber structure

3. Transmission characteristics

4. Optimization of the fiber geometry

5. Conclusion

Acknowledgement

References and links

Cited By

Figures (12)

Equations (7)

Optics Express