兆赫波為頻率介於高頻微波和遠紅外線之間的訊號，一般最常見的兆赫波波導為金屬波導及介質波導，但是由於金屬波導的肌膚效應和介電材料的高材料吸收損耗，導致兆赫波導的效益不佳。有鑑於此，我們提出一個結構簡單的空心管狀介質波導來達到低損耗之兆赫波傳輸。在本論文中，我們利用一個擁有完美匹配層的有限差分頻域法去分析我們所設計的兆赫波波導，由模擬結果可看出，此兆赫波導是利用反共振反射原理導波。而我們更利用共振腔原理計算出介質層的共振頻率，計算的結果和有限差分頻域法的模擬數值是相當吻合的。我們並且利用有限差分頻域法，藉由改變空氣孔洞的大小，將兆赫波導的傳輸損耗由原本10-3 cm-1 (0.0043 dB/cm)降低至10-4 cm-1 (4.34×10-4 dB/cm)，而利用改變介質層的厚度，我們可以設計寬頻譜兆赫波波導，由頻寬0.06THz 展延至0.13THz。

此外，我們更提出一個雙層的空心介質波導結構，我們分析其
外層介質厚度與材料對兆赫波波導侷限效應的影響。結果顯示，外層介質厚度提高將導致共振頻率點產生藍位移的現象，而介質厚度和共振頻率點位移的關係為 0.125GHz/μm。另一方面，我們發現外層介質的材料係數和共振頻率點位移的關係為指數遞減。這些計算結果顯示，我們所提出的空心介質管狀波導不僅可以有效地傳遞兆赫波，更可被應用在介質薄膜的感測器上。

In most terahertz (THz) systems, the propagation of THz signals relies on metal or dielectric waveguides which suffer from high conductivity losses caused by the skin
effect or dielectric losses resulted from the material absorption. Due to this reason, we propose and demonstrate a simple low-loss air-core tube strucutre for THz waveguiding. The simulation method we utilized is the finite-difference frequency-domain (FDFD) method with the perfectly matched layers (PMLs). The modal indices and propagation losses of the guided core modes on the THz tube waveguide are successfully obtained. The simulation results show that the guiding mechanism of the hollow tube waveguide is based on the antiresonant reflecting
optical waveguide (ARROW) model. We also utilize a Fabry-Perot resonantor model to find out the resonance frequencies of the dielectric layer, which match well with
the results of the FDFD method. By varying the core size, it is observed that the propagation losses are reduced when the core size is increased. The propagation losses can be reduced from 10-3 cm-1 (0.0043 dB/cm) to 10-4 cm-1 (4.34×10-4 dB/cm). In addition, we can use the thin dielectric layer to provide a broad transmission band
with Δf = 0.13THz.
We also propose a novel tube THz waveguide sensor. The influence of the thickness and material of the dielectric layer 2 are investigated. We can observe that the shift of the propagation loss peak is inversely proportional to the thickness of dielectric layer 2, which can be used as a thickness sensor with the sensing sensitivity being 0.125 GHz/μm. On the other hand, the index of the dielectric layer 2 and the position of the propagation loss peak are in an exponential relationship. These properties of the tube waveguide can be applied in the dielectric-film sensing.

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Numerical Method 13
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Finite-Difference Frequency-Domain Method . . . . . . . . . . . 13
2.3 FDFD Method with Perfect Matched Layers . . . . . . . . . . . . 17
2.4 Index Averaging Scheme . . . . . . . . . . . . . . . . . . . . 22
3 Numerical Results for Single-Layer Hollow THz Waveguides 27
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Air-Core THz Waveguide . . . . . . . . . . . . . . . . . . 27
3.3 Asymmetric Structure of Air-Core THz Waveguide . . . . . . . . . 31
4 Numerical Results for Double-Layer Hollow THz Waveguides 48
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Double-Layer Air-Core THz Waveguide . . . . . . . . . . . . . . 48
5 Conclusions 58
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