數種光波與兆赫波導波結構之有限差分數值研究

Finite-Difference Numerical Investigation of Several Optical and Terahertz Guided-Wave Structures

賴志賢(Chih-Hsien Lai)

指導教授 ： 張宏鈞

國立臺灣大學/電機資訊學院/光電工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.00725

摘要

本研究分析數種操作在光波與兆赫波頻率的導波結構，使用的數值工具為基於余式網格的有限差分頻域法與波束傳播法。在求解洩漏式波導的模態時，我們採用完美匹配層作為計算空間的邊界條件。研究結果顯示，完美匹配層的其中一項參數，即反射係數，對洩漏模態的分析有顯著的影響，而且該項參數的理想值比傳統所使用的數值小非常多。
我們提出一種適合兆赫波傳導的洩漏式結構，即管狀波導。它的結構相當簡單，僅是一個空心管子，具有一個很大的空氣核芯，管壁很薄，由均勻的低折射率介電材料所構成。我們分析管狀波導在兆赫波頻率的各種模態特性，包括計算不同參數（核芯直徑、管壁厚度、管壁材料折射率）下的模態指數與衰減常數。數值結果顯示，其核芯模態的導波機制是反共振反射。我們也畫出了管狀波導其基本模態與高階模態的模態分布，包括強度分布與電場向量分布；這些分布和傳統躍階折射率光纖的模態分布很相似。
我們接著分析在管狀波導外面鍍上金屬的效應。針對一維結構，即平板式管狀波導，研究結果指出橫向電場(TE)極化的衰減頻譜會平移半個週期，但是橫向磁場(TM)極化的頻譜不會移動。這是因為TE波的電場值在金屬與介電質介面的兩側必須連續，而TM波的電場值不必連續所造成。此一頻譜移動的現象，很適合作為兆赫波極化分離器的應用。針對二維結構，即圓形的管狀波導，研究結果顯示TE01模態的頻譜仍會平移半個週期，TM01模態的頻譜仍然保持不動。但是HE11與HE21模態的頻譜，週期則是變為原來的一半；因為它們具有TE和TM混合的性質。
同時我們也分析了二種兆赫波的耦合器。一種是由平板式的管狀波導所構成，另一種是由次波長的介電纖維所構成。在第一種兆赫波耦合器中，它的奇對稱系統模態在靠近反共振頻率的時候不穩定，使得這種耦合器無法像傳統光纖式耦合器一般使用。這個問題可以藉由在二個平板式管狀波導中間加入一層物質而解決。在第二種兆赫波耦合器中，當二根介電纖維的間距比較小的時候，奇對稱系統模態會出現截止，只剩下偶對稱系統模態會被傳導。此時在傳統光纖式耦合器中經常可以觀察到的系統模態之間的干涉現象，在這裡便不會發生。當介電纖維間距比較小時，x-極化偶對稱系統模態的場型分布，會遠比y-極化的場型分布來得集中；此一現象和槽型波導的行為很相似，並且導致二種極化的特性大不相同。由於以上這些特性，使得第二種兆赫波耦合器可以應用在諸如功率分配器與極化分離器等兆赫波元件。
本研究的最後一個部份分析幾種操作在光波頻率的導波結構，包括二種根據不同的脊狀波導而設計的極化轉換器，以及發生增益飽和的增益導波暨折射率反導波平板波導。增益飽和對後者的效應，藉由模擬其基本模態沿著波導傳播方向的變化，可以清楚的觀察出來。

關鍵字

兆赫波 ； 波導 ； 耦合器 ； 導波結構 ； 有限差分法

並列摘要

In this research several optical and terahertz (THz) guided-wave structures are analyzed using the Yee-mesh-based finite-difference frequency-domain (FDFD) method and beam propagation method (BPM). When solving leaky waveguide modes, the perfectly matched layer (PML) is employed as the boundary condition. Our results show that the reflection coefficient, which is one PML parameter, has a significant effect on leaky-mode analysis and its preferred magnitude is much smaller than the conventional values.
We propose a simple leaky structure for THz waveguiding, i.e., the pipe waveguide, which is a simple pipe with a large air core and a thin dielectric layer with uniform but low index. Modal characteristics of the pipe waveguide are investigated in the THz region, by calculating the modal indices and attenuation constants of the core modes for various core diameters, cladding thicknesses, and cladding refractive indices. Numerical results reveal that the guiding mechanism of the core modes is that of the antiresonant reflecting guiding. Moreover, modal patterns including modal intensity distributions and electric field vector distributions are shown for the fundamental mode and the higher order modes, and these patterns resemble those of the conventional step-index fiber.
Then, the effect of metallic coating on pipe waveguide is investigated. For the 1-D case, i.e., the slab-type pipe waveguide, numerical results indicate that the loss spectrum will shift half period for TE polarization, but will not for TM polarization. This is because the magnitudes of the electric field for TE waves must be continuous in both sides of the metal-dielectric interface; whereas for TM waves, the magnitudes can be different. Such spectral shift phenomenon is promising for the application of the THz polarization filter. For the 2-D case, i.e., the circular pipe waveguide, the spectrum of TE01 mode will shift half period and the spectrum of TM01 mode remains unmoved. While for the HE11 and HE21 modes, their period becomes one half owing to their hybrid nature (mixed TE and TM).
We also study two types of THz couplers. One is composed of two slab-type pipe waveguides and the other is composed of two subwavelength dielectric fibers. For the first type THz coupler, the odd system mode of the coupler is unstable near the antiresonant frequencies, which makes the coupler unable to be operated like the conventional fiber-optic ones. Adding an additional layer between the two slab-type pipe waveguides can solve this problem. For the second type THz coupler, when the fiber separation is small, odd-mode cutoff occurs and only the even system mode is guided. Thus the beating phenomenon usually observed in conventional fiber-optic couplers can not take place. The x-polarized even system mode has a more confined field distribution than that of the y-polarized one when the fiber separation is small, similar to the behavior of a slot waveguide, which leads to different attributes between the two polarizations. With these characteristics, the THz couplers might be applied to THz devices such as power dividers and polarization filters.
In the final part, behaviors of some optical guided-wave devices are investigated, including two different types of rib-waveguide based polarization convertors and the gain-guided and index-antiguided slab waveguide which is subject to gain saturation. The effect of gain saturation is observed from the propagation of the fundamental mode.

並列關鍵字

Terahertz ； Waveguides ； Couplers ； Guided-Wave Strucutre ； Finite-Difference Method

參考文獻

Chiu, C. M., H. W. Chen, Y. R. Huang, Y. J. Hwang, W. J. Lee, H. Y. Huang, and C. K. Sun, “All-terahertz fiber-scanning near-field microscopy,” Opt. Lett., vol. 34, pp. 1084-1086, 2009.

Chen, H. W., C. M. Chiu, C. H. Lai, J. L. Kuo, P. J. Chiang, Y. J. Hwang, H. C. Chang, and C. K. Sun, “Subwavelength dielectric-fiber-based THz coupler,” J. Lightwave Technol., vol. 27, pp. 1489-1495, 2009.

Lai, C. H., Y. C. Hsueh, H. W. Chen, Y. J. Huang, H. C. Chang, and C. K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett., vol. 34, pp. 3457-3459 2009.

Litchinitser, N. M., S. C. Dunn, B. Usner, B. J. Eggleton, T. P. White, R. C. McPhedran, and C. Martijn de Sterke, “Resonances in microstructured optical waveguides,” Opt. Express, vol. 11, pp. 1243-1251, 2003.

Köhler, R., A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Lotti, and F. Rossi, “Terahertz semiconductor- heterostructure laser,” Nature, vol. 417, pp. 156-159, 2002.