臺灣博碩士論文加值系統

隙環共振器在週期性排列的狀態下受外來電磁波影響，會在其共振頻率附近產生負值的等效磁導率，基於此特殊電磁特性又被稱為磁子。其在適當的安排下與週期性的細金屬線陣列作結合，能在某特定頻段產生負折射的現象，而此形式的複合材料又稱超穎材料，同時負折射特性又稱左手系材料。然而負磁導率只存在於隙環共振器之共振頻率附近的一小段頻率區間內，意即隙環共振器主導整各超穎材料的左手頻帶位子。基於此特殊的電磁特性，其應用正被廣泛研究與開發中，如天線、超稜鏡、隱形…等。SRR 基本構型的被動性與靜態性限制其本身的商業價值，在工業上，材料的可調性對於設計與應用方面一直是高度需求的，是以可調式的隙環共振器的發展勢在必行。針對可調式隙環共振器之研究，現有的可調式隙環共振器（VLSRR）的方式乃使用外載一可調電容的方式，嘗試改變係環共振器等效電路的電容值，唯其1.0GHz的可調範圍仍待改善。
本研究主要針對隙環共振器的各項參數進行模擬驗證（包含尺寸大小、環隙間距、基板介電常數與基板厚度），藉由比較四種SRR 以找出最佳的調控因子與調控結構，並改良先前的設計。研究中利用ANSOFT 模擬軟體模擬改變基板的介電常數去達到調控隙環共振器之共振頻率的方法，能達到較VLSRR 數倍的可調頻率範圍，相較下，調變基板厚度與環隙間距之效果較差。當基板介電常數在越低的值變化，對共振頻率的偏移越敏感，亦即基板的ε從1~10 變化的可調範
圍遠大於基板的ε從10~20 變化，而液晶材料提供較合適的特性。在構型方面，在比較SRR、SRRs、MSRR 與Cut-Wire Pairs 四種常見之隙環共振器的構型後，Cut-Wire Pairs 的構型提供較佳的可調性，此外隨著尺寸的縮小，共振頻率偏移範圍會增加。結合Cut-Wire Pairs 與液晶的SRR 結構，討論不同的極化軸變化，發現最大可達1.16GHz 的調變區間，這是現有VLSRR 的兩倍，數值模擬的結果
顯示存在負磁導率的頻率區段同樣可達近乎1.16GHz 的調變區間。最後，本文的討論對於日後嘗試設計可調式SRR 提供了一參考依據。

The periodic split-ring resonator (SRR), magnetic atom, array have negative effect permeability near the resonance frequency when surrounding by external electromagnetic wave. Metamaterial(MTM) which has negative refractive index
materials, so called Left-Hand Material (LHM), within negative dielectric permittivity and negative magnetic permeability in some frequency ranges is structured by
periodic thin wire and SRR array. However, SRR dominates the negative refractive index frequency of MTM due to the narrow negative permeability frequency ranges rather than negative permittivity frequency ranges. In the past few years, new developments and applications of SRR have been studied extensively, one much-debated example is the concept of a perfect lens that enables imaging with
sub-wavelength image resolution, and the else like applications of antenna, filter, cloaking…etc. Tunable properties of materials are highly desirable in applications and designs of industry , the trend of tunable SRR will increase its worth and break the limit of traditional SRR（passive and static）. Existent tunable SRR, varactor-loaded split-ring resonator (VLSRR), change the effective capacitance of effective circuit by
tuning the voltage of varactor in the gap of SRR, has 1.0GHz shifted resonance frequency.
This paper is a numerical study of the effect of substrate properties and structure parameters on the effective properties of a metamaterial slab, we attend to find the factor and structure with wider tunable range, and then promote the design before. In our study, extracting the effective permeability and S parameter by the soft ANSOFT HFSS using finite element method, we got the wider tunable range by tuning the dielectric permittivity of substrate. As the dielectric permittivity of substrate varied in lower value, the variation of shifted resonance frequency become more bigger. In the aspect of structure, Cut-Wire Pairs provide the best tunablity rather than SRR, SRRs, and MSRR. The range of shifted resonance frequency increase when scale down. We combined the Cut-Wire Pairs and nematic liquid crystal with ferroelectric nanoparticles, our result show that the maximum tunable range 1.16GHz is ten times the traditional tunable SRR based on nematic liquid crystal. Then the numeral
simulation show that the negative permeability shifted between the same frequency interval. If we combined the suitable thin wire array, we get the tunable MTM or
tunable LHM.Finally, the result of our discuss provide a reference for design tunable SRR.

目錄
中文摘要 ..........................................................Ⅰ
ABSTRACT........................................................Ⅱ
誌謝...............................................................Ⅲ
目錄...............................................................Ⅳ
圖目錄............................................................Ⅵ
符號說明..........................................................Ⅷ
第一章 緒論........................................................1
1.1 前言..........................................................1
1.2 超穎材料（METAMATERIAL，MTM）簡介..........................1
1.3 文獻回顧......................................................3
1.3.1 隙環共振器討論............................................3
1.3.2 可調式設計討論............................................4
1.3.3 相關應用與設計............................................4
1.4 本文架構......................................................5
第二章 數值方法...................................................11
2.1 前言.........................................................11
2.2 有限元素法...................................................11
2.2.1 有限元素法之推導.........................................11
2.2.2 邊界條件.................................................12
2.3 等效介質.....................................................13
2.4 傳遞矩陣法（TRANSFER MATRIX METHOD，TMM） .................13
2.5 反推萃取法...................................................20
第三章 隙環共振器（SPLIT-RING RESONATOR，SRR） ....................24
3.1 隙環共振器的種類.............................................24
3.2 模擬條件設定.................................................25
3.3 影響因子.....................................................26
3.3.1 結構參數影響.............................................27
3.3.2 材料參數影響.............................................29
第四章 添加可調介電材料之隙環共振器...............................37
4.1 可調介電材料.................................................37
4.2 非等向性介電基板之SRR ......................................38
4.3 焦電材料基板之SRR ..........................................39
4.4 添加液晶之SRR ..............................................39
第五章 結論與討論.................................................50
5.1 綜合結論.....................................................50
5.2 未來展望.....................................................50
參考文獻..........................................................51

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