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姓名	楊棕仁(Zong-Ren Yang)  查詢紙本館藏	畢業系所	光電科學與工程學系
論文名稱	微環形共振腔非線性效應與壓縮光之研究 (Theoretic study of nonlinear effect and squeezed light in micro-ring resonators)
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摘要(中)	相較於傳統的金屬電纜，矽光子技術使用光線作為資訊載體，具有低損耗與高頻寬的優點，符合資訊產業大量資料傳輸的需求。在生醫檢測、神經網路、量子資訊等領域上也有矽光子可以發揮的空間。在矽光子技術發展中，微環形共振腔是其中一個重要光學元件，在做為線性元件時能做為調變器、感測器、開關、濾波器。在作為非線性元件時，微環形共振腔利用非線性轉換產生之光學梳，可用來做為波長分波多工(WDM)系統中的光源，取代傳統使用的分散回饋(Distributed Feedback, DFB)雷射二極體陣列。微環形共振腔所建構之非線性轉換，也可應用於量子光路中做為單光子光源。 本論文以氮化矽波導製成的高品質因子微環形共振腔為研究目標，並以LLE(Lugiato-Lefever equation)模型為理論基礎進行模擬分析，討論分別於零色散、正常色散、異常色散條件下所形成的非線性現象，諸如光孤子、暗孤子、Turing rolls等，並由光學梳轉換效率、產生機制、光學梳間隔等方面分析各個非線性現象於應用面的優劣。 第二部分在既有的LLE模型中引入模態交互作用。此模態交互作用可以利用雙環形波導(dual ring)設計、不同極化模態、高階模態耦合以及反向散射的方式產生。在正常色散裡，模態交互作用能夠在局部模態上造成等效異常色散，促使調變不穩定性(modulational instability)發生，在共振腔裡產生光學梳。由於多數非線性材料在紅外光譜屬於正常色散，模態交互作用將能增加微環形共振腔在波導結構與材料選擇的多樣性。針對共振腔的工作範圍，我們透過特徵值分析得到模態交互作用造成的模態增益，並計算出調變不穩定性的發生閥值，由此閥值得知光學梳只會在一部分的輸入光功率範圍內出現。因為光學梳是產生自正增益，與光孤子、暗孤子相較不會有初始電場的要求，能夠作為穩定的光源。在光場數值模擬中，模態交互作用不影響光學梳的頻率轉換效率，在高失諧的區域裡，光學梳的產生閥值受到雙穩態區域的影響，在文中有更多的介紹。 第三部分藉由半經典LLE模型(semi classical model)，得到在低於光學梳產生閥值時旁頻帶上(sideband)的自發輻射(spontaneous emission)光譜，光譜將可用於確保在微環形共振腔在作為量子光路的光源時，光子確實源自自發輻射。在高於光學梳產生閥值時，受激發射(stimulated emission)產生壓縮光光譜，經過比較後得知在此氮化矽微環形共振腔中Turing rolls能夠做為壓縮光的光源。而壓縮程度則隨著光譜頻寬增加而減少。
摘要(英)	Optical communication using light as the carrier signal has advantages of high-speed transmission because of the low propagation loss and high bandwidth. It has been widely used in datacenters and submarine cables for long distance telecommunications. Recently, the development of silicon photonics technology helps to integrate optical elements, such as light sources, modulators, and receivers, together on a single silicon chip, providing a compact, low-power system for optical communications. Micro-ring resonator (MRR) is one of the most applied optical components in silicon photonics. In linear optics, MRRs can be used for signal modulating, bio-sensing, and optical logical operation. In nonlinear optics, broadband frequency combs delivering from MRR can replace the traditional distributed feedback laser diodes, and this multi-wavelength source can be used in a wavelength division multiplexing system. Moreover, for quantum optics, MRRs can also generate entangled photons when the input power is under threshold, this helps to provide a light source in quantum optical circuits. In this thesis, the author theoretically discusses the nonlinear dynamics and squeezing effect in silicon nitride based MRRs. Utilizing the silicon nitride waveguide MRRs with high quality factor, it provides strong cavity enhancement and therefore results in significant nonlinear processes, such as four-wave-mixing (FWM) and frequency comb generation. The light field in the MRR is numerically analyzed by the spatiotemporal Lugiato-Lefever equation (LLE) model. The cavity dispersion strongly alters the nonlinear dynamics in MRRs. Here, the dispersion effect will be discussed both in normal and anomalous dispersion. The nonlinear phenomena including dark, bright soliton(s) and Turing rolls are further analyzed by comb conversion efficiency, frequency comb repetition rate, and generation dynamics. In addition, the mode coupling / interaction will be investigated in the LLE. Experimentally, there are several methods, such as polarization modes interaction, higher order modes interaction, or back scattering, can introduce mode interaction in MRRs. In normal dispersion, mode interaction causes avoid mode crossing and generates anomalous dispersion locally. The effectively anomalous dispersion further induces modulational instability (MI) and the cascaded FWM leads the generation of frequency combs. Since normal dispersion is much more common in silicon photonics, mode interaction provides more flexibility in the designs of waveguide structures and materials. Thresholds of MI and mode gain are then obtained from the eigenvalue analysis by solving the nonlinear equations. The threshold with mode interaction shows that the comb generation has upper and lower boundaries in input pump power, exhibiting significant difference to the MI and comb generation in anomalous dispersion. In comparison with the bright and dark soliton case, comb generation by the aid of mode interaction does not require a specific electric field as the initial condition. Numerical analysis shows comparable conversion efficiency for comb generation in normal dispersion with mode interaction to the conventional comb generation in an anomalous-dispersion MRR. In addition, with large detuning, the comb generation shows hysteresis and the threshold is strongly altered by the bistability of cavity power. Last, the semi-classical LLE modal was introduced to study the quantum effects in the MRR. When MRR is acting as an entangled photon source, it is important to ensure that the light is produced by spontaneous emission. The spontaneous emission spectra will be investigated under different detunings. On the other hand, when MMR is working above comb generation threshold, squeezed light is studied from the stimulated emission. High degree of squeezing can be achieved in silicon nitride MRRs, especially in the form of Turing rolls.
關鍵字(中)	★ 矽光子 ★ 微環形共振腔	關鍵字(英)	★ silicon photonics ★ micro ring resonator
論文目次	中文摘要 i ABSTRACT iii 誌謝 v 目錄 vi 圖目錄 ix 表目錄 xii 第一章 緒論 1 1-1 研究背景 1 1-1-1 基礎原理 2 1-1-2 微環形共振腔內的非線性效應 7 1-1-3 應用 9 1-2 Lugiato-Lefever equation 9 1-3 模擬方法 10 1-3-1 牛頓法 10 1-3-2 分步傅立葉法 11 1-3-3 波導耦合區 13 1-3-4 穩態判定 14 1-4 論文架構 14 第二章 微環形共振腔的光場演變 16 2-1 零色散(zeros dispersion) 17 2-1-1 雙穩態曲線 17 2-1-2 Ikeda map 22 2-1-3 閥值 23 2-2 異常色散(Anomalous dispersion) 25 2-2-1 特性分析 28 2-2-2 光學梳轉換效率分析 36 2-2-3 模態增益 37 2-3 正常色散(Normal dispersion) 39 2-3-1 暗孤子 39 2-3-2 Turing roll 42 第三章 模態交互作用效應 43 3-1 雙環形波導結構 43 3-2 波導正常色散(Normal dispersion) 46 3-2-1 光學梳產生閥值 46 3-2-2 失諧調製方向與頻率轉換效率分析 50 3-2-3 Lorentz分布的模態交互作用 54 3-3 波導異常色散(Anomalous dispersion) 56 第四章 壓縮光模型 57 4-1 壓縮光 57 4-2 半經典LLE 58 4-3 Spontaneous emission (低於閥值) 59 4-3-1 公式推導 60 4-3-2 光譜分析 61 4-4 Stimulated emission (高於閥值) 63 4-4-1 公式推導 63 4-4-2 光譜分析 66 第五章 結論 69 參考文獻 71
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指導教授	王培勳(Pei-Hsun Wang)	審核日期	2022-8-22
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