發光與非發光週期性結構之電磁場數值分析

Electromagnetic Modeling of Emitting and Non-Emitting Periodic Structures

葉文嵐(Wen-Lan Yeh)

指導教授 ： 邱奕鵬

國立臺灣大學/電機資訊學院/光電工程學研究所/博士(2014年)

https://doi.org/10.6342/NTU.2014.10923

摘要

拜近代製程技術的進步, 光學元件體積縮小化，具有週期性排列結 構的繞射式光學元件 (Diffractive Optical Elements, DOEs) 乃為備受重用 的積體光路元件，本論文利用兩種嚴謹電磁數值方法模擬含有繞射光 柵的非發光性與自發光性的元件，並對其進行光學特性分析。

微米尺寸或次微米金屬光柵近來開始受到注目，但其劇烈變化的折射率差異造成數值模擬的困難。本論文發展一項多區域頻譜法模擬具有高導電性的金屬光柵，能夠準確有效率的分析其光學特性。藉由柴比雪夫多項式類頻譜法 (Chebyshev pseudospectral method)，我們將模擬區域分割為數個子區域，藉由各區域相鄰介面須滿足電磁連續的邊界條件，重新整合為一系統，能穩定並有效率的模擬高導電性的金屬光柵，而且分析精準度極高。因為柴比雪夫多項式類頻譜法的特性，具有極佳的計算效率，也避免掉常見的朗格插值震盪 (Runge phenomenon) 跟吉布斯現象（Gibbs phenomenon）的干擾，達到穩定跟高精準的收斂效果。

另外，本論文利用嚴格耦合波分析法 (Rigorous coupled-wave analysis) 研究了利用繞射光柵增益自發光元件的光學出光效率。我們先利用古典電磁學表示電偶極的發光特性，並結合嚴格耦合波分析法計算含有光柵的光學微共振腔發光元件的出光效率。薄膜發光二極體跟有機發光二極體均在討論範圍內。由模擬結果找出最佳化發光結構。

最後本論文建構一套系統，結合嚴謹電磁模型跟幾何光學，能分析包含釐米尺寸的微透鏡發光元件。

關鍵字

繞射式光學元 ； 週期結構 ； 發光元件 ； 嚴格耦合波分析法 ； 多區域類頻譜法 ； 柴比雪夫多項式 ； 光柵

並列摘要

Optical diffraction elements have received a great deal of attention over the last decade, largely due to improved numerical modeling and advances in fabrication technologies. The purpose of this dissertation is to develop high accuracy spectral numerical models to model non-emitting and emitting periodic structures.

The metallic gratings, especially the highly conductive gratings, have recently brought to light by surface plasmon-polaritons (SPPs). Rigorous electromagnetic modelings are required to analyze the resonant modes of the wavelength scale diffraction gratings. However, the properties of highly conductive gratings make the numerical analysis more challenging, for example, the large index difference at the abrupt interface and sign change of the real part of the dielectric function across the interface, especially in the case of transverse magnetic (TM) polarization. The multidomain pseudospectral method based on Chebyshev collocation method are developed which is essential in achieving high numerical accuracy. The Chebyshev method avoids the Runge phenomenon and Gibbs phenomenon to own high spectral accuracy in the single domain. We divide the computational area into nonoverlapping subdomains and apply the multidomain method to form an eigenvalue problem according to the Helmholtz equation. The transfer matrix method is adopted for different layers to evaluate the diffraction efficiencies.

The optical enhancement mechanism of emitting periodic structures is also discussed. The modeling is mainly based on the rigorous coupled-wave analysis (RCWA) and transfer matrix methods and the whole simulation processes are calculated in a lap top and electromagnetic wave analysis only. In order to extract the photons trapped within the non-radiative mode, we insert a one-dimensional grating. The optimal structure parameters are proposed. Thin-film light emitting diodes and organic light emitting diodes are both discussed.

We also have developed an efficient system combing transfer matrix method and ray-tracing technique for simulating layer structure with microlens arrays.
The systematical analysis of the mechanism of the enhancement of microlens arrays and the relation between the optimal geometric structure of that and the emitting angular spectrum is investigated.

並列關鍵字

Diffractive Optical Elements ； grating ； emitting devices ； Rigorous coupled-wave analysis ； multidomain pseudospectral method ； Chebyshev polynomial

參考文獻

References

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