臺灣博碩士論文加值系統

本論文包含二個研究主題，分別在第三章及第四章提及。第三章提供抑制在絕緣層上矽光子平台之垂直槽狀波導環型共振腔之極化相依性之設計方法，意即在考慮波導色散下，使準TE與準TM模態之極化相依性在寬頻帶中達到最小。過去發表的文獻僅能在特定單一波長達到零極化相依性，然而在本論文之設計利用垂直槽狀波導之幾何結構，與過去發表文獻相比能夠增加一個可用設計維度。藉由調變矽波導及溝槽之寬度，可控制準TE 與準TM 模態之等效折射率以及在寬頻帶中之色散行為。因此，我們可以獲得在通訊波段(1510−1590 nm) 中使元件之極化相依性達到最小值之設計參數，能夠讓準TE與準TM模態在環型共振腔中傳播一周後累積幾乎相同之相位，因此能使共振波長差異達到最小值。我們亦針對不同用途提供兩種設計，利用有限元素法分析可得到環型共振腔準TE 與準TM 模態之頻率響應。
第四章討論任意比例寬頻光耦合器之設計方法，而最佳化設計參數可藉由基因演算法求得。在設計流程中，我們將元件幾何離散化成多段小區段，而每一小區段皆由梯形構成，而其中每一截梯形之耦合係數與傳播常數皆為最佳化之變數。因為在此設計中，變數眾多且搜尋範圍廣大，又難以預測因變數變化造成的計算結果，基因演算法可為一種適用之最佳化方式。藉由建立針對耦合係數與傳播常數之對照表，在最佳化過程中關於寬頻帶之頻率響應可利用耦合模態理論求得。此最佳化設計亦可使用較嚴謹之數值方法: 光束封包法以及有限元素法作進一步驗證，其結果與耦合模態理論相當吻合。在波長範圍為1530−1630 nm 中(C 至L 頻帶)，對於任意比例之光耦合器皆可達到近乎無波長相依性之頻譜響應。

The dissertation consists of two research topics, which are respectively discussed in Chapters 3 and 4. In Chapter 3, we propose the design of a vertical slot waveguide-based optical ring resonator on the silicon-on-insulator (SOI) platform platform with minimized polarization mode dispersion (PMD) in the presence of waveguide dispersion over a wide spectral range. As compared to previous studies with regard to achieving the zero-birefringence condition (ZBC) at a specific wavelength, one additional degree of freedom is used by implementing vertical slot waveguides. Effective refractive indices, as well as the dispersion curves of quasi-TE and quasi-TM modes, can be determined
by controlling the widths of silicon strips or the slot. Therefore, the minimum PMD over the communication wavelengths can be obtained, which leads to nearly identical accumulated phase in the optical ring resonator for quasi-TE and quasi-TM modes, and thus the resonant wavelength mismatch between the quasi-TE and quasi-TM modes can be minimized in the spectral range from 1510 to 1590 nm. The spectral response of the optical ring resonator is simulated using the finite element method (FEM), with two design configurations presented for different uses.
A design of broadband dual channel directional couplers with arbitrary coupling ratios based on a genetic algorithm (GA) is proposed in Chapter 4. The device is segmented into trapezoidal short sections, and the propagation constant and the coupling coefficient of each section are viewed as variables during the optimization process. Since the problem contains a wide variety of variable combinations, and the solution space is poorly understood, a GA can be a promising candidate for the optimization method in this case. A lookup table of the propagation constants and coupling coefficients for a wide variety of variable combinations is constructed and therefore the spectral response of the system can be analyzed by the coupled mode theory (CMT) during the
optimization process. The optimal design is further verified by using the beam envelope method (BEM) and the FEM. The results indicate a good agreement with the CMT. The spectral response is nearly wavelength-independent over a wide band for λ = 1530−1630 nm (C + L band) for the design of arbitrary target coupling ratios.

口試委員審定書 i
致謝 ii
中文摘要 iii
Abstract iv
Contents vi
List of Figures ix
List of Tables xiii
1 Introduction 1
1.1 Waveguide components on the silicon-on-insulator (SOI) platform 1
1.1.1 Directional couplers 2
1.1.2 Ring resonators 3
1.2 Research motivation and objectives 5
1.3 Structure of the dissertation 6
2 Theoretical Background 8
2.1 Mode analysis in optical waveguides 8
2.1.1 Slab waveguides 8
2.1.2 Waveguides with arbitrary geometries 10
2.2 Working principle of slot waveguides 11
2.3 Coupled mode theory 14
2.4 Working principle of optical ring resonators 15
2.5 Methods 17
2.5.1 Genetic algorithm (GA) 17
2.5.2 Finite element method (FEM) 19
2.5.3 Beam envelope method (BEM) 20
3 Micro-ring resonator composed of vertical slot waveguides with minimum polarization mode dispersion over a wide spectral range 21
3.1 Introduction 21
3.2 Zero-birefringence condition 23
3.3 Numerical simulations 28
3.4 Summary 33
4 Broadband optical waveguide couplers with arbitrary coupling ratios designed using a genetic algorithm 34
4.1 Introduction 34
4.2 System analysis 36
4.2.1 Waveguide properties 36
4.2.2 CMT in transfer matrix form 40
4.3 Optimization based on GA 41
4.4 Numerical simulations 50
4.5 Fabrication tolerance analysis 52
4.6 Summary 53
5 Conclusion 55
5.1 Summary 55
5.2 Suggestion for future work 56
References 58
List of publications 68

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