21,412 research outputs found
Robust Calculation of Chromatic Dispersion Coefficients of Optical Fibers From Numerically Determined Effective Indices Using Chebyshev–Lagrange Interpolation Polynomials
No full textDevelopment of Multidomain Pseudospectral Mode Solvers for Optical Waveguides and Photonic Crystals
No full text本論文發展一項採用多區塊類頻譜法之全向量模態解析模型以分析任意階射率分布之光波導問題。藉由柴比雪夫和雷建德多項式類頻譜法，我們將介質分割成多個區塊，再利用曲線變形技巧使得每個區塊組合成元件截面結構的形狀，最後再將區塊與區塊介面間之適當的邊界條件引入，如此可大大增加分析的精準程度。除此之外，為了處理洩漏波導問題，我們應用完美匹配層吸收邊界於模型中，得以計算複數傳播常數。本研究利用此新模型分析傳統的光波導結構以及新穎的光子晶體光纖結構，並與正解和其他數值分析方法做比較，以證明新模型分析結果的可靠性及準確性。
再者，本研究首次利用類頻譜模態解析法計算二維光子晶體的頻帶圖，並且展示此方法對於如三角晶格與四方晶格等不同週期性結構，不論是橫向電場或橫向磁場光波都能獲得高精準度收斂的結果。本研究亦展示對於極微小頻帶寬度間的能隙的分析亦可獲得極佳的精準度，證明所建立新方法的價值與重要性。
本論文在附錄中另提出一項利用柴比雪夫類頻譜法做內差的方式計算各種光纖的色散係數，相較於傳統的直接差分計算須利用相當多波長取樣點的方式，本方法僅須用到數個波長上的有效折射率，因此有極佳的計算效率。A new full-vectorial pseudospectral mode solver based on multidomain pseudospectral
methods for optical waveguides with arbitrary step-index profile is presented. Both Legendre and Chebyshev collocation methods are employed. The multidomain advantage helps in proper fulfillment of dielectric interface conditions, which is essential in achieving high numerical accuracy. Suitable multidomain division of the computational domain is performed to deal with general curved interfaces of the permittivity profile and field continuity conditions are carefully imposed across the dielectric interfaces. Therefore, a curvilinear coordinate mapping technique is introduced to perfectly deal with curved boundaries. Each contiguous subdomain is joined by intensionally imposing different types of boundary conditions to enhance the accuracy. Moreover, perfectly matched layer (PML) absorbing boundary conditions are incorporated into the model so that leaky
modes with complex propagation constants can be analyzed. The solver is applied to the calculation of guided modes on optical fibers, fused fiber couplers, D-shaped fibers, channel waveguides, rib waveguides, and photonic crystal fibers, and comparison with analytical results or reported ones based on other methods is made. It is demonstrated that numerical accuracy in the effective index up to the remarkable 10⣵76;10 order can be easily achieved.
The multidomain pseudospectral scheme is for the first time applied to the calculation of the band diagrams of two-dimensional photonic crystals with the inclusion of the required periodic boundary conditions, and is again shown to possess excellent numerical convergence behavior and accuracy. The proposed method shows uniformly excellent convergence characteristics for both the transverse-electric and transverse-magnetic waves in the analysis of di_erent structures. The analysis of a mini band gap with the normalized frequency gap width as small as on the order of 107 is also shown to demonstrate the extremely high accuracy of the proposed method.
A novel numerical calculation of chromatic dispersion coefficients of optical fibers including holy fibers is also proposed in this research using a procedure involving Chebyshev-Lagrange interpolation polynomials. Only numerically determined effective indices at several wavelengths are needed for obtaining the dispersion curve and no direct numerical differentiation of the effective refractive index is involved.1 Introduction 1
1.1 History of the Spectral Methods . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Application of Spectral Methods to Electromagnetics Problems . . . . . . 3
1.3 Modal Analysis of Optical Waveguides and Photonic Crystals . . . . . . . 4
1.4 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Contributions of the Present Work . . . . . . . . . . . . . . . . . . . . . . 8
2 Fundamentals of Spectral Methods 14
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Spectral Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Galerkin-Type Method . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Pseudospectral Method . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Pseudospectral Fourier Method . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Pseudospectral Legendre Method . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Pseudospectral Chebyshev Method . . . . . . . . . . . . . . . . . . . . . . 23
2.6 Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Mathematical Formulation and Boundary Conditions for OpticalWaveg-
uides 31
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 The Physical Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 The Helmholtz Equation . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 The Numerical Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
i
3.3.1 2-D Pseudospectral Formulae in Curvilinear Form . . . . . . . . . . 35
3.3.2 Formulation of the PSMS . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Setting Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.1 Dielectric Boundary without Corners . . . . . . . . . . . . . . . . . 42
3.5 The Perfectly Matched Layer . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.5.1 The Berenger's Perfectly Matched Layer . . . . . . . . . . . . . . . 44
3.5.2 The Anisotropic Perfectly Matched Layer . . . . . . . . . . . . . . . 47
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Numerical Results for Analysis of Various Optical Waveguide Struc-
tures 58
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2 Circular Waveguide: Comparison of Pseudospectral Chebyshev and Legendre
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 The D-Shaped Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4 Symmetrical 2 2 Strongly Fused Fiber-Optical Couplers . . . . . . . . . . 61
4.4.1 Fused Coupler with No Cores . . . . . . . . . . . . . . . . . . . . . 63
4.4.2 Fiber-Core E ects in Fused Fiber-Optical Coupler . . . . . . . . . . 64
4.5 Analysis of Waveguides with Corners . . . . . . . . . . . . . . . . . . . . . 64
4.5.1 Dielectric Boundary with Corners . . . . . . . . . . . . . . . . . . . 65
4.5.2 Rectangular Channel Waveguide . . . . . . . . . . . . . . . . . . . 66
4.5.3 Rib Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.6 Photonic Crystal Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Analysis of Band Structures in Two-Dimensional Photonic Crystals 110
5.1 The Physical Picture for 2-D Photonic Crystals . . . . . . . . . . . . . . . 110
5.2 Mathematical Formulation of the PSMS . . . . . . . . . . . . . . . . . . . 111
5.3 Imposing Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . 113
5.3.1 Boundary Conditions Between Adjacent Sub-domains . . . . . . . . 113
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5.3.2 Periodic Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 117
5.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.4.1 PC with Square Lattice . . . . . . . . . . . . . . . . . . . . . . . . 120
5.4.2 PC with Triangular Lattice . . . . . . . . . . . . . . . . . . . . . . 123
5.4.3 PC with Large Air Holes . . . . . . . . . . . . . . . . . . . . . . . . 124
5.4.4 PC with Large Dielectric Pixels . . . . . . . . . . . . . . . . . . . . 124
5.4.5 Analysis of a Mini Band Gap . . . . . . . . . . . . . . . . . . . . . 125
6 Summary and Future Works 145
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A Robust Calculation of Chromatic Dispersion Coe cients of Optical Fibers
from Numerically Determined E ective Indices Using Chebyshev-Lagrange
Interpolation Polynomials 1 148
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
A.2 The Chebyshev Collocation Method . . . . . . . . . . . . . . . . . . . . . . 150
A.3 An Idealistic Waveguide Having Analytical Chromatic Dispersion Characteristics
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
A.4 Dispersion in Holey Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
A.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
B List of Acronyms 16
Customer Value Evaluation-Using Quantile Regressions:Case Study of Taiwan 3C Retailer
No full text「顧客關係管理」(Customer Relationship Management)觀念在零售業行之有年，透過數位技術的發展、資料庫的建立，企業蒐集顧客個人資料與觀察其交易行為已非難事，但如何妥善地運用統計工具分析手中資料，藉以適切配置行銷資源，進而吸引不同屬性、行為的顧客群，才是發展顧客關係管理、資料庫行銷的核心目標。於企業資源有限，且各自擁有不同的核心能力，顧客價值(Customer Value)的衡量成為行銷研究領域不可或缺的重要項目。透過RFM指標與資料庫中各統計變數的關聯性分析，可帶給行銷人員科學化的策略建議。然而，目前行銷研究中最常使用的OLS迴歸分析法，其假設樣本母體呈現常態分配，而以平均數或中位數的概念設法找出變數間的相互關係，是否真能符合真實世界的樣貌？因此，本研究採用Koenker & Bassett (1978)提出的分量迴歸方式(Quantile Regression) ，以國內3C連鎖零售賣場為研究標的，進行顧客價值分析。希望能藉此發掘不同的統計方式帶來的不同分析結果，也藉此驗證分量迴歸分析在行銷上的應用是否合宜。研究分析區分成兩個部分：第一部分利用RFM指標來界定顧客價值，並透過資料庫所提供之人口統計變數、顧客消費行為變數與顧客價值作交叉分析。並同時進行OLS一般迴歸的分析，藉以比較兩種迴歸模型的異同。第二部分則選擇三項產品線作為研究主體，分析購買其高低價位商品的顧客之人口統計變數與交易行為，藉此可探討通路導入新產品時，其定位在不同價位可採取的不同行銷策略。究結果可明顯發現分量迴歸在分析具有極端值與偏態較大樣本時，相對於OLS一般迴歸，擁有較佳的母體分辨能力。同時也呼應了行銷學上對於顧客「異質性」的強調，使得行銷人員得以更了解位於不同分量的客群，不同的行為特質。“Customer Relationship Management” now is a common concept for retail business. It has become much easier for enterprise to collect customer information and observe their behavior with the development of database technology. However, choosing the correct statistics tool to analyze information, to allocate resource and attract target customer is always a big issue for the marketers.ecause of the limited resource and different core competence, “customer value” has become an essential part in marketing research. By analyzing the correlation of RFM indicator and information collected by customer database, the marketers can get scientific cues for marketing strategy decision. owever, Ordinary Least Squares (OLS) regression model, which is commonly adopted in recent marketing research, describes sample as a normal distribution. Therefore, OLS method analyzes the correlation within factors by their average. To reflect the real distribution of the sample and get more precise result, this research adopt Quantile Regression(QR) model, which was brought up by Koenker & Bassett(1978), to analyze customer value of 3C retail chain store in Taiwan. Hoping to discover different result leads to different statistics tool and verify QR`s application in marketing.謝辭 ii要 iiibstract iv錄 v次 vii次 viii一章 緒論 1一節 研究背景與動機 1二節 研究目的 2三節 研究範圍 3四節 研究架構 4二章 文獻探討 5一節 顧客關係管理的思潮演進 5二節 顧客價值 18三章 研究方法 23一節 普通最小平方法(OLS)模型 24二節 分量迴歸(Quantile Regression；QR)模型 24三節 分量迴歸的估計 28四節 分量迴歸的應用 29四章 資料分析與結果 31一節 樣本描述及分析變數定義 31二節 顧客貢獻價值：顧客到店消費總金額分析 39三節 顧客價值-顧客到店消費平均金額分析 44四節 顧客價值-顧客活躍性指數分析 51五節 顧客價值-產品部門顧客消費分析 57六節 顧客價值-同一種類高低單價與顧客消費行為分析 69五章 結論與建議 87一節 研究結論與策略意涵 87二節 研究限制 90三節 後續研究建議 90考文獻 9
Effect of dissolved organic carbon (DOC) by different thinning intensities in temperate forest.
No full textFull-Vectorial Optical Waveguide Mode Solvers Using Multidomain Pseudospectral Frequency-Domain (PSFD) Formulations
No full textsj-docx-1-tam-10.1177_17588359221106558 – Supplemental material for Cancer-cell-derived cell-free DNA can predict distant metastasis earlier in pancreatic cancer: a prospective cohort study
No full textSupplemental material, sj-docx-1-tam-10.1177_17588359221106558 for Cancer-cell-derived cell-free DNA can predict distant metastasis earlier in pancreatic cancer: a prospective cohort study by Chien-Jui Huang, Wen-Yen Huang, Chien-Yu Chen, Ying-Jui Chao, Nai-Jung Chiang and Yan-Shen Shan in Therapeutic Advances in Medical Oncology</p
sj-tif-3-tam-10.1177_17588359221106558 – Supplemental material for Cancer-cell-derived cell-free DNA can predict distant metastasis earlier in pancreatic cancer: a prospective cohort study
No full textSupplemental material, sj-tif-3-tam-10.1177_17588359221106558 for Cancer-cell-derived cell-free DNA can predict distant metastasis earlier in pancreatic cancer: a prospective cohort study by Chien-Jui Huang, Wen-Yen Huang, Chien-Yu Chen, Ying-Jui Chao, Nai-Jung Chiang and Yan-Shen Shan in Therapeutic Advances in Medical Oncology</p
sj-tif-2-tam-10.1177_17588359221106558 – Supplemental material for Cancer-cell-derived cell-free DNA can predict distant metastasis earlier in pancreatic cancer: a prospective cohort study
No full textSupplemental material, sj-tif-2-tam-10.1177_17588359221106558 for Cancer-cell-derived cell-free DNA can predict distant metastasis earlier in pancreatic cancer: a prospective cohort study by Chien-Jui Huang, Wen-Yen Huang, Chien-Yu Chen, Ying-Jui Chao, Nai-Jung Chiang and Yan-Shen Shan in Therapeutic Advances in Medical Oncology</p
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