臺灣博碩士論文加值系統

分散式布拉格反射器適合作為摻鉺鈮酸鋰波導雷射的共振腔反射鏡。它可以提供高反射率、窄頻寬，並且能與其它的積體光學元件進行單晶整合。然而傳統在鈮酸鋰波導上蝕刻出溝槽所製成的表層起伏式反射器只有微弱的等效折射率調變效果，也因此僅提供了有限的反射率。如果在鈮酸鋰波導上先附著一層高折射率的矽，再把週期性的溝槽蝕刻在矽層的表面，反射率將會有明顯的改善。論文中，這種「高折射率表層起伏式布拉格反射器」的效能將以耦合模態方程式進行理論研究。模擬結果顯示，耦合強度對於矽層的厚度非常敏感。這是因為主要的模態光場分佈會由鈮酸鋰波導區向上躍遷至矽層所致。當我們把模態場形的不匹配所造成的饋入損耗也列入考慮之後，最大有效反射率的最佳化結構參數將可以被求算出來。根據這樣的設計結果，一個3mm的均勻布拉格反射器將可以有99.5%的反射率峰值和僅0.4nm的反射頻寬。最後，轉換矩陣法將被用來分析非週期性布拉格反射器的頻譜特性，並討論其廣泛的實際應用。

Distributed Bragg reflector (DBR) is found to be suitable as the cavity mirror of an erbium-doped LiNbO3 waveguide laser, because it may provide sufficiently high reflectivity, narrow bandwidth, and is capable of monolithically integrating with other integrated optical devices. Whereas, the traditional surface-relief DBR produced by etching grooves on the LiNbO3 waveguide usually exhibits very weak mode-index modulation, and therefore limited reflectivity. Significant improvements could be carried out if the Si-on-LiNbO3 structure is used, and the periodic corrugations are then introduced on the surface of silicon overlay. In this work, the novel features of the corrugated high index overlay (CHIO) DBR are theoretically investigated by the coupled-mode equations. Simulation results indicate that the coupling strength is sensitive to the Si-layer thickness, which is attributed to the transition of dominant mode intensity distribution from the LiNbO3 waveguide region up to the Si-layer. The optimum structural parameters for maximum effective reflectivity could be obtained after the insertion loss caused by mode profile mismatch is also taken into account. From which, a 3mm uniform DBR with peak reflectivity of 99.5% and bandwidth of 0.4nm could be anticipated. Finally, the spectral characteristics of various aperiodic CHIO DBR''s will be analyzed in terms of the fundamental matrix method, which demonstrate a wide variety of practical applications.

Chapter 1Motivation 1
Chapter 2Analysis Methods 4
2-1Bragg Condition 4
2-2Wave Impedance Transformation 4
2-3Transfer Matrix Method 5
2-4Coupled-Mode Theory 7
2-5Finite Difference Time Domain (FDTD)12
Chapter 3Implementation of Programs 14
3-1Fundamental DBR Configuration14
3-2Finite Difference Mode Solver15
3-2.1Dirichlet Boundary Condition16
3-2.2Transparent Boundary Condition (TBC)17
3-3Shifted Inverse Power Method21
Chapter 4Analysis of Uniform DBR23
4-1Investigation of Several DBR Structures23
4-2Corrugated High Index Overlay (CHIO) Structure 24
4-2.1Effect of Silicon Layer Thickness24
4-2.2Effect of Groove Depth26
4-2.3Reflection Spectra27
4-2.4Choice of Overlay Material29
Chapter 5Extension to Aperiodic DBR 30
5-1Fundamental Matrix Method30
5-2Practical Applications32
5-2.1Apodization32
5-2.2Chirping33
5-2.3Phase-shift34
5-2.4Super Structure34
5-2.5Dispersion Compensation36
Chapter 6Conclusions38
Figures40
Tables73
References74

[1] R. Brinkmann, "Continuous-wave Erbium-diffused LiNbO3 waveguide laser", Electronics Letters, vol. 27, no. 5, pp. 415-417, 1991.
[2]I. Baumann, "Er-doped integrated optical devices in LiNbO3", IEEE Journal of Selected Topics in Quantum Electronics, vol. 2, no. 2, pp. 355-365, 1996.
[3]Hermann A. Haus, Waves and Fields in Optoelectronics, Prentice-Hall. 1984.
[4]Amnon Yariv, and Pochi Yeh, Optical Waves in Crystals, John Wiley & Sons, 1984.
[5]S. Fouchet, "Ti-implanted Bragg reflectors on LiNbO3:Ti strip waveguides", Applied Physics Letters, vol. 58, no. 14, pp. 1518-1520, 1991.
[6]K. O. Hill, "Photosensitivity in optical fiber waveguides: application to reflection filter fabrication", Applied Physics Letters, vol. 32, no. 10, pp. 647-649, 1978.
[7]K. O. Hill, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask", Applied Physics Letters, vol. 62, no. 10, pp. 1035-1037, 1993.
[8]Keiji Tsunetomo, "Direct formation of a surface-relief grating on glass by ultraviolet-visible laser irradiation", Optics Letters, vol. 22, no. 6, pp.411-413, 1997.
[9]P. E. Dyer, "Amplification of fiber Bragg grating reflectivity by post-writing exposure with a 193nm ArF laser", Electronics Letters, vol. 30, no. 14, pp. 1133-1134, 1994.
[10]G. P. Luo, "Fabrication of LiNbO3 phase gratings by excimer laser ablation through a silica phase mask", Japanese Journal of Applied Physics, vol. 35, part -2, no. 12A, pp. L1593-L1595, 1996.
[11]Curtis F. Gerald, Applied Numerical Analysis (5th edition), Addison Wesley, 1994.
[12]G. Mur, "Absorbing boundary conditions for finite-difference approximation of time-domain Electromagnetic-field equations", IEEE Transactions on Electromagnetic Compatibility, vol. EMC-23, no. 4, pp. 377-382, 1981.
[13]R. Holland, "Total-field versus scattered-field finite-difference codes: A comparative assessment", IEEE Transactions on Nuclear Science, vol. NS-30, no. 6, pp. 4583-4588, 1983.
[14]J. P. Berenger, "A perfected matched layer for the absorption of electromagnetic waves", Journal of Computational Physics, vol. 114, pp.185-200, 1994.
[15]Junji Yamauchi, "Analysis of optical waveguides with high-reflection coatings using the FD-TD method", IEEE Photonics Technology Letters, vol. 10, no. 1, pp. 111-113, 1998.
[16]G. R. Hadley, "Transparent boundary condition for beam propagation", Optics Letters, vol. 16, no. 9, pp. 624-626, 1991.
[17]G. R. Hadley, "Transparent boundary condition for the beam propagation method", IEEE Journal of Quantum Electronics, vol. 28, no. 1, pp. 363-370, 1992.
[18]C. Vassallo, "Comparison of a few transparent boundary conditions for finite-difference optical mode-solvers", Journal of Lightwave Technology, vol. 15, no.2, pp. 397-402, 1997.
[19]C. P. Hussell, "High-index overlay for high reflectance DBR gratings in LiNbO3 channel waveguides", IEEE Photonics Technology Letters, vol. 9, no. 5, pp.636-638, 1997.
[20]T. Conese, "Finite element analysis of LiNbO3 waveguides with Is or Si/SiO2 overlay ", Journal of Lightwave Technology, vol. 16, no. 6, pp. 1113-1122, 1998.
[21]P. K. Tien, "Light waves in thin films and integrated optics", Applied Optics, vol. 10, no. 11, pp. 2395-2413, 1971.
[22]Robert S. Elliott, Antenna Theory and Design, Prentice-Hall, 1981.
[23]T. Erdogan, "Fiber grating spectra", Journal of Lightwave Technology, vol. 15, no. 8, pp. 1277-1294, 1997.
[24]Makoto Yamada, "Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach", Applied Optics, vol. 26, no. 16, pp. 3474-3478, 1987.
[25]F. Ouellette, "Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides", Optics Letters, vol. 12, no. 10, pp. 847-849, 1987.
[26]Hermann A. Haus, "Antisymmetric taper of distributed feedback lasers", IEEE Journal of Quantum Electronics, vol. QE-12, no. 9, pp. 532-539, 1976.
[27]Hiroyuki Ishii, "Multiple-phase-shift super structure grating DBR lasers for broad wavelength tuning", IEEE Photonics Technology Letters, vol. 5, no. 6, pp.613-615, 1993.
[28]B. J. Eggleton, "Long periodic superstructure Bragg gratings in optical fibers", Electronics Letters, vol. 30, no. 19, pp.1620-1622, 1994.
[29]Fumiyoshi Kano, "Characteristics of super structure grating (SSG) DBR lasers under broad range wavelength tuning", IEEE Photonics Technology Letters, vol. 5, no. 6, pp. 611-613, 1993.
[30]F. Ouelette, "Limits of chirped pulse compression with an unchirped Bragg grating filter", Applied Optics, vol. 29, no. 32, pp. 4826-4829, 1990.
[31]Sadiku, and N. O. Matthew, Numerical techniques in Electromagnetics, CRC Press, 1992.