基于信号流程图理论的微环谐振腔特性分析
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摘要
随着人们对信息的需求越来越多,提高光纤通信容量和速度已经成当前亟待解决的问题。大规模集成光学作为未来全光网络的重要组成部分,其发展无疑对这一问题的解决有着重大意义。微环谐振腔以其功能多样、结构简洁、集成度高等特点已经成为集成光学领域的研究热点。
研究微环谐振腔最典型的方法是在麦克斯韦电磁方程组基础上发展起来的耦合模理论,这种方法无论是在空间还是在时间上都可以用数学方程来表示。但是在研究多环系统时显得比较繁琐,不利于实际应用。本文中运用了一种简便、直观的图示法——信号流程图法(SFG),对微环谐振腔的输出特性进行分析。
本论文的主要工作是建立在基于传输矩阵法的通用参量模型基础上。首先,以全通型单环谐振腔为例介绍了信号流程图法(SFG)在光信号系统中推导功率传递函数的步骤,并分析了系统的谐振条件。其次,利用信号流程图法推导了平行信道单环、串联双环和并联双环谐振滤波器的系统传递函数。对于串联耦合结构,影响传输特性的主要是环与环间的耦合系数,通过模拟分析得出实现最大平坦输出波峰的临界耦合系数;对于并联结构,通过优化环与环间直波导的长度,实现下载端输出光谱的对称性。最后,对竖直信道单环谐振波分复用器的系统传递函数行进了推导,分析和讨论了耦合系数对于下载端输出光谱宽度、插入损耗以及信道间串扰的影响。
With more and more increasing demands for information, enhancing the capacity and speed of the optical fiber communication has become a problem to be urgently solved. Large-scale integrated optics is an important part of all-optical networks, its development undoubtedly has great significance in solving this problem. The micro-ring resonator with multiplex function, structural simplicity and high integration has become a research focus in the fields of integrated optics.
The typical researching approach to micro-ring resonator is the coupled mode theory which is based on Maxwell equations. The method either in space or in time can be expressed by equations. However, studying multi-ring system with the approach more complicated, so it is not fit for practical application. In this paper, a simple, intuitive graphic method called signal flow graph method to analyze the output characteristics of micro-ring resonator.
The main work of this paper is founded on the model of general parameters based on transfer matrix. Firstly, using the all-pass single micro-ring resonator as an example, the approach of the signal flow graph method (SFG) in optical signal system are introduced, and the condition of resonance of the system is analyzed. Secondly, the system transfer function of the add/drop single micro-ring resonator filter with parallel channel, add/drop“Series-coupled”and“Parallel-coupled”double micro-ring resonator filter with parallel channel are derived using the signal flow graph method. For the“Series-coupled”structure, the performance is mainly determined by the coupling coefficients between ring and ring. The critical coupling coefficient is obtained by simulation when achieving the maximal flat output wave crest. For the“Parallel-coupled”structure, the good ship of spectral response is achieved by optimizing the ring distance. Finally, the transfer function of single micro-ring resonators wavelength multiplexers with vertical channel is derived. The influence of coupling coefficient on the drop port output spectrum width, the insertion loss, and the crosstalk between channels is analyzed and discussed.
研究微环谐振腔最典型的方法是在麦克斯韦电磁方程组基础上发展起来的耦合模理论,这种方法无论是在空间还是在时间上都可以用数学方程来表示。但是在研究多环系统时显得比较繁琐,不利于实际应用。本文中运用了一种简便、直观的图示法——信号流程图法(SFG),对微环谐振腔的输出特性进行分析。
本论文的主要工作是建立在基于传输矩阵法的通用参量模型基础上。首先,以全通型单环谐振腔为例介绍了信号流程图法(SFG)在光信号系统中推导功率传递函数的步骤,并分析了系统的谐振条件。其次,利用信号流程图法推导了平行信道单环、串联双环和并联双环谐振滤波器的系统传递函数。对于串联耦合结构,影响传输特性的主要是环与环间的耦合系数,通过模拟分析得出实现最大平坦输出波峰的临界耦合系数;对于并联结构,通过优化环与环间直波导的长度,实现下载端输出光谱的对称性。最后,对竖直信道单环谐振波分复用器的系统传递函数行进了推导,分析和讨论了耦合系数对于下载端输出光谱宽度、插入损耗以及信道间串扰的影响。
With more and more increasing demands for information, enhancing the capacity and speed of the optical fiber communication has become a problem to be urgently solved. Large-scale integrated optics is an important part of all-optical networks, its development undoubtedly has great significance in solving this problem. The micro-ring resonator with multiplex function, structural simplicity and high integration has become a research focus in the fields of integrated optics.
The typical researching approach to micro-ring resonator is the coupled mode theory which is based on Maxwell equations. The method either in space or in time can be expressed by equations. However, studying multi-ring system with the approach more complicated, so it is not fit for practical application. In this paper, a simple, intuitive graphic method called signal flow graph method to analyze the output characteristics of micro-ring resonator.
The main work of this paper is founded on the model of general parameters based on transfer matrix. Firstly, using the all-pass single micro-ring resonator as an example, the approach of the signal flow graph method (SFG) in optical signal system are introduced, and the condition of resonance of the system is analyzed. Secondly, the system transfer function of the add/drop single micro-ring resonator filter with parallel channel, add/drop“Series-coupled”and“Parallel-coupled”double micro-ring resonator filter with parallel channel are derived using the signal flow graph method. For the“Series-coupled”structure, the performance is mainly determined by the coupling coefficients between ring and ring. The critical coupling coefficient is obtained by simulation when achieving the maximal flat output wave crest. For the“Parallel-coupled”structure, the good ship of spectral response is achieved by optimizing the ring distance. Finally, the transfer function of single micro-ring resonators wavelength multiplexers with vertical channel is derived. The influence of coupling coefficient on the drop port output spectrum width, the insertion loss, and the crosstalk between channels is analyzed and discussed.
引文
[1] Agrawal G. P. Fiber-Optic Communications Systems.(Third edition) [M]. New York, US: John wiley & Sons, Inc. 2002, 1-19.
[2]曹茂虹,刘礼.光纤通信技术的现状及发展趋势[M].光机电信息,2007,5:34-37.
[3]李玮.浅析光纤通信技术的发展与展望[J].科技风,2009,21.
[4]张煦.OFC--2002关于光纤传输系统的实验报道[J].光通信技术,2002,3,(26).
[5] Raj Jain. All-Optical Networks,专题报告[R].2002
[6] Miller S. E. Intergrated Optics: An Introduction [J]. Bell Labs Technical Journal, 1969,48: 2059-2061
[7] Marcatili E. A. J. Bends in optical dielectric guides [J]. Bell Labs Technical Journal, 1969, 48:2103-2132
[8]李卫彬.信号流程图理论及其在光学环谐振腔特性分析中应用的研究[D].博士论文,华中科技大学,2009.
[9] Baehr-Jones T., Hochberg M., Walker C., et al. High-Q ring resonators in thin silicon-on-insulator [J]. Applied Physics Letter, 2004, 85(16): 3346-3347.
[10] Grover R., Van V., Ibrahim T. A., et al. parallel-cascaded semiconductor micro-ring resonators for high-order and wide-FSR filters [J]. Journal of Lightwave Technology, 2002, 20(5):900-905.
[11] Choi S. J., Peng Z., Yang Q., et al. An eight-channel demultiplexing swith array using vertically coupled active semiconductor microdisk resonators [J]. IEEE photonics Technology Letter, 2004, 16(11): 2517-2519.
[12] Rabiei P., Steier W. H. Tunable polymer double micro-ring filers [J]. IEEE Photonics Technology Letters, 2003, 15(9): 1255-1257.
[13] Kim D. H., Im J. G., Lee S. S., et al. Polymeric microring resonator using nanoimprint technique based on a stamp incorporating a soothing buffer layer [J]. IEEE Photonics Technology Letters, 2005, 17(11):2352-2354.
[14] Huang S. W., Chen S. L., Ling T., et al. Low-noise wideband ultrasound detection using polymer micro-ring resonators [J]. Applied Physics Letters, 2008, 92, (19).
[15] Huang W. P. Coupled-mode theory for optical waveguide: an overview [J]. Journal of the Optical Society of America A, 1994, 11(3): 963-983.
[16]马春生,刘式墉.光波导模式理论[M].长春:吉林大学出版社,2006: 352-355
[17]闫欣.微环谐振波分复用器的模拟与分析[D].博士论文,吉林大学,2006.
[18]杨建义,江晓清,王明华等.采用单环微谐振器的光滤波器特性及其局限性[J].光电子·激光, 2003,14(1) :12-16
[19]董小伟,裴丽,简水生.传输矩阵法分析多环高阶谐振滤波器特性[J].中国激光,2005,7,(32):929-932.
[20]张小贝,黄修德,洪伟等.传输矩阵法分析微环谐振器阵列传输特性[J].光学学报,2007,9,(27):1586-1592.
[21]张小贝.微环谐振器及应用的理论和实验研究[D].博士论文,华中科技大学,2009.
[22] Taflove A., Hagness S. C. Computational Electrodynamics: The finite-difference time-domain method (Second Edition) [M]. Norwood, US: Artech House, Inc, 2000. 67-106.
[23] Chen W., Chen W., Chen Y.-J. A Characteristic matrix approach for analyzing resonant ring lattice devices [J]. IEEE, Photonics Technology Letters, 2004, 16 (2):458-460.
[24] Chen W., Wang Z., Chen W., et al. General ring resonator analysis and characterization by characteristic matrix [J]. Journal of Lightwave Technology,2005, 23(2): 915-922.
[25] Chin M K, Chu D Y, Ho S T. Estimation of the spontaneous emission factor for microdisk lasers vea the approximation of whispering gallery mode [J]. Journal of Applied Physics, 1994, 75:3302-3305.
[26] Yariv A. Universal relations for coupling of optical power between microresonators and dielectric waveguides [J]. Electronics Letters, 2000, 36(4):321-322.
[27] Mason S J. Feedback Theory -Further Properties of Signal flow graphs [J]. Proceedings of the IRE, 1956, 44: 920-926.
[28] Yariv A., Xu Y., Lee R.K., etal. Coupled-resonator optical waveguide: a proposal and analysis [J].Optics Letters, 1999, 24(11):711-713
[29] Poon J. K. S., Scheuer J., Xu Y., et al. Designing coupled-resonator optical waveguide delay lines [J]. Journal of the Optical Society of America B, 2004, 21(9): 1665-1673.
[30] Little B E, Haus H A, Foresi J S, et al. Wavelength selective switch using thermally tunable microring resonators [J]. Photonics technology letters, 1998, 10(16): 816-818.
[31] Emelett S J, Soref R A. Analysis of dual micro-ring resonator cross connect switches and modulators[J]. Optics Express, 2005, 13(20):7840-7853
[32] Polson R C, Levina G, Vardeny Z V. Spectral analysis of polymer micro-ring lasers [J]. Applied Physics letters, 2000, 76 (26):3858-3860.
[33] Sorel M., Laybourn P. J. R., Giuliani G., et al. Unidirectional bistability in semiconductor waveguide ring lasers [J]. Applied physics letters, 2002, 80,(17): 3050-3051.
[34] Sorel M., Giuliani G., Scire A., et al. Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model[J]. IEEE Journal of quantum electronics, 2003, 39(10): 1187-1195.
[35] Yu S., Wang Z., Yuan G., et al. Optically triggered monostable and bistable flip-flop operation of a monolithic semiconductor ring laser. In: Photonics in switching [M]. San Francisco, 2007: 115-116.
[36] Hill M. T., Dorren H. J.S., De Vries T., et al. A fast low-power optical memory based on coupled micro-ring lasers [J]. Nature, 2004, 432(7014): 206-209
[37] Wang Z., Yuan G., Verschaffelt G., et al. Storing 2 bit of information in a novel single semiconductor microring laser memory cell [J]. IEEE Photonics technology letters, 2008, 20(14): 1228-1230.
[38] Xu Q F, Schmidt B, Pradhan S, et al. Micro-metre scale silicon electro optic modulator[J]. Nature, 2005(435):325-327
[39] Chao C Y, Guo L J. Biochemical sensors using high Q polymer micro-ring [J]. Applied Physics Letters, 2003, 83(8):1527-1529
[40] Barrios C. A., Gylfason K. B., Schez B., et al. Slot-waveguide biochemical sensor [J]. Optics letters, 2007, 32(21): 3080-3082.
[41] Sang-Yeon C., Dobbs G., Jokerst N. M. et al. Optical microring resonator sensors with selective membrane surface customization [J]. In: CLEO. Baltimore, US: 2007. CWE4.
[42] Dai D., He S. Highly-sensitive sensor with large measurement range realized with two cascaded-microring resonators [J]. Optics communications, 2007, 279(1): 89-93.
[43] Kwon M.-S., Steier W. H. Microring-resonator-based sensor measuring both the concentration and temperature of a solution [J]. Optics express, 2008, 16(13): 9372-9377.
[44] Siegfried J., Adam D., Dan-Xia X., et al. Densely folded silicon photonic wire biosensors in ring resonator and Mach-Zender configurations [J]. In: CLEO. San jose, US: 2008.CWP6.
[45] Xia Z., Chen Y., Zhou Z. Dual waveguide coupled microring resonator sensorbased on inensity detection [J]. IEEE Journal of quantum electronics, 2008, 44(1): 100-107.
[46] Hryniewicz J. V., Absil P. P., Little B. E., et al. Higher order filter response in coupled micro-ring resonators [J]. IEEE Photonics Technology Letters, 2000, 12(3):320-322.
[47] Little B. E., Chu S. T., Absil P. P., et al. Very high-order micro-ring resonator filers the WDM applications[J]. IEEE Photonics Technology Letters, 2004, 16(10):2263-2265
[48] Popovic M. A., Barwicz T., Watts M.R., et al. Multistage high-order micro-ring resonator add-drop filers [J]. Optics letters, 2006, 31(17): 2571-2573
[49] Griffel G. Synthesis of optical filters using ring resonator arrays [J]. IEEE Photonics Technology Letters, 2000, 12(7):810-812
[50] Little B. E., Chu S. T., Hryniewicz J. V., et al. Filer synthesis for periodically coupled micro-ring resonators [J]. Optics Letters, 2000, 25(5):344-346
[51] Ma Y., Chang S.H., Chang S. S., et al. Improved optical filter responses in cascaded InGaAsP/InP micro-disk resonators [J]. Electronics Letters, 2001, 37(9): 564-565
[52]闫欣,马春生,徐元哲等.硅基M×N型微环阵列谐振滤波器的理论分析[J ].半导体学报, 2005 , 26(11) : 2223-2229.
[53]张小贝,黄德修,洪伟等.传输矩阵法分析微环谐振器阵列传输特性[J].光学学报,2007,9(27):1586-1592.
[54] Chu S.T., Little B.E., Pan W., et al. An eight-channel add-drop filter using vertically coupled micro-ring resonators over a cross grid [J]. IEEE, Lightwave Technol, 1999, 11(6):691-693
[55] Suzuki S., Hatakeyama Y., et al. Precise control of wavelength channel spacing of micro-ring resonator Add-Drop filter array [J]. Lightwave Technol.2002, 20(4):745
[56] Mason S J. Feedback Theory -Further Properties of Signal flow graphs [J]. Proceedings of the IRE, 1956, 44: 920-926.
[57]管致中,夏恭恪.信号与线性系统(第三版)上册[M].北京:高等教育出版社,1992:334-345.
[58]李堂翔.信号流图及其应用[J].武汉粮食工业学院学报,1991: 50-55.
[59] A.Melloni, M. Martinelli, Synthesis of direct coupled resonators bandpass filters for WDM systems [J]. IEEE, Lightwave technol, 2002, 20: 296-303.
[60] Madsen C.K., Zhao J.H.. Optical Filter Design and Analysis: A Signal Processing Approach [M]. Wiley, New York, 1999:95-146.
[61]张彬,毛陆虹,谢生等.一种基于spice的硅基微环光学谐振器模型及其在光学滤波器中的应用[J].光学学报,2010,2(30):537-541.
[62] J. P. Lee, et al., Resonance characteristics of waveguide-coupled polyimide micro-ring resonator [J]. Opt Materials, 2002, 3(21): 535-541.
[63] P. P. Absil, et al., Vertically coupled micro-ring resonators using polymer wafer bonding [J]. IEEE Photon, Technol. Lett. 2001, 13(1): 49-50.
[2]曹茂虹,刘礼.光纤通信技术的现状及发展趋势[M].光机电信息,2007,5:34-37.
[3]李玮.浅析光纤通信技术的发展与展望[J].科技风,2009,21.
[4]张煦.OFC--2002关于光纤传输系统的实验报道[J].光通信技术,2002,3,(26).
[5] Raj Jain. All-Optical Networks,专题报告[R].2002
[6] Miller S. E. Intergrated Optics: An Introduction [J]. Bell Labs Technical Journal, 1969,48: 2059-2061
[7] Marcatili E. A. J. Bends in optical dielectric guides [J]. Bell Labs Technical Journal, 1969, 48:2103-2132
[8]李卫彬.信号流程图理论及其在光学环谐振腔特性分析中应用的研究[D].博士论文,华中科技大学,2009.
[9] Baehr-Jones T., Hochberg M., Walker C., et al. High-Q ring resonators in thin silicon-on-insulator [J]. Applied Physics Letter, 2004, 85(16): 3346-3347.
[10] Grover R., Van V., Ibrahim T. A., et al. parallel-cascaded semiconductor micro-ring resonators for high-order and wide-FSR filters [J]. Journal of Lightwave Technology, 2002, 20(5):900-905.
[11] Choi S. J., Peng Z., Yang Q., et al. An eight-channel demultiplexing swith array using vertically coupled active semiconductor microdisk resonators [J]. IEEE photonics Technology Letter, 2004, 16(11): 2517-2519.
[12] Rabiei P., Steier W. H. Tunable polymer double micro-ring filers [J]. IEEE Photonics Technology Letters, 2003, 15(9): 1255-1257.
[13] Kim D. H., Im J. G., Lee S. S., et al. Polymeric microring resonator using nanoimprint technique based on a stamp incorporating a soothing buffer layer [J]. IEEE Photonics Technology Letters, 2005, 17(11):2352-2354.
[14] Huang S. W., Chen S. L., Ling T., et al. Low-noise wideband ultrasound detection using polymer micro-ring resonators [J]. Applied Physics Letters, 2008, 92, (19).
[15] Huang W. P. Coupled-mode theory for optical waveguide: an overview [J]. Journal of the Optical Society of America A, 1994, 11(3): 963-983.
[16]马春生,刘式墉.光波导模式理论[M].长春:吉林大学出版社,2006: 352-355
[17]闫欣.微环谐振波分复用器的模拟与分析[D].博士论文,吉林大学,2006.
[18]杨建义,江晓清,王明华等.采用单环微谐振器的光滤波器特性及其局限性[J].光电子·激光, 2003,14(1) :12-16
[19]董小伟,裴丽,简水生.传输矩阵法分析多环高阶谐振滤波器特性[J].中国激光,2005,7,(32):929-932.
[20]张小贝,黄修德,洪伟等.传输矩阵法分析微环谐振器阵列传输特性[J].光学学报,2007,9,(27):1586-1592.
[21]张小贝.微环谐振器及应用的理论和实验研究[D].博士论文,华中科技大学,2009.
[22] Taflove A., Hagness S. C. Computational Electrodynamics: The finite-difference time-domain method (Second Edition) [M]. Norwood, US: Artech House, Inc, 2000. 67-106.
[23] Chen W., Chen W., Chen Y.-J. A Characteristic matrix approach for analyzing resonant ring lattice devices [J]. IEEE, Photonics Technology Letters, 2004, 16 (2):458-460.
[24] Chen W., Wang Z., Chen W., et al. General ring resonator analysis and characterization by characteristic matrix [J]. Journal of Lightwave Technology,2005, 23(2): 915-922.
[25] Chin M K, Chu D Y, Ho S T. Estimation of the spontaneous emission factor for microdisk lasers vea the approximation of whispering gallery mode [J]. Journal of Applied Physics, 1994, 75:3302-3305.
[26] Yariv A. Universal relations for coupling of optical power between microresonators and dielectric waveguides [J]. Electronics Letters, 2000, 36(4):321-322.
[27] Mason S J. Feedback Theory -Further Properties of Signal flow graphs [J]. Proceedings of the IRE, 1956, 44: 920-926.
[28] Yariv A., Xu Y., Lee R.K., etal. Coupled-resonator optical waveguide: a proposal and analysis [J].Optics Letters, 1999, 24(11):711-713
[29] Poon J. K. S., Scheuer J., Xu Y., et al. Designing coupled-resonator optical waveguide delay lines [J]. Journal of the Optical Society of America B, 2004, 21(9): 1665-1673.
[30] Little B E, Haus H A, Foresi J S, et al. Wavelength selective switch using thermally tunable microring resonators [J]. Photonics technology letters, 1998, 10(16): 816-818.
[31] Emelett S J, Soref R A. Analysis of dual micro-ring resonator cross connect switches and modulators[J]. Optics Express, 2005, 13(20):7840-7853
[32] Polson R C, Levina G, Vardeny Z V. Spectral analysis of polymer micro-ring lasers [J]. Applied Physics letters, 2000, 76 (26):3858-3860.
[33] Sorel M., Laybourn P. J. R., Giuliani G., et al. Unidirectional bistability in semiconductor waveguide ring lasers [J]. Applied physics letters, 2002, 80,(17): 3050-3051.
[34] Sorel M., Giuliani G., Scire A., et al. Operating regimes of GaAs-AlGaAs semiconductor ring lasers: experiment and model[J]. IEEE Journal of quantum electronics, 2003, 39(10): 1187-1195.
[35] Yu S., Wang Z., Yuan G., et al. Optically triggered monostable and bistable flip-flop operation of a monolithic semiconductor ring laser. In: Photonics in switching [M]. San Francisco, 2007: 115-116.
[36] Hill M. T., Dorren H. J.S., De Vries T., et al. A fast low-power optical memory based on coupled micro-ring lasers [J]. Nature, 2004, 432(7014): 206-209
[37] Wang Z., Yuan G., Verschaffelt G., et al. Storing 2 bit of information in a novel single semiconductor microring laser memory cell [J]. IEEE Photonics technology letters, 2008, 20(14): 1228-1230.
[38] Xu Q F, Schmidt B, Pradhan S, et al. Micro-metre scale silicon electro optic modulator[J]. Nature, 2005(435):325-327
[39] Chao C Y, Guo L J. Biochemical sensors using high Q polymer micro-ring [J]. Applied Physics Letters, 2003, 83(8):1527-1529
[40] Barrios C. A., Gylfason K. B., Schez B., et al. Slot-waveguide biochemical sensor [J]. Optics letters, 2007, 32(21): 3080-3082.
[41] Sang-Yeon C., Dobbs G., Jokerst N. M. et al. Optical microring resonator sensors with selective membrane surface customization [J]. In: CLEO. Baltimore, US: 2007. CWE4.
[42] Dai D., He S. Highly-sensitive sensor with large measurement range realized with two cascaded-microring resonators [J]. Optics communications, 2007, 279(1): 89-93.
[43] Kwon M.-S., Steier W. H. Microring-resonator-based sensor measuring both the concentration and temperature of a solution [J]. Optics express, 2008, 16(13): 9372-9377.
[44] Siegfried J., Adam D., Dan-Xia X., et al. Densely folded silicon photonic wire biosensors in ring resonator and Mach-Zender configurations [J]. In: CLEO. San jose, US: 2008.CWP6.
[45] Xia Z., Chen Y., Zhou Z. Dual waveguide coupled microring resonator sensorbased on inensity detection [J]. IEEE Journal of quantum electronics, 2008, 44(1): 100-107.
[46] Hryniewicz J. V., Absil P. P., Little B. E., et al. Higher order filter response in coupled micro-ring resonators [J]. IEEE Photonics Technology Letters, 2000, 12(3):320-322.
[47] Little B. E., Chu S. T., Absil P. P., et al. Very high-order micro-ring resonator filers the WDM applications[J]. IEEE Photonics Technology Letters, 2004, 16(10):2263-2265
[48] Popovic M. A., Barwicz T., Watts M.R., et al. Multistage high-order micro-ring resonator add-drop filers [J]. Optics letters, 2006, 31(17): 2571-2573
[49] Griffel G. Synthesis of optical filters using ring resonator arrays [J]. IEEE Photonics Technology Letters, 2000, 12(7):810-812
[50] Little B. E., Chu S. T., Hryniewicz J. V., et al. Filer synthesis for periodically coupled micro-ring resonators [J]. Optics Letters, 2000, 25(5):344-346
[51] Ma Y., Chang S.H., Chang S. S., et al. Improved optical filter responses in cascaded InGaAsP/InP micro-disk resonators [J]. Electronics Letters, 2001, 37(9): 564-565
[52]闫欣,马春生,徐元哲等.硅基M×N型微环阵列谐振滤波器的理论分析[J ].半导体学报, 2005 , 26(11) : 2223-2229.
[53]张小贝,黄德修,洪伟等.传输矩阵法分析微环谐振器阵列传输特性[J].光学学报,2007,9(27):1586-1592.
[54] Chu S.T., Little B.E., Pan W., et al. An eight-channel add-drop filter using vertically coupled micro-ring resonators over a cross grid [J]. IEEE, Lightwave Technol, 1999, 11(6):691-693
[55] Suzuki S., Hatakeyama Y., et al. Precise control of wavelength channel spacing of micro-ring resonator Add-Drop filter array [J]. Lightwave Technol.2002, 20(4):745
[56] Mason S J. Feedback Theory -Further Properties of Signal flow graphs [J]. Proceedings of the IRE, 1956, 44: 920-926.
[57]管致中,夏恭恪.信号与线性系统(第三版)上册[M].北京:高等教育出版社,1992:334-345.
[58]李堂翔.信号流图及其应用[J].武汉粮食工业学院学报,1991: 50-55.
[59] A.Melloni, M. Martinelli, Synthesis of direct coupled resonators bandpass filters for WDM systems [J]. IEEE, Lightwave technol, 2002, 20: 296-303.
[60] Madsen C.K., Zhao J.H.. Optical Filter Design and Analysis: A Signal Processing Approach [M]. Wiley, New York, 1999:95-146.
[61]张彬,毛陆虹,谢生等.一种基于spice的硅基微环光学谐振器模型及其在光学滤波器中的应用[J].光学学报,2010,2(30):537-541.
[62] J. P. Lee, et al., Resonance characteristics of waveguide-coupled polyimide micro-ring resonator [J]. Opt Materials, 2002, 3(21): 535-541.
[63] P. P. Absil, et al., Vertically coupled micro-ring resonators using polymer wafer bonding [J]. IEEE Photon, Technol. Lett. 2001, 13(1): 49-50.