基于SOI波导非线性效应的光脉冲开关设计及分析
|
摘要
近年来,绝缘体上的硅(SOI)波导引起了业界的广泛关注,人们对其理论和实验的研究也日渐增多。由于SOI波导结构具有很强的光场约束性能,它的材料具有双光子吸收等特性,这决定了它拥有多种非线性效应。
本论文研究了皮秒和飞秒量级的光脉冲在SOI波导中的非线性过程,并利用这个过程所表现出来的函数,设计了各种光开关模型,并对其进行热稳定分析。主要的研究成果如下：
(1)综述了近年来硅基光电子器件的发展状况以及它们在非线性光开关上的应用趋势。在参考相关理论的基础上,得到了较完善的光脉冲非线性传输方程。
(2)介绍了矢量有限单元法的电磁学分析理论,并把这种方法应用于聚合物波导的模式分析中,得到更加精确的计算结果。还把这种方法应用于光电印刷电路板(EOPCB)的45°全内反射波导镜的误差分析中,得出了相对功率变化和制作误差之间的关系；计算出了制作误差的容限,这有利于指导实际的45°全内反射波导镜的制作。还把这种方法应用于EOPCB的45°全内反射波导镜和波导的对齐误差的分析中,得出了相对功率变化和对齐误差之间的关系；计算出了对齐误差的容限,有利于指导实际的45°全内反射波导镜和波导对齐的制作。
(3)介绍了非线性薛定谔方程的常用解法——分步傅立叶方法,但这个方法的缺点是需要大量的计算机内存和计算时间；因此,本论文提出了分步多小波方法来求解非线性薛定谔方程。它将光脉冲信号进行取样、压缩之后再计算,这样可以节省计算机的内存和计算时间,而计算精度却没有明显的下降。并且,把这个方法应用于两芯非线性光脉冲开关的求解中,在和其他的方法相比之后,发现耦合器的功率转移效率没有明显变化,但计算机的内存和计算时间却减少很多,此方法有利于偏微分方程的迭代求解。
(4)分析了刻蚀深度扰动条件下的线性负切趾SOI布拉格光栅(LNTSBGDC)两芯变系数耦合器的功率传递效率。对于高斯、指数和升余弦变耦合系数来说,当相对功率传递效率分别低于0.02时,光脉冲开关的性能基本上不受影响；此时得到了刻蚀深度的容限,有利于指导实际的制作这种光开关。另外,设计了级联的SOI非线性光脉冲开关,分别计算了耦合长度,芯距比对开关功能的影响。在对脉冲光开关的切换功能影响不大的前提下,计算出芯层的高度、宽度和芯距比的制作容限。在此容限范围内,他们对功率转移效率和相对功率转移效率误差的影响很有限。当四个不同功率的光脉冲输入时,他们分别被切换到不同的端口输出。尽管输出脉冲有一点压缩和损耗,但输出脉冲的波形基本上没有太大变化。而光脉冲开关的功能却实现了,这个设计证明是有效的。
(5)分析了基于非对称三芯SOI变高斯耦合系数光脉冲开关的功率转移效率和消光比的热稳定性。因为Si和Si02材料的折射率受温度变化的影响,那么非线性耦合器的有效折射率也相应的变化。当耦合系数的参数以及温度变化时,分别得到相对转移效率误差值、相对消光比变化值。当温度在±100K的范围内变化时,计算出了耦合系数参数的设计范围；在这个范围内光脉冲开关的功率转移效率和消光比能够稳定工作。另外,研究了双光子吸收效应引起的光脉冲波长选择开关阵列的性能变化。因为双光子吸收效应能够使整个阵列的温度发生变化,而温度的变化将导致材料的有效折射率以及布拉格波长发生变化；这将造成功率转移效率,脉冲峰值幅度比和相对消光比发生变化。经过计算,得到归一化输入功率的取值范围；在此范围内,相对转移效率值变化的最小,光脉冲开关的切换功能基本上不受影响。脉冲波长选择的功能得以可靠实现。这对于指导实际的制作光脉冲波长选择开关阵列是有意义的。
In recent years, silicon on insulator (SOI) waveguide is concerned by the semiconductor researchers and its theoretical and experimental studies have gradually increased. Because its structure has a strong light-binding property and its material has a Kerr and two-photon absorption property, these determine that it has a variety of nonlinear effects.
In this thesis, we have researched the nonlinear processes in SOI waveguide used an ultrafast picosecond or femtosecond optical pulse. Then, we have used these functions obtained in these processes to design some optical switch models and analyzed their thermal stability. The main results are as follows:
(1) We have summarized the recent development about silicon-based optoelectronic devices as well as their applying trend on nonlinear optical switches. On the basis of existing theories, we obtain a better light pulse nonlinear propagation equation in the SOI waveguide.
(2) The vector finite element method is introduced to the electromagnetic field theory and is applied to analyze the modes of polymer waveguide for more accurate results. This method is also used to analyze the errors about 45°total internal reflection waveguide mirror in the electro-optic printed circuit board (EOPCB), the relationship between fabrication errors and relative power change is obtained. The fabrication error tolerance is calculated, it is beneficial to direct the actual 45°total internal reflection waveguide mirror production. Moreover, this method is also applied to analyze the misalignment errors between the 45°total internal reflection waveguide mirror and waveguide in the EOPCB. The relationship between relative power change and misalignment errors is obtained. The misalignment error tolerance is achieved, it is useful to guide the actual alignment fabrication between the 45°total internal reflection waveguide mirror and waveguide.
(3) The conventional solution to nonlinear Schrodinger equation, Split-step Fourier method, is introduced. But, this method requires a large amount of computer memory and time, so, we propose a Split-step multi-wavelet method for solving nonlinear Schrodinger equation. This method will sample and compress the optical pulse signal in order to save computer memory and time and preserve calculating accuracy. We have applied this method to solve the two-core nonlinear optical pulse switch. Compared with other methods, we find the power transmission efficiency do not loss significantly in the coupler, but the computational memory and time has clearly decreased. This method is beneficial to iteratively solve the differential equations.
(4) We have analyzed the power transmission efficiency in the two-core linear negative tapered SOI Bragg grating directional coupler (LNTSBGDC) under etching depth perturbation. For the Gaussian, exponential and raised cosine variable coupling coefficient, when the power transmission efficiency is lower than 0.02, the performance of optical pulse switch is essentially unaffected and the etching depth tolerance is achieved. It is useful to actually guide to fabricate optical switches. Moreover, we have also designed the cascaded SOI nonlinear optical pulse switch. The coupling length and the core-distance-ratio of switch are calculated. When the function of optical pulse switch is unaffected, the tolerance of height and width in the core layer and tolerance of core-distance-ratio is calculated. In the range of tolerance, the power transmission efficiency and relative power transmission efficiency error have been not seriously affected by the variation. When four pulses with different power are input, they are switched to different output ports. Although the output pulses have a little compression and loss, these output pulse waveforms are essentially unchanged. The optical pulse switch function is achieved, so, this design is effective.
(5) The thermal stability of power transmission efficiency and extinction ratio in the optical pulse switch is analyzed. The switch has a three-core asymmetric SOI variable Gaussian coupling coefficient. Because the refractive indices of Si and SiO2 are affected by temperature, the effective refractive indices in the nonlinear coupler change correspondingly. When the coupling coefficients and temperature vary, the relative transmission efficiency errors and the relative extinction ratios are obtained respectively. When temperature change during±100K, the design parameter scope of coupling coefficient is obtained. The power transmission efficiency and extinction ratio in the optical pulse switch can work stably in this area. In addition, we have researched the switch performance in the optical pulse wavelength selective switch array, which is disturbed by two-photon absorption. Because two-photon absorption can change the temperature in this array, the temperature will affect the effective refractive index of material and shift the Bragg wavelength; this will disturb the power transmission efficiency, pulse peak-amplitude-ratio and relative extinction ratio. The normalized input power range is calculated in order to minimize the variation of relative transmission efficiency. So, the switch function of optical pulses is essentially unaffected. Pulse wavelength selection function can be achieved reliably. It is useful to actually guide to fabricate optical pulse wavelength selection switch array.
本论文研究了皮秒和飞秒量级的光脉冲在SOI波导中的非线性过程,并利用这个过程所表现出来的函数,设计了各种光开关模型,并对其进行热稳定分析。主要的研究成果如下：
(1)综述了近年来硅基光电子器件的发展状况以及它们在非线性光开关上的应用趋势。在参考相关理论的基础上,得到了较完善的光脉冲非线性传输方程。
(2)介绍了矢量有限单元法的电磁学分析理论,并把这种方法应用于聚合物波导的模式分析中,得到更加精确的计算结果。还把这种方法应用于光电印刷电路板(EOPCB)的45°全内反射波导镜的误差分析中,得出了相对功率变化和制作误差之间的关系；计算出了制作误差的容限,这有利于指导实际的45°全内反射波导镜的制作。还把这种方法应用于EOPCB的45°全内反射波导镜和波导的对齐误差的分析中,得出了相对功率变化和对齐误差之间的关系；计算出了对齐误差的容限,有利于指导实际的45°全内反射波导镜和波导对齐的制作。
(3)介绍了非线性薛定谔方程的常用解法——分步傅立叶方法,但这个方法的缺点是需要大量的计算机内存和计算时间；因此,本论文提出了分步多小波方法来求解非线性薛定谔方程。它将光脉冲信号进行取样、压缩之后再计算,这样可以节省计算机的内存和计算时间,而计算精度却没有明显的下降。并且,把这个方法应用于两芯非线性光脉冲开关的求解中,在和其他的方法相比之后,发现耦合器的功率转移效率没有明显变化,但计算机的内存和计算时间却减少很多,此方法有利于偏微分方程的迭代求解。
(4)分析了刻蚀深度扰动条件下的线性负切趾SOI布拉格光栅(LNTSBGDC)两芯变系数耦合器的功率传递效率。对于高斯、指数和升余弦变耦合系数来说,当相对功率传递效率分别低于0.02时,光脉冲开关的性能基本上不受影响；此时得到了刻蚀深度的容限,有利于指导实际的制作这种光开关。另外,设计了级联的SOI非线性光脉冲开关,分别计算了耦合长度,芯距比对开关功能的影响。在对脉冲光开关的切换功能影响不大的前提下,计算出芯层的高度、宽度和芯距比的制作容限。在此容限范围内,他们对功率转移效率和相对功率转移效率误差的影响很有限。当四个不同功率的光脉冲输入时,他们分别被切换到不同的端口输出。尽管输出脉冲有一点压缩和损耗,但输出脉冲的波形基本上没有太大变化。而光脉冲开关的功能却实现了,这个设计证明是有效的。
(5)分析了基于非对称三芯SOI变高斯耦合系数光脉冲开关的功率转移效率和消光比的热稳定性。因为Si和Si02材料的折射率受温度变化的影响,那么非线性耦合器的有效折射率也相应的变化。当耦合系数的参数以及温度变化时,分别得到相对转移效率误差值、相对消光比变化值。当温度在±100K的范围内变化时,计算出了耦合系数参数的设计范围；在这个范围内光脉冲开关的功率转移效率和消光比能够稳定工作。另外,研究了双光子吸收效应引起的光脉冲波长选择开关阵列的性能变化。因为双光子吸收效应能够使整个阵列的温度发生变化,而温度的变化将导致材料的有效折射率以及布拉格波长发生变化；这将造成功率转移效率,脉冲峰值幅度比和相对消光比发生变化。经过计算,得到归一化输入功率的取值范围；在此范围内,相对转移效率值变化的最小,光脉冲开关的切换功能基本上不受影响。脉冲波长选择的功能得以可靠实现。这对于指导实际的制作光脉冲波长选择开关阵列是有意义的。
In recent years, silicon on insulator (SOI) waveguide is concerned by the semiconductor researchers and its theoretical and experimental studies have gradually increased. Because its structure has a strong light-binding property and its material has a Kerr and two-photon absorption property, these determine that it has a variety of nonlinear effects.
In this thesis, we have researched the nonlinear processes in SOI waveguide used an ultrafast picosecond or femtosecond optical pulse. Then, we have used these functions obtained in these processes to design some optical switch models and analyzed their thermal stability. The main results are as follows:
(1) We have summarized the recent development about silicon-based optoelectronic devices as well as their applying trend on nonlinear optical switches. On the basis of existing theories, we obtain a better light pulse nonlinear propagation equation in the SOI waveguide.
(2) The vector finite element method is introduced to the electromagnetic field theory and is applied to analyze the modes of polymer waveguide for more accurate results. This method is also used to analyze the errors about 45°total internal reflection waveguide mirror in the electro-optic printed circuit board (EOPCB), the relationship between fabrication errors and relative power change is obtained. The fabrication error tolerance is calculated, it is beneficial to direct the actual 45°total internal reflection waveguide mirror production. Moreover, this method is also applied to analyze the misalignment errors between the 45°total internal reflection waveguide mirror and waveguide in the EOPCB. The relationship between relative power change and misalignment errors is obtained. The misalignment error tolerance is achieved, it is useful to guide the actual alignment fabrication between the 45°total internal reflection waveguide mirror and waveguide.
(3) The conventional solution to nonlinear Schrodinger equation, Split-step Fourier method, is introduced. But, this method requires a large amount of computer memory and time, so, we propose a Split-step multi-wavelet method for solving nonlinear Schrodinger equation. This method will sample and compress the optical pulse signal in order to save computer memory and time and preserve calculating accuracy. We have applied this method to solve the two-core nonlinear optical pulse switch. Compared with other methods, we find the power transmission efficiency do not loss significantly in the coupler, but the computational memory and time has clearly decreased. This method is beneficial to iteratively solve the differential equations.
(4) We have analyzed the power transmission efficiency in the two-core linear negative tapered SOI Bragg grating directional coupler (LNTSBGDC) under etching depth perturbation. For the Gaussian, exponential and raised cosine variable coupling coefficient, when the power transmission efficiency is lower than 0.02, the performance of optical pulse switch is essentially unaffected and the etching depth tolerance is achieved. It is useful to actually guide to fabricate optical switches. Moreover, we have also designed the cascaded SOI nonlinear optical pulse switch. The coupling length and the core-distance-ratio of switch are calculated. When the function of optical pulse switch is unaffected, the tolerance of height and width in the core layer and tolerance of core-distance-ratio is calculated. In the range of tolerance, the power transmission efficiency and relative power transmission efficiency error have been not seriously affected by the variation. When four pulses with different power are input, they are switched to different output ports. Although the output pulses have a little compression and loss, these output pulse waveforms are essentially unchanged. The optical pulse switch function is achieved, so, this design is effective.
(5) The thermal stability of power transmission efficiency and extinction ratio in the optical pulse switch is analyzed. The switch has a three-core asymmetric SOI variable Gaussian coupling coefficient. Because the refractive indices of Si and SiO2 are affected by temperature, the effective refractive indices in the nonlinear coupler change correspondingly. When the coupling coefficients and temperature vary, the relative transmission efficiency errors and the relative extinction ratios are obtained respectively. When temperature change during±100K, the design parameter scope of coupling coefficient is obtained. The power transmission efficiency and extinction ratio in the optical pulse switch can work stably in this area. In addition, we have researched the switch performance in the optical pulse wavelength selective switch array, which is disturbed by two-photon absorption. Because two-photon absorption can change the temperature in this array, the temperature will affect the effective refractive index of material and shift the Bragg wavelength; this will disturb the power transmission efficiency, pulse peak-amplitude-ratio and relative extinction ratio. The normalized input power range is calculated in order to minimize the variation of relative transmission efficiency. So, the switch function of optical pulses is essentially unaffected. Pulse wavelength selection function can be achieved reliably. It is useful to actually guide to fabricate optical pulse wavelength selection switch array.
引文
[1]G. T. Reed, A. P. Knights. Silicon Photonics:An introduction. Chichester:John Wiley,2004.56～67
[2]L. Pavesi, D. J. Lockwood. Silicon photonics. New York:Springer-Verlag,2004. 78～89
[3]B. Jalali, S. Yegnanarayanan, T. Yoon, et al. Advances in Silicon-on-insulator optoelectronics. IEEE J. Selected Topics in Quantum Electron.,1998,4(6): 938-947
[4]B. Jalali, V. Raghunathan, D. Dimitropoulos, et al. Raman-based silicon photonics. IEEE J. Selected Topics in Quantum Electron.,2006,12(3):412～421
[5]B. Jalali, S. Fathpour. Silicon photonics. J. Lightwave Technol.,2006,24(12):4600 ～4615
[6]R. Soref. The past, present, and future of silicon photonics. IEEE J. Selected Topics in Quantum Electron.,2006,12(6):1678～1687
[7]H. Rong, A. Liu, R. Jones, et al. An all-silicon Raman laser. Nature,2005, 433(7023):292～294
[8]H. Rong, R. Jones, A. Liu, et al. A continuous-wave Raman silicon laser. Nature, 2005,433(7027):725～728
[9]M. Foster, A. Turner, J. Sharping, et al. Broad-band optical parametric gain on a silicon photonic chip. Nature Photon.,2006,441(7096):960～963
[10]S. Lin, Y. Kobayashi, Y. Ishikawa, et al. Luminescence enhancement by Si ring resonator structures on silicon on insulator. Appl. Phys. Lett.,2008,92(2):021～031
[11]T. Liang, H. Tsang. Efficient Raman amplification in silicon-on-insulator waveguides. Appl. Phys. Lett.,2004,85(16):3343～3345
[12]R. Espinola, J. Dadap, R. Osgood, et al. Raman amplification in ultrasmall silicon-on-insulator wire waveguides. Opt. Express,2004,12(16):3713～3718
[13]B. Jalali, R. Claps, D. Dimitropoulos, et al. Light generation, amplification, and wavelength conversion via stimulated Raman scattering in silicon microstructures. Silicon Photonics,2004,94:199-238
[14]V. Sih, S. Xu, Y. Kuo, et al. Raman amplification of 40 Gb/s data in low-loss silicon waveguides. Opt. Express,2007,15(2):357～362
[15]C. Png, S. Chan, S. Lin, et al. Optical phase modulators for MHz and GHz modulation in silicon-on-insulator (SOI). J. Lightwave Technol.,2004,22(6): 1573～1582
[16]C. Manolatou, M. Lipson. All-optical silicon modulators based on carrier injection by two-photon absorption. J. Lightwave technol.,2006,24(3):1433～1439
[17]R. Chuang, M. Hsu. Silicon optical modulators in silicon-on-insulator substrate based on the p-i-n waveguide structure. J. Appl. Phys.,2007,46(4):2445～2449
[18]M. Foerst, J. Niehusmann, T. Plotzing, et al. High-speed all-optical switch in ion-implanted silicon-on-insulator or microring resonators. Opt. Lett.,2007,32(14): 2046～2048
[19]F. Sun, J. Yu, S. Chen. A 2x2 optical switch based on plasma dispersion effect in silicon-on-insulator. Optics Commun.,2006,262(2):164～169
[20]F. Sun, J. Yu, S. Chen. High speed 2x2 optical switch in silicon-on-insulator based on plasma dispersion effect. Chinese Phys. Lett.,2005,22(12):3097～3099
[21]D. Beggs, T. White, L. O'Faolain, et al. Ultracompact and low-power optical switch based on silicon photonic crystals. Opt. Lett.,2008,33(2):147～149
[22]Q. Fang, P. Chen, H. Xin, et al. Low power-consumption and high response frequency thermo-optic variable optical Attenuators based on silicon-on-insulator materials. Chinese Phys. Lett.,2005,22(6):1452～1455
[23]Y. Li, Y. Chen, S. Chen, et al. Silicon-on-insulator thermo-optic variable attenuator module with fast response. Opt. Engineering,2005,44(6):62～66
[24]J. Xia, J. Yu. Thermo-optic variable optical attenuator with low power consumption fabricated on silicon-on-insulator by anisotropic chemical etching. Opt. Lett.,2004, 43(4):189～790
[25]W. Ye, D. Xu, S. Janz, et al. Passive broadband silicon-on-insulator polarization splitter. Opt. Lett.,2007,32(11):1492～1494
[26]A. Kazmierczak, M. Briere, E. Drouard, et al. Design, simulation, and characterization of a passive optical add-drop filter in silicon-on-insulator technology. IEEE Photonics Technolo. Lett.,2005,17(7):1447～1449
[27]A. Shinya, S. Mitsugi, E. Kuramochi, et al. Ultrasmall multi-port channel drop filter in two-dimensional photonic crystal on silicon-on-insulator substrate. Optics Express,2006,14(25):12394～12400
[28]R. A. Soref, J. Schmidtchen, K. Petermann. Large single-mode waveguides in GeSi-Si and Si-on-SiO2. IEEE J. Quantum Electron.,1991,27(8):1971～1974
[29]S. Pogossian, L. Vescan, A. Vonsovici. The single-mode condition for semiconductor rib waveguides with large cross section. J. Lightwave Technol.,1998, 16(10):1851～1853
[30]J. D. Plummer, M. D. Deal, P. B. Griffin. Silicon VLSI technology:Fundamentals, Practice, and Modeling. London:Prentice Hall,2000.106～114
[31]G. Celler., S. Cristoloveanu. Frontiers of silicon-on-insulator. J. Appl. Phys.,2003, 93(9):4955～4978
[32]J. Plaza, J. Esteve, E. Lora-Tamavo. Simple technology for bulk accelerometer based on bond and etch back silicon on insulator wafers. Sensors and Actuators A-Physical,1998,68(3):299-302
[33]M. Tajima, S. Ibuka, H. Aga, et al. Characterization of bond and etch-back silicon-on-insulator wafers by photoluminescence under ultraviolet excitation. Appl. Phys. Lett.,1997,70(2):231～233
[34]G. K. Celler, S. Cristoloveanu. Applied physics reviews-focused review. J. Appl. Phys.,2003,93(9):4955-4978
[35]冯倩,郝跃.新型绝缘体上硅技术的发展与展望.西安电子科技大学学报(自然科学版),2001,28(6)：792-796
[36]A. Ploβl, G. Krauter. Silicon-on-insulator:materials aspects and applications. Solid-State Electron.,2000,44:775-782
[37]T. Liang, H. Tsang, I. Day, et al. Silicon waveguide two-photon absorption detector at 1.5 mu m wavelength for autocorrelation measurements. Appl. Phys. Lett.,2002, 81(7):1323～1325
[38]H. Tsang, C. Wong, T. Liang, et al. Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 mu m wavelength. Appl. Phys. Lett.,2002,80(3):416～418
[39]T. Liang, H. Tsang. Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides. Appl. Phys. Lett.,2004,84(15): 2745～2747
[40]R. Salem, T. Murphy. Polarization-insensitive cross correlation using two-photon absorption in a silicon photodiode. Opt. Lett.,2004,29(13):1524-1526
[41]C. Bosshard, R. Spreiter, M. Zgonik, et al. Kerr Nonlinearity via cascaded otpical rectification and the linear electro-optic effect. Phys. Rev. Lett.,1995,74(14): 2816-2819
[42]R. D. Coso, J. Solis. Relation between nonlinear refractive index and third-order susceptibility in absorbing media. J. Opt. Soc. Am. B,2004,21(3):640～644
[43]R. Stolen, A. Ashkin. Optical kerr effect in glass waveguide. IEEE J. Quantum Electron.,1972,8(6):548～549
[44]O. Boyraz, T. Indukuri, B. Jalali. Self-phase-modulation induced spectral broadening in silicon waveguides. Opt. Express,2004,12(5):829～834
[45]E. Dulkeith, Y. Vlasov, X. Chen, et al. Self-phase-modulation in submicron silicon-on-insulator photonic wires. Opt. Express,2006,14(12):5524～5534
[46]G. Rieger, K. Virk, J. Young. Nonlinear propagation of ultrafast 1.5 mu m pulses in high-index-contrast silicon-on-insulator waveguides. Appl. Phys. Lett.,2004,84(6): 900-902
[47]A. Cowan, G. Rieger, J. Young. Nonlinear transmission of 1.5 μm pulses through single-mode silicon-on-insulator waveguide structures. Opt. Express,2004,12(8): 1611～1621
[48]R. Dekker, A. Driessen, T. Wahlbrink, et al. Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 mu m femtosecond pulses. Opt. Express,2006,14(18):8336～8346
[49]I. Hsieh, X. Chen, J. Dadap, et al. Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides. Opt. Express,2006,14(25): 12380～12387
[50]R. Dekker, N. Usechak, M. Forst, et al. Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides. J. Phys. D-Appl. Phys.,2007,40(14):249～271
[51]I. Hsieh, X. Chen, J. Dadap, et al. Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires. Opt. Express,2007,15(3):1135～1146
[52]O. Boyraz, P. Koonath, V. Raghunathan, et al. All optical switching and continuum generation in silicon waveguides. Opt. Express,2004,12(17):4094～4102
[53]Q. Lin, O. J. Painter, G. P. Agrawal. Nonlinear optical phenomena in silicon waveguides:Modeling and applications. Opt. Express,2007,15(25):16604～16644
[54]X. Chen, N. Panoiu, R. Osgood. Theory of Raman-mediated pulse amplification in silicon-wire waveguides. IEEE J. Quantum Electron.,2006,42(2):160～170
[55]D. Moss, L. Fu, I. Littler, et al. Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides. Electron. Lett.,2005,41(6):320-321
[56]T. Liang, L. Nunes, M. Tsuchiya, et al. High speed logic gate using two-photon absorption in silicon waveguides. Opt. Commun.,2006,265(1):171～174
[57]J. Mork, A. Mecozzi. Theory of nondegenerate four-wave mixing between pulses in a semiconductor waveguide. IEEE J. Quantum Electron.,1997,33(4):545～555
[58]K. Lor, K. Chiang. Theory of nondegenerate four-wave mixing in a birefringent optical fibre. Opt. Commun.,1998,152(1):26～30
[59]V. Passaro, F. De Leonardis. All-optical and gate based on Raman effect in silicon-on-insulator waveguide. Opt. and Quantum Electron.,2006,38(9):877～888
[60]Z. Li, G. Li. Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier. IEEE Photon. Technol. Lett.,2006,18(9): 1341-1343
[61]F. Martelli, A. Mecozzi, A. Dottavi, et al. Noise in wavelength conversion using four-wave mixing in semiconductor optical amplifiers. Appl. Phys. Lett.,1997, 70(3):306～308
[62]F. Geraghty, R. Lee, K. Vahala, et al. Wavelength conversion up to 18 run at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier. IEEE Photon. Technol. Lett.,1997,9(4):452～454
[63]S. Kumar, A. Willner. Simultaneous four-wave mixing and cross-gain modulation for implementing an all-optical XNOR logic gate using a single SOA. Opt. Express, 2006,14(12):5092～5097
[64]S. Mikroulis, H. Simos, E. Roditi, et al. Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator. IEEE Photon. Technol. Lett.,2005,17(9):1878～1880
[65]R. Salem, M. A. Foster, A. C. Turner, et al. Signal regeneration using low-power four-wave mixing on silicon chip. Nature Photon.,2008,2(1):35～38
[66]R. Soref, J. Lorenzo. All-silicon active and passive guided-wave components for λ=1.3 and 1.6μm. IEEE J. Quantum Electron.,1986,22(6):873～879
[67]V. Passaro, F. De Leonardis. Modeling and design of a novel high-sensitivity electric field silicon-on-tnsulator sensor based on a whispering-gallery-mode resonator. IEEE J. Selected Topics in Quantum Electron.,2006,12(1):124～133
[68]B. Schuppert, J. Schmidtchen, K. Petermann. Optical channel waveguides in silicon diffused from GeSi alloy. Electron. Lett.,1989,25(22):1500～1502
[69]J. W. M. Menezes, W. B. de Fraga, G. F. Guimaraes, et al, Optical switches and all-fiber logical devices based on triangular and planar three-core nonlinear optical fiber couplers. Opt. Commun.,2007,276:107～115
[70]Y. Vlasov, W. M. J. Green, F. Xia. High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks. Nature Photon.,2008, 2(4):242～246
[71]H. Wei, J. Yu, X. Zhang. Compact 3-dB tapered multimode interference coupler in silicon-on-insulator. Opt. Lett.,2001,26(12):878～880
[72]Y. Li, J. Yu, S. Chen. Submicrosecond rearrangeable nonblocking silicon-on-insulator thermo-optic 4×4 switch matrix. Opt. Lett.,2007,32(6):603～604
[73]Li Hong, Huang De-Xiu, Wang Dong-Ning, Influence of group-velocity mismatch on soliton switching in a nonlinear fiber coupler. Chin. Phys. Soc.,2003,12(4): 415～418
[74]B. M. Liang, G. J. Liu, Q. Li, et al. Coupled mode analysis of the nonlinear switching in the couplers with variable coupling coefficient. Opt. Commun.,2003, 223:195～200
[75]Y. Wang, W. Wang. Study of ultra-fast optical pulse propagation in a nonlinear directional coupler. Appl. Phys. B,2004,79:51～55
[76]F. M. Castro, M. I. Molina, W. D. Deering. Controlling all-optical switching in multicore nonlinear couplers. Opt. Commun.,2003,226:199～204
[77]Youfa Wang, Wenfeng Wang. Nonlinear optical pulse coupling dynamics. J. Lightwave Technol.,2006,24(6):2458～2464
[78]X. Chen, N. C. Paoiu, I. Hsieh. Third-order dispersion and ultrafast-pulse propagation in silicon wire waveguides,2006,18(24):2617～2619
[79]A. Barkai, Y. Chetrit, O. Cohen, et al. Integrated silicon photonics for optical networks. J. Optical Networking,2007,6(1):25～47
[80]B. Jalali, S. Fathpour. Silicon Photonics. J. Lightwave Technol.,2006,24: 4600～4614
[81]P. Dumon, G. Priem, L. Nunes, et al. Linear and nonlinear nanophotonic devices based on silicon-on-insulator wire waveguides. J. Appl. Phys.,2006,45(8):6589-6602
[82]P. Dumon, W. Bogaerts, V. Wiaux, et al. Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography. IEEE Photon. Technol. Lett.,2004, 16(5):1328～1330
[83]W. Bogaerts, V. Wiaux, D. Taillaert, et al. Fabrieation of Photonic crystals in silicon-on-insulator using 248-nm deep UV Lithography. IEEE J. Sel. Top. Quantum Eleetron.,2002,8(4):928～934
[84]W. Bogaerts, R. Baets, R. Dumon, et al. Nanophotonic waveguides in Silieon-on-insulator fabricated with CMOS technology. J. Lightwave Technol., 2005,23(1):401～412
[85]Y. A. Vlasov, S. J. McNab. Losses in single-more silicon-on-insulator strip waveguides and bends. Opt. Express,2004,12(8):1622～1631
[86]H. Yamada, T. Chu, S. Ishida, et al. Si photonic wire waveguide devices. IEICE Trans. Eleetron.,2007,90(1):59～64
[87]S. J. McNab, N. Moll, Y. A. Vlasov. Ultra-low loss photonic integrated circuits with membrane-type Photonic crystal waveguides. Opt. Express,2003,11(22):2927-2939
[88]D. K. Sparaein, S. J. Spector, L. C. Kimerling. Silicon waveguide sidewall smoothing by wet chemical oxidation. J. Lightwave Technol.,2005,23(8):2455-2461
[89]K. K. Lee, D. R. Lim, L. C. Kimerling, et al. Fabrication of ultra low-loss Si/SiO2 waveguides by roughness reduction, Opt. Lett.,2001,26(23):1888～1890
[90]O.C.齐基威次,Y.K.邱,结构和连续力学中的有限单元体法.北京：国防工业出版社,1967.78-90
[91]P.P.席尔维斯特,R.L.弗拉里.有限单元法在电气工程中的应用.(第2版).杭州：浙江大学出版社,1995.131-137
[92]J. H. Coggon. Electromagnetic and electrical modeling by the finite element method. Geophysics,1971,36(1):132～155
[93]李大潜.有限元素法在电法测井中的应用.北京：石油工业出版社,1980.76-82
[94]周熙襄,钟本善.有限单元法在直流电法勘探正问题中的应用.物探化探计算技术.1980,(3)：1-57
[95]周熙襄,钟本善.电法勘探数值模拟技术.成都：四川科学技术出版社,1986. 54-63
[96]罗延钟,孟永良.有关用有限单元法对二维构造作电阻率法模拟的几个问题.地球物理学报,1986,6：201-207
[97]罗延钟,张桂青.电子计算机在电法勘探中的应用.武汉：地质学院出版社,1987.97-108
[98]延钟,昌彦君.G-S变换的快速算法.地球物理学报,2000,43(5)：684-690
[99]熊彬,罗延钟.电导率分块均匀的瞬变电磁2.5D有限元数值模拟.地球物理学报,2006,49(2)：590-597
[100]H. Whitney. Geometric Integration Theory. Princeton:Princeton University Press, 1957.84～102
[101]A. Bossavit, J. C. Verite. A mixed FFM-BIEM method to solve 3-D eddy current problems. IEEE Trans. Magnetics,1982,18:431-435
[102]K. Sakiyama, H. Kotera, A. Ahagon.3-D electromagnetic field mode analysis using finite element method by edge element. IEEE Transaction on Magnetics,1990, 26(9):1759～1761
[103]饶明忠,谭邦定,黄键.电磁场计算中的棱边有限元法.中国电机工程学报,1994,14(5)：63-69
[104]Xueming Shi, Hisashi Utada, Jiaying Wang, et al. Three dimensional magnetotelluric forward modeling using vector finite element method combined with divergence corrections. Induction Workshop#17,2004.18～23
[105]Myung Jin Nam, Hee Joon Kim, Yoonho Song, et al.3D magnetotelluric modeling including surface topography Geophysical prospecting,2007,55:277～287
[106]王烨.基于矢量有限元的高频大地电磁法三维数值模拟：[博士学位论文].长沙：中南大学,2008
[107]金建铭.电磁场有限元方法.西安：西安电子科技大学出版社,1998.97-98
[108]Z. J. Cendes. Vector finite elements for electromagnetic field. IEEE Trans.,1991,27: 3958～3966
[109]J. F. Lee, D. K. Sun, Z. J. Cendes. Tangential vector finite elements for electromagnetic field computation. IEEE Trans.,1991,27:4032～4035
[110]ZHANG Li-guo, CHEN Di, YANG Fan, et al. Research on SU-8 resist photolithography process. Optics and Precision Engineering,2002,10(3):266～269
[111]ZHENG Xiao-hu. Fabrication of micro-structure by using epoxy-based negative photoresist. Opto-Electronic Engineering,2006,33(11):36～39
[112]Svante Finnveden, Martin Fraggstedt. Waveguide finite elements for curved structures. J. Sound Vib.,2008,312:644～671
[113]Kokou Dossou, Marie Fontaine. A high order isoparametric finite element method for the computation of waveguide modes. Comput. Methods Appl. Mech. Eng., 2005,194:837～858
[114]P. Diament. Wave transmission and Fiber Optics. New York:Macmillan,1990. 82～120
[115]T. N. T. Goodman, S. L. Lee. Wavelet of multiplicity. Amer Math Soc,1994, 338(2):639～654
[116]J. Geronimo, D. Hardin, P. R. Massopust. Fractal functions and wavelet expansions based on several func-tions. J Approx Theory,1994,78:373～401
[117]Geronimo, Hardin, Massopust. Construction of orthogonal wavelets using fractal interpolution functions. SIAM J. Math Anal,1996,27:1158～119
[118]C. K. Chui, J. Lian. A study of orthogonormal multiwavelet. J. Approx Numer Math, 1996,20:273～29
[119]G. Plonka, V. Strela. Construction of multi-scaling functions with approximation and symmetry. SIAM J. Math Anal,1998,29:481～510
[120]A. Yariv. Optical Electronics in Modern Communications. Oxford:Oxford University Press,1997.213～234
[121]K. Okamoto. Fundamentals of Optical Waveguide. Orlando:Academic Press,2000. 256～273
[122]T. Tamir. Topics in applied physics. New York:Springer-Verlag Berlin Heidelberg, 1997.160～169
[123]R. G. Hunsperger. Integrated optics. New York:Springer-Verlag Berlin Heidelberg, 2002.93～108
[124]M. N. Islam. Ultrafast fiber switching devices and systems. New York:Cambridge University Press,1992.85～103
[125]S. M. Jensen. The nonlinear coherent coupler. IEEE J. Quantum Electron,1982,12: 1490～1496
[126]A. A. Maiser. Self switching of light in a directional coupler. Sov. J. Quantum Electron,1982,12:1490～1498
[127]S. R. Friberg, A. M. Weiner, Y. Silberberg, et al. Femotosecond switching in a dual-core-fiber nonlinear coupler. Opt.Lett.,1988,13:904～909
[128]S. Trillo, S. Wabnitz, R. H. Stolen, et al. Experimental observation of polarization instability in a birefringent optical fiber. Appl. Phys Lett.,1986,49:1224～1231
[129]G. P. Agrawal. Nonlinear Fiber Optics. Orlando:Academic Press,1995.76～93
[130]J. Hubner, D. Zauner, M. Kristensen. Strong sampled Bragg grating for WDM applications. IEEE Photonics Technology Letters,1998,10(4):552～554
[131]W. H. Loh, F. Q. Zhou, J. J. Pan. Novel designs for sampled grating-based multiplexers-demultiplexers. Optics Letters,1999,24(21):1457～1459
[132]V. Mizrahi. Four channel fiber grating demultiplexer. Electronics Letters,1994, 30(10):780～781
[133]A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, et al. Long-period fiber-grating-based gain equalizers. Optics Letters,1996,21(3):336～338
[134]R. Kashyap, R. Wyatt, P. E. Mekee. Wavelength flattened saturated erbium amplifier using multiple side-tap Bragg grating. Electron Lett.,1993,29(11): 1025～1026
[135]M. Roehette, M. Guy, S. Larochelle. Gain equalization of EDFA's with Bragg gratings. IEEE Photonics Technology Letters,1999,11(5):536～538
[136]V. Mizrahi, J. E. Sipe. Optical properties of photosensitive fiber phase Gratings. J. Lightwave Technol.,1993,11:1513～1517
[137]杨世铭,陶文锉.传热学.(第3版).北京：高等教育出版社,2006.23-29
[138]俞昌铭.热传导及其数值分析.北京：清华大学出版社,1981.56-68
[139]M. Iodice, G. Mazzi, L. Sirleto. Thermo-optical static and dynamic analysis of a digital optical switch based on amorphous silicon waveguide. Opt. Express,2006, 14(12):5266～5278
[140]杨建义,江晓清,杨方辉等.有机聚合物热光器件的热学模型.光电激光,2000,11(4)：349-352
[141]于辉,江晓清,杨建义等.有机聚合物热光器件热场的解析模型.半导体学报,2004,25：995-999
[142]S. V. J. Narumanehi, J. Y. Murthy, C. H. Amon. Comparison of different Phonon Transport models for Predicting heat conduction in silicon-on-insulator transistors. J. Heat Transf.,2005,127(7):713～723
[143]T. Yamane, N. Nagai, S. Katayama, et al. Measurement of thermal conductivity of silicon dioxide thin films using a 3w method. J. APPl. Phys.,2002,91(12): 9772～9776
[144]许晓波.微环谐振器阵列滤波器研究：[硕士学位论文].长春：长春理工大学光学系,2007
[145]C. Manolatou, M. J. Khan, S. Fan. Coupling of modes analysis of resonant channel add drop filters. J. Quantum Electron.,1999,5(9):1322～1325
[146]马春生,刘式墉.光波导模式理论.长春：吉林大学出版社,2006.231-250
[147]Shijun Xiao, M. H. Khan, Hao Shen, et al. Two-Photon Absorption induced thermal-Optic effect in high-Q Silicon microring resonators. Lasers and Electro-Optics Society 2007,2007.890～891
[2]L. Pavesi, D. J. Lockwood. Silicon photonics. New York:Springer-Verlag,2004. 78～89
[3]B. Jalali, S. Yegnanarayanan, T. Yoon, et al. Advances in Silicon-on-insulator optoelectronics. IEEE J. Selected Topics in Quantum Electron.,1998,4(6): 938-947
[4]B. Jalali, V. Raghunathan, D. Dimitropoulos, et al. Raman-based silicon photonics. IEEE J. Selected Topics in Quantum Electron.,2006,12(3):412～421
[5]B. Jalali, S. Fathpour. Silicon photonics. J. Lightwave Technol.,2006,24(12):4600 ～4615
[6]R. Soref. The past, present, and future of silicon photonics. IEEE J. Selected Topics in Quantum Electron.,2006,12(6):1678～1687
[7]H. Rong, A. Liu, R. Jones, et al. An all-silicon Raman laser. Nature,2005, 433(7023):292～294
[8]H. Rong, R. Jones, A. Liu, et al. A continuous-wave Raman silicon laser. Nature, 2005,433(7027):725～728
[9]M. Foster, A. Turner, J. Sharping, et al. Broad-band optical parametric gain on a silicon photonic chip. Nature Photon.,2006,441(7096):960～963
[10]S. Lin, Y. Kobayashi, Y. Ishikawa, et al. Luminescence enhancement by Si ring resonator structures on silicon on insulator. Appl. Phys. Lett.,2008,92(2):021～031
[11]T. Liang, H. Tsang. Efficient Raman amplification in silicon-on-insulator waveguides. Appl. Phys. Lett.,2004,85(16):3343～3345
[12]R. Espinola, J. Dadap, R. Osgood, et al. Raman amplification in ultrasmall silicon-on-insulator wire waveguides. Opt. Express,2004,12(16):3713～3718
[13]B. Jalali, R. Claps, D. Dimitropoulos, et al. Light generation, amplification, and wavelength conversion via stimulated Raman scattering in silicon microstructures. Silicon Photonics,2004,94:199-238
[14]V. Sih, S. Xu, Y. Kuo, et al. Raman amplification of 40 Gb/s data in low-loss silicon waveguides. Opt. Express,2007,15(2):357～362
[15]C. Png, S. Chan, S. Lin, et al. Optical phase modulators for MHz and GHz modulation in silicon-on-insulator (SOI). J. Lightwave Technol.,2004,22(6): 1573～1582
[16]C. Manolatou, M. Lipson. All-optical silicon modulators based on carrier injection by two-photon absorption. J. Lightwave technol.,2006,24(3):1433～1439
[17]R. Chuang, M. Hsu. Silicon optical modulators in silicon-on-insulator substrate based on the p-i-n waveguide structure. J. Appl. Phys.,2007,46(4):2445～2449
[18]M. Foerst, J. Niehusmann, T. Plotzing, et al. High-speed all-optical switch in ion-implanted silicon-on-insulator or microring resonators. Opt. Lett.,2007,32(14): 2046～2048
[19]F. Sun, J. Yu, S. Chen. A 2x2 optical switch based on plasma dispersion effect in silicon-on-insulator. Optics Commun.,2006,262(2):164～169
[20]F. Sun, J. Yu, S. Chen. High speed 2x2 optical switch in silicon-on-insulator based on plasma dispersion effect. Chinese Phys. Lett.,2005,22(12):3097～3099
[21]D. Beggs, T. White, L. O'Faolain, et al. Ultracompact and low-power optical switch based on silicon photonic crystals. Opt. Lett.,2008,33(2):147～149
[22]Q. Fang, P. Chen, H. Xin, et al. Low power-consumption and high response frequency thermo-optic variable optical Attenuators based on silicon-on-insulator materials. Chinese Phys. Lett.,2005,22(6):1452～1455
[23]Y. Li, Y. Chen, S. Chen, et al. Silicon-on-insulator thermo-optic variable attenuator module with fast response. Opt. Engineering,2005,44(6):62～66
[24]J. Xia, J. Yu. Thermo-optic variable optical attenuator with low power consumption fabricated on silicon-on-insulator by anisotropic chemical etching. Opt. Lett.,2004, 43(4):189～790
[25]W. Ye, D. Xu, S. Janz, et al. Passive broadband silicon-on-insulator polarization splitter. Opt. Lett.,2007,32(11):1492～1494
[26]A. Kazmierczak, M. Briere, E. Drouard, et al. Design, simulation, and characterization of a passive optical add-drop filter in silicon-on-insulator technology. IEEE Photonics Technolo. Lett.,2005,17(7):1447～1449
[27]A. Shinya, S. Mitsugi, E. Kuramochi, et al. Ultrasmall multi-port channel drop filter in two-dimensional photonic crystal on silicon-on-insulator substrate. Optics Express,2006,14(25):12394～12400
[28]R. A. Soref, J. Schmidtchen, K. Petermann. Large single-mode waveguides in GeSi-Si and Si-on-SiO2. IEEE J. Quantum Electron.,1991,27(8):1971～1974
[29]S. Pogossian, L. Vescan, A. Vonsovici. The single-mode condition for semiconductor rib waveguides with large cross section. J. Lightwave Technol.,1998, 16(10):1851～1853
[30]J. D. Plummer, M. D. Deal, P. B. Griffin. Silicon VLSI technology:Fundamentals, Practice, and Modeling. London:Prentice Hall,2000.106～114
[31]G. Celler., S. Cristoloveanu. Frontiers of silicon-on-insulator. J. Appl. Phys.,2003, 93(9):4955～4978
[32]J. Plaza, J. Esteve, E. Lora-Tamavo. Simple technology for bulk accelerometer based on bond and etch back silicon on insulator wafers. Sensors and Actuators A-Physical,1998,68(3):299-302
[33]M. Tajima, S. Ibuka, H. Aga, et al. Characterization of bond and etch-back silicon-on-insulator wafers by photoluminescence under ultraviolet excitation. Appl. Phys. Lett.,1997,70(2):231～233
[34]G. K. Celler, S. Cristoloveanu. Applied physics reviews-focused review. J. Appl. Phys.,2003,93(9):4955-4978
[35]冯倩,郝跃.新型绝缘体上硅技术的发展与展望.西安电子科技大学学报(自然科学版),2001,28(6)：792-796
[36]A. Ploβl, G. Krauter. Silicon-on-insulator:materials aspects and applications. Solid-State Electron.,2000,44:775-782
[37]T. Liang, H. Tsang, I. Day, et al. Silicon waveguide two-photon absorption detector at 1.5 mu m wavelength for autocorrelation measurements. Appl. Phys. Lett.,2002, 81(7):1323～1325
[38]H. Tsang, C. Wong, T. Liang, et al. Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 mu m wavelength. Appl. Phys. Lett.,2002,80(3):416～418
[39]T. Liang, H. Tsang. Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides. Appl. Phys. Lett.,2004,84(15): 2745～2747
[40]R. Salem, T. Murphy. Polarization-insensitive cross correlation using two-photon absorption in a silicon photodiode. Opt. Lett.,2004,29(13):1524-1526
[41]C. Bosshard, R. Spreiter, M. Zgonik, et al. Kerr Nonlinearity via cascaded otpical rectification and the linear electro-optic effect. Phys. Rev. Lett.,1995,74(14): 2816-2819
[42]R. D. Coso, J. Solis. Relation between nonlinear refractive index and third-order susceptibility in absorbing media. J. Opt. Soc. Am. B,2004,21(3):640～644
[43]R. Stolen, A. Ashkin. Optical kerr effect in glass waveguide. IEEE J. Quantum Electron.,1972,8(6):548～549
[44]O. Boyraz, T. Indukuri, B. Jalali. Self-phase-modulation induced spectral broadening in silicon waveguides. Opt. Express,2004,12(5):829～834
[45]E. Dulkeith, Y. Vlasov, X. Chen, et al. Self-phase-modulation in submicron silicon-on-insulator photonic wires. Opt. Express,2006,14(12):5524～5534
[46]G. Rieger, K. Virk, J. Young. Nonlinear propagation of ultrafast 1.5 mu m pulses in high-index-contrast silicon-on-insulator waveguides. Appl. Phys. Lett.,2004,84(6): 900-902
[47]A. Cowan, G. Rieger, J. Young. Nonlinear transmission of 1.5 μm pulses through single-mode silicon-on-insulator waveguide structures. Opt. Express,2004,12(8): 1611～1621
[48]R. Dekker, A. Driessen, T. Wahlbrink, et al. Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 mu m femtosecond pulses. Opt. Express,2006,14(18):8336～8346
[49]I. Hsieh, X. Chen, J. Dadap, et al. Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides. Opt. Express,2006,14(25): 12380～12387
[50]R. Dekker, N. Usechak, M. Forst, et al. Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides. J. Phys. D-Appl. Phys.,2007,40(14):249～271
[51]I. Hsieh, X. Chen, J. Dadap, et al. Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires. Opt. Express,2007,15(3):1135～1146
[52]O. Boyraz, P. Koonath, V. Raghunathan, et al. All optical switching and continuum generation in silicon waveguides. Opt. Express,2004,12(17):4094～4102
[53]Q. Lin, O. J. Painter, G. P. Agrawal. Nonlinear optical phenomena in silicon waveguides:Modeling and applications. Opt. Express,2007,15(25):16604～16644
[54]X. Chen, N. Panoiu, R. Osgood. Theory of Raman-mediated pulse amplification in silicon-wire waveguides. IEEE J. Quantum Electron.,2006,42(2):160～170
[55]D. Moss, L. Fu, I. Littler, et al. Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides. Electron. Lett.,2005,41(6):320-321
[56]T. Liang, L. Nunes, M. Tsuchiya, et al. High speed logic gate using two-photon absorption in silicon waveguides. Opt. Commun.,2006,265(1):171～174
[57]J. Mork, A. Mecozzi. Theory of nondegenerate four-wave mixing between pulses in a semiconductor waveguide. IEEE J. Quantum Electron.,1997,33(4):545～555
[58]K. Lor, K. Chiang. Theory of nondegenerate four-wave mixing in a birefringent optical fibre. Opt. Commun.,1998,152(1):26～30
[59]V. Passaro, F. De Leonardis. All-optical and gate based on Raman effect in silicon-on-insulator waveguide. Opt. and Quantum Electron.,2006,38(9):877～888
[60]Z. Li, G. Li. Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier. IEEE Photon. Technol. Lett.,2006,18(9): 1341-1343
[61]F. Martelli, A. Mecozzi, A. Dottavi, et al. Noise in wavelength conversion using four-wave mixing in semiconductor optical amplifiers. Appl. Phys. Lett.,1997, 70(3):306～308
[62]F. Geraghty, R. Lee, K. Vahala, et al. Wavelength conversion up to 18 run at 10 Gb/s by four-wave mixing in a semiconductor optical amplifier. IEEE Photon. Technol. Lett.,1997,9(4):452～454
[63]S. Kumar, A. Willner. Simultaneous four-wave mixing and cross-gain modulation for implementing an all-optical XNOR logic gate using a single SOA. Opt. Express, 2006,14(12):5092～5097
[64]S. Mikroulis, H. Simos, E. Roditi, et al. Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator. IEEE Photon. Technol. Lett.,2005,17(9):1878～1880
[65]R. Salem, M. A. Foster, A. C. Turner, et al. Signal regeneration using low-power four-wave mixing on silicon chip. Nature Photon.,2008,2(1):35～38
[66]R. Soref, J. Lorenzo. All-silicon active and passive guided-wave components for λ=1.3 and 1.6μm. IEEE J. Quantum Electron.,1986,22(6):873～879
[67]V. Passaro, F. De Leonardis. Modeling and design of a novel high-sensitivity electric field silicon-on-tnsulator sensor based on a whispering-gallery-mode resonator. IEEE J. Selected Topics in Quantum Electron.,2006,12(1):124～133
[68]B. Schuppert, J. Schmidtchen, K. Petermann. Optical channel waveguides in silicon diffused from GeSi alloy. Electron. Lett.,1989,25(22):1500～1502
[69]J. W. M. Menezes, W. B. de Fraga, G. F. Guimaraes, et al, Optical switches and all-fiber logical devices based on triangular and planar three-core nonlinear optical fiber couplers. Opt. Commun.,2007,276:107～115
[70]Y. Vlasov, W. M. J. Green, F. Xia. High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks. Nature Photon.,2008, 2(4):242～246
[71]H. Wei, J. Yu, X. Zhang. Compact 3-dB tapered multimode interference coupler in silicon-on-insulator. Opt. Lett.,2001,26(12):878～880
[72]Y. Li, J. Yu, S. Chen. Submicrosecond rearrangeable nonblocking silicon-on-insulator thermo-optic 4×4 switch matrix. Opt. Lett.,2007,32(6):603～604
[73]Li Hong, Huang De-Xiu, Wang Dong-Ning, Influence of group-velocity mismatch on soliton switching in a nonlinear fiber coupler. Chin. Phys. Soc.,2003,12(4): 415～418
[74]B. M. Liang, G. J. Liu, Q. Li, et al. Coupled mode analysis of the nonlinear switching in the couplers with variable coupling coefficient. Opt. Commun.,2003, 223:195～200
[75]Y. Wang, W. Wang. Study of ultra-fast optical pulse propagation in a nonlinear directional coupler. Appl. Phys. B,2004,79:51～55
[76]F. M. Castro, M. I. Molina, W. D. Deering. Controlling all-optical switching in multicore nonlinear couplers. Opt. Commun.,2003,226:199～204
[77]Youfa Wang, Wenfeng Wang. Nonlinear optical pulse coupling dynamics. J. Lightwave Technol.,2006,24(6):2458～2464
[78]X. Chen, N. C. Paoiu, I. Hsieh. Third-order dispersion and ultrafast-pulse propagation in silicon wire waveguides,2006,18(24):2617～2619
[79]A. Barkai, Y. Chetrit, O. Cohen, et al. Integrated silicon photonics for optical networks. J. Optical Networking,2007,6(1):25～47
[80]B. Jalali, S. Fathpour. Silicon Photonics. J. Lightwave Technol.,2006,24: 4600～4614
[81]P. Dumon, G. Priem, L. Nunes, et al. Linear and nonlinear nanophotonic devices based on silicon-on-insulator wire waveguides. J. Appl. Phys.,2006,45(8):6589-6602
[82]P. Dumon, W. Bogaerts, V. Wiaux, et al. Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography. IEEE Photon. Technol. Lett.,2004, 16(5):1328～1330
[83]W. Bogaerts, V. Wiaux, D. Taillaert, et al. Fabrieation of Photonic crystals in silicon-on-insulator using 248-nm deep UV Lithography. IEEE J. Sel. Top. Quantum Eleetron.,2002,8(4):928～934
[84]W. Bogaerts, R. Baets, R. Dumon, et al. Nanophotonic waveguides in Silieon-on-insulator fabricated with CMOS technology. J. Lightwave Technol., 2005,23(1):401～412
[85]Y. A. Vlasov, S. J. McNab. Losses in single-more silicon-on-insulator strip waveguides and bends. Opt. Express,2004,12(8):1622～1631
[86]H. Yamada, T. Chu, S. Ishida, et al. Si photonic wire waveguide devices. IEICE Trans. Eleetron.,2007,90(1):59～64
[87]S. J. McNab, N. Moll, Y. A. Vlasov. Ultra-low loss photonic integrated circuits with membrane-type Photonic crystal waveguides. Opt. Express,2003,11(22):2927-2939
[88]D. K. Sparaein, S. J. Spector, L. C. Kimerling. Silicon waveguide sidewall smoothing by wet chemical oxidation. J. Lightwave Technol.,2005,23(8):2455-2461
[89]K. K. Lee, D. R. Lim, L. C. Kimerling, et al. Fabrication of ultra low-loss Si/SiO2 waveguides by roughness reduction, Opt. Lett.,2001,26(23):1888～1890
[90]O.C.齐基威次,Y.K.邱,结构和连续力学中的有限单元体法.北京：国防工业出版社,1967.78-90
[91]P.P.席尔维斯特,R.L.弗拉里.有限单元法在电气工程中的应用.(第2版).杭州：浙江大学出版社,1995.131-137
[92]J. H. Coggon. Electromagnetic and electrical modeling by the finite element method. Geophysics,1971,36(1):132～155
[93]李大潜.有限元素法在电法测井中的应用.北京：石油工业出版社,1980.76-82
[94]周熙襄,钟本善.有限单元法在直流电法勘探正问题中的应用.物探化探计算技术.1980,(3)：1-57
[95]周熙襄,钟本善.电法勘探数值模拟技术.成都：四川科学技术出版社,1986. 54-63
[96]罗延钟,孟永良.有关用有限单元法对二维构造作电阻率法模拟的几个问题.地球物理学报,1986,6：201-207
[97]罗延钟,张桂青.电子计算机在电法勘探中的应用.武汉：地质学院出版社,1987.97-108
[98]延钟,昌彦君.G-S变换的快速算法.地球物理学报,2000,43(5)：684-690
[99]熊彬,罗延钟.电导率分块均匀的瞬变电磁2.5D有限元数值模拟.地球物理学报,2006,49(2)：590-597
[100]H. Whitney. Geometric Integration Theory. Princeton:Princeton University Press, 1957.84～102
[101]A. Bossavit, J. C. Verite. A mixed FFM-BIEM method to solve 3-D eddy current problems. IEEE Trans. Magnetics,1982,18:431-435
[102]K. Sakiyama, H. Kotera, A. Ahagon.3-D electromagnetic field mode analysis using finite element method by edge element. IEEE Transaction on Magnetics,1990, 26(9):1759～1761
[103]饶明忠,谭邦定,黄键.电磁场计算中的棱边有限元法.中国电机工程学报,1994,14(5)：63-69
[104]Xueming Shi, Hisashi Utada, Jiaying Wang, et al. Three dimensional magnetotelluric forward modeling using vector finite element method combined with divergence corrections. Induction Workshop#17,2004.18～23
[105]Myung Jin Nam, Hee Joon Kim, Yoonho Song, et al.3D magnetotelluric modeling including surface topography Geophysical prospecting,2007,55:277～287
[106]王烨.基于矢量有限元的高频大地电磁法三维数值模拟：[博士学位论文].长沙：中南大学,2008
[107]金建铭.电磁场有限元方法.西安：西安电子科技大学出版社,1998.97-98
[108]Z. J. Cendes. Vector finite elements for electromagnetic field. IEEE Trans.,1991,27: 3958～3966
[109]J. F. Lee, D. K. Sun, Z. J. Cendes. Tangential vector finite elements for electromagnetic field computation. IEEE Trans.,1991,27:4032～4035
[110]ZHANG Li-guo, CHEN Di, YANG Fan, et al. Research on SU-8 resist photolithography process. Optics and Precision Engineering,2002,10(3):266～269
[111]ZHENG Xiao-hu. Fabrication of micro-structure by using epoxy-based negative photoresist. Opto-Electronic Engineering,2006,33(11):36～39
[112]Svante Finnveden, Martin Fraggstedt. Waveguide finite elements for curved structures. J. Sound Vib.,2008,312:644～671
[113]Kokou Dossou, Marie Fontaine. A high order isoparametric finite element method for the computation of waveguide modes. Comput. Methods Appl. Mech. Eng., 2005,194:837～858
[114]P. Diament. Wave transmission and Fiber Optics. New York:Macmillan,1990. 82～120
[115]T. N. T. Goodman, S. L. Lee. Wavelet of multiplicity. Amer Math Soc,1994, 338(2):639～654
[116]J. Geronimo, D. Hardin, P. R. Massopust. Fractal functions and wavelet expansions based on several func-tions. J Approx Theory,1994,78:373～401
[117]Geronimo, Hardin, Massopust. Construction of orthogonal wavelets using fractal interpolution functions. SIAM J. Math Anal,1996,27:1158～119
[118]C. K. Chui, J. Lian. A study of orthogonormal multiwavelet. J. Approx Numer Math, 1996,20:273～29
[119]G. Plonka, V. Strela. Construction of multi-scaling functions with approximation and symmetry. SIAM J. Math Anal,1998,29:481～510
[120]A. Yariv. Optical Electronics in Modern Communications. Oxford:Oxford University Press,1997.213～234
[121]K. Okamoto. Fundamentals of Optical Waveguide. Orlando:Academic Press,2000. 256～273
[122]T. Tamir. Topics in applied physics. New York:Springer-Verlag Berlin Heidelberg, 1997.160～169
[123]R. G. Hunsperger. Integrated optics. New York:Springer-Verlag Berlin Heidelberg, 2002.93～108
[124]M. N. Islam. Ultrafast fiber switching devices and systems. New York:Cambridge University Press,1992.85～103
[125]S. M. Jensen. The nonlinear coherent coupler. IEEE J. Quantum Electron,1982,12: 1490～1496
[126]A. A. Maiser. Self switching of light in a directional coupler. Sov. J. Quantum Electron,1982,12:1490～1498
[127]S. R. Friberg, A. M. Weiner, Y. Silberberg, et al. Femotosecond switching in a dual-core-fiber nonlinear coupler. Opt.Lett.,1988,13:904～909
[128]S. Trillo, S. Wabnitz, R. H. Stolen, et al. Experimental observation of polarization instability in a birefringent optical fiber. Appl. Phys Lett.,1986,49:1224～1231
[129]G. P. Agrawal. Nonlinear Fiber Optics. Orlando:Academic Press,1995.76～93
[130]J. Hubner, D. Zauner, M. Kristensen. Strong sampled Bragg grating for WDM applications. IEEE Photonics Technology Letters,1998,10(4):552～554
[131]W. H. Loh, F. Q. Zhou, J. J. Pan. Novel designs for sampled grating-based multiplexers-demultiplexers. Optics Letters,1999,24(21):1457～1459
[132]V. Mizrahi. Four channel fiber grating demultiplexer. Electronics Letters,1994, 30(10):780～781
[133]A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, et al. Long-period fiber-grating-based gain equalizers. Optics Letters,1996,21(3):336～338
[134]R. Kashyap, R. Wyatt, P. E. Mekee. Wavelength flattened saturated erbium amplifier using multiple side-tap Bragg grating. Electron Lett.,1993,29(11): 1025～1026
[135]M. Roehette, M. Guy, S. Larochelle. Gain equalization of EDFA's with Bragg gratings. IEEE Photonics Technology Letters,1999,11(5):536～538
[136]V. Mizrahi, J. E. Sipe. Optical properties of photosensitive fiber phase Gratings. J. Lightwave Technol.,1993,11:1513～1517
[137]杨世铭,陶文锉.传热学.(第3版).北京：高等教育出版社,2006.23-29
[138]俞昌铭.热传导及其数值分析.北京：清华大学出版社,1981.56-68
[139]M. Iodice, G. Mazzi, L. Sirleto. Thermo-optical static and dynamic analysis of a digital optical switch based on amorphous silicon waveguide. Opt. Express,2006, 14(12):5266～5278
[140]杨建义,江晓清,杨方辉等.有机聚合物热光器件的热学模型.光电激光,2000,11(4)：349-352
[141]于辉,江晓清,杨建义等.有机聚合物热光器件热场的解析模型.半导体学报,2004,25：995-999
[142]S. V. J. Narumanehi, J. Y. Murthy, C. H. Amon. Comparison of different Phonon Transport models for Predicting heat conduction in silicon-on-insulator transistors. J. Heat Transf.,2005,127(7):713～723
[143]T. Yamane, N. Nagai, S. Katayama, et al. Measurement of thermal conductivity of silicon dioxide thin films using a 3w method. J. APPl. Phys.,2002,91(12): 9772～9776
[144]许晓波.微环谐振器阵列滤波器研究：[硕士学位论文].长春：长春理工大学光学系,2007
[145]C. Manolatou, M. J. Khan, S. Fan. Coupling of modes analysis of resonant channel add drop filters. J. Quantum Electron.,1999,5(9):1322～1325
[146]马春生,刘式墉.光波导模式理论.长春：吉林大学出版社,2006.231-250
[147]Shijun Xiao, M. H. Khan, Hao Shen, et al. Two-Photon Absorption induced thermal-Optic effect in high-Q Silicon microring resonators. Lasers and Electro-Optics Society 2007,2007.890～891