This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres wi...This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d1, diameters of outer core holes d2 and hole to hole pitch A on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.展开更多
Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earlie...Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.展开更多
基金Project supported by the National Key Basic Research Special Foundation of China (Grant No. 2010CB327605)the National High-Technology Research and Development Program of China (Grant No. 2009AA01Z220)+2 种基金the Key Grant of the Chinese Ministry of Education (Grant No. 109015)the Discipline Co-construction Project of Beijing Municipal Commission of Education (Grant No. YB20081001301)the Open Fund of Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), Ministry of Education,and the Specialized Research Fund for the Doctoral Program of Beijing University of Posts and Telecommunications (Grant No. CX201023)
文摘This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d1, diameters of outer core holes d2 and hole to hole pitch A on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.
基金research projects“Elements of Continuity between Mathematical Writings from the Thirteenth to the Fifteenth Century in China(十三至十五世纪中国数学著作连续性Y950051)”“Transmission of the Knowledge of Science and Technology along the Silk Road(丝绸之路科技知识传播Y921011012,Director:Guo Yuanyuan郭园园)”of the Institute for the History of Natural Sciences,Chinese Academy of Sciences.The paper has been copyedited by John Moffett。
文摘Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.
