Theoretical analysis of the fiber-lens TEC （Thermally Expended Core） /Coreless/GRIN （Graded-Index） based on thin lens equivalence Js presented in this paper, On condition that the TEC part adjusts the waist radius...Theoretical analysis of the fiber-lens TEC （Thermally Expended Core） /Coreless/GRIN （Graded-Index） based on thin lens equivalence Js presented in this paper, On condition that the TEC part adjusts the waist radius of an incident Gaussian beam,that the coreless part controlls the space between the beam waist and the thin lens, and that the GRIN part acts as the thin lens with its focal length determined by fiber index distribution parameter g, the analytic expressions of the waist spot size and the working distance of the output Gaussian beam are derived, and the influence of the coreless fiber and the length of the GRIN fiber upon the fiber-lens parameter is discussed based on the numerical simulation results. It is concluded that, if a GRIN style fiber-lens is used as a collimator, the maximum of the spot waist can be up to 80μm and the divergence angle of single-mode optical fiber can be reduced by 8 times. If it is applied to a MEMS device, the maximum working distance can be up to 3 mm.展开更多
Higher mathematics is more extensive, profound and abstract than elementary mathematics; it is the development and sublimation of elementary mathematics. They have a deep connection, determinant and matrix theories or...Higher mathematics is more extensive, profound and abstract than elementary mathematics; it is the development and sublimation of elementary mathematics. They have a deep connection, determinant and matrix theories originated in Elementary Mathematics, in tum, they also can be used as tools to solve related problems, and they have important roles in guiding the study of elementary mathematics. This paper will introduce the methods of solving some recursive sequence problems by constructing determinants and matrices.展开更多
A row of dominoes which stand on edge will undergo a cascade when the first domino is tipped. First domino strokes the next and the wave of falling dominoes propagates. The purpose of this work is to investigate wave ...A row of dominoes which stand on edge will undergo a cascade when the first domino is tipped. First domino strokes the next and the wave of falling dominoes propagates. The purpose of this work is to investigate wave speed dependence on various domino parameters as the number of elements and the distance between dominoes and their dimensions. Theoretical examination of falling dominoes process is to create the mathematical model of the process and compare between the calculations and experimental results. An experiment with using of the speed camera was made. The dominoes of three different types of material were used. For theoretical investigation of the problem, the model [1] was used. The program for computer calculations was written. Time of a dominoes row falling was calculated without taking friction between neighbours. The calculation results show that the speed of falling dominoes reaches its constant value. This stable velocity depends on the geometric parameters of dominoes and the surface friction between dominoes but does not depend on the mass of dominoes.展开更多
文摘Theoretical analysis of the fiber-lens TEC （Thermally Expended Core） /Coreless/GRIN （Graded-Index） based on thin lens equivalence Js presented in this paper, On condition that the TEC part adjusts the waist radius of an incident Gaussian beam,that the coreless part controlls the space between the beam waist and the thin lens, and that the GRIN part acts as the thin lens with its focal length determined by fiber index distribution parameter g, the analytic expressions of the waist spot size and the working distance of the output Gaussian beam are derived, and the influence of the coreless fiber and the length of the GRIN fiber upon the fiber-lens parameter is discussed based on the numerical simulation results. It is concluded that, if a GRIN style fiber-lens is used as a collimator, the maximum of the spot waist can be up to 80μm and the divergence angle of single-mode optical fiber can be reduced by 8 times. If it is applied to a MEMS device, the maximum working distance can be up to 3 mm.
文摘Higher mathematics is more extensive, profound and abstract than elementary mathematics; it is the development and sublimation of elementary mathematics. They have a deep connection, determinant and matrix theories originated in Elementary Mathematics, in tum, they also can be used as tools to solve related problems, and they have important roles in guiding the study of elementary mathematics. This paper will introduce the methods of solving some recursive sequence problems by constructing determinants and matrices.
文摘A row of dominoes which stand on edge will undergo a cascade when the first domino is tipped. First domino strokes the next and the wave of falling dominoes propagates. The purpose of this work is to investigate wave speed dependence on various domino parameters as the number of elements and the distance between dominoes and their dimensions. Theoretical examination of falling dominoes process is to create the mathematical model of the process and compare between the calculations and experimental results. An experiment with using of the speed camera was made. The dominoes of three different types of material were used. For theoretical investigation of the problem, the model [1] was used. The program for computer calculations was written. Time of a dominoes row falling was calculated without taking friction between neighbours. The calculation results show that the speed of falling dominoes reaches its constant value. This stable velocity depends on the geometric parameters of dominoes and the surface friction between dominoes but does not depend on the mass of dominoes.
