This paper presents an approximate expression to transmission capacity of ad hoc networks by using stochastic geometry. For there is no general close-form expression to the transmission capacity of ad hoc networks, by...This paper presents an approximate expression to transmission capacity of ad hoc networks by using stochastic geometry. For there is no general close-form expression to the transmission capacity of ad hoc networks, by using Taylor series, we obtain the exact series expression to transmission capacity first, then we take partial summation to yield an n-th order approximate expression. Further- more, compared with the exact expression under a special case, the accuracy of the n-th order ap- proximation has been studied. The numerical results show that the accuracy of the approximation is mainly determined by the order n, and a high accuracy can be obtained when the node density or the outage constraint is close to zero .展开更多
A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the spec...A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular mo- mentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respec- tively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter y, and transfer matrix ele- ments A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in op- tical micromanipulation.展开更多
文摘This paper presents an approximate expression to transmission capacity of ad hoc networks by using stochastic geometry. For there is no general close-form expression to the transmission capacity of ad hoc networks, by using Taylor series, we obtain the exact series expression to transmission capacity first, then we take partial summation to yield an n-th order approximate expression. Further- more, compared with the exact expression under a special case, the accuracy of the n-th order ap- proximation has been studied. The numerical results show that the accuracy of the approximation is mainly determined by the order n, and a high accuracy can be obtained when the node density or the outage constraint is close to zero .
基金the support by the National Natural Science Foundation of China (Grant Nos.10974179 and 61178016),the support by the National Natural Science Foundation of China (Grant No.10904102)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No.200928)+2 种基金the Natural Science of Jiangsu Province (Grant No.BK2009114)the Huo Ying Dong Education Foundation of China (Grant No.121009)the Key Project of Chinese Ministry of Education (Grant No.210081)
文摘A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular mo- mentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respec- tively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter y, and transfer matrix ele- ments A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in op- tical micromanipulation.
