Core mode cutoff is a useful concept not only for a tapered single-core fiber(SCF) but also for a tapered multicore fiber(MCF) to realize cladding mode transmission. In this paper, cut-off conditions of either core mo...Core mode cutoff is a useful concept not only for a tapered single-core fiber(SCF) but also for a tapered multicore fiber(MCF) to realize cladding mode transmission. In this paper, cut-off conditions of either core mode for tapered SCFs or supermodes for MCFs are theoretically investigated. Rigorous analytical formulas are derived for the modes of SCF by a three-layer waveguide model, and an approximation formula of the cut-off condition is given for the LP01 mode. The supermodes of MCFs are analyzed by the coupling mode theory, and the cut-off condition is calculated by a numerical method. Simulation results show that the in-phase supermode of MCFs has a similar cut-off condition with that of SCF. Based on this property, a convenient approximate formula is given to estimate the cut-off condition of the in-phase supermode for tapered MCFs.展开更多
We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in deta...We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.展开更多
文摘Core mode cutoff is a useful concept not only for a tapered single-core fiber(SCF) but also for a tapered multicore fiber(MCF) to realize cladding mode transmission. In this paper, cut-off conditions of either core mode for tapered SCFs or supermodes for MCFs are theoretically investigated. Rigorous analytical formulas are derived for the modes of SCF by a three-layer waveguide model, and an approximation formula of the cut-off condition is given for the LP01 mode. The supermodes of MCFs are analyzed by the coupling mode theory, and the cut-off condition is calculated by a numerical method. Simulation results show that the in-phase supermode of MCFs has a similar cut-off condition with that of SCF. Based on this property, a convenient approximate formula is given to estimate the cut-off condition of the in-phase supermode for tapered MCFs.
基金supported by National Natural Science Foundations of China (Grant Nos. 10771216 and 11071259)
文摘We consider a modified Markov branching process incorporating with both state-independent immigration-migration and resurrection. The effect of state-independent immigration-migration is firstly in- vestigated in detail. The explicit expressions for the extinction probabilities and mean extinction times are presented. The ergodicity and stability properties of the process incorporating with resurrection structure are then investigated. The conditions for recurrence, ergodicity and exponential ergodicity are obtained. An explicit expression for the equilibrium distribution is also presented. As a preparation, the criteria for regularity and uniqueness for such structure are firstly established.
