In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wa...In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wave method. The results show that the birefringence of the fibre is induced by asymmetries of both the cladding and the core. Moreover, by adjusting the non-symmetrical ratio factor of cladding η from 0.4 to 1 in step 0.1, we find the optimized design parameters of the fibre with high birefringence and limited polarization mode dispersion, operating in a single mode regime at an appropriate wavelength range. The range of wavelength approaches the visible and near-infrared which is consistent with the communication windows of polymer optical fibres.展开更多
In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at in...In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities.展开更多
基金Project supported by National Nature Science Foundation of China （Grant No 60437020） and the Science and Technology Plan Project of Shannxi Province （Grant No 2004K05-G47）.
文摘In this paper, polarization properties and propagation characteristics of polymer photonic crystal fibres with elliptical core and non-hexagonal symmetry structure are investigated by using the full vectorial plane wave method. The results show that the birefringence of the fibre is induced by asymmetries of both the cladding and the core. Moreover, by adjusting the non-symmetrical ratio factor of cladding η from 0.4 to 1 in step 0.1, we find the optimized design parameters of the fibre with high birefringence and limited polarization mode dispersion, operating in a single mode regime at an appropriate wavelength range. The range of wavelength approaches the visible and near-infrared which is consistent with the communication windows of polymer optical fibres.
基金carried out in the framework of the Labex Archimède(ANR-11-LABX-0033)the A*MIDEX project(ANR-11-IDEX-0001-02)+6 种基金funded by the "Investissements d’Avenir" French Government program managed by the French National Research Agency(ANR)funding from the European Research Council under the European Union’s Seventh Framework Programme(FP/2007-2013)ERC Grant Agreement n.321186-ReaDiReaction-Diffusion Equations,Propagation and Modelling and from the ANR NONLOCAL project(ANR-14-CE25-0013)supported by INRIA-Team MEPHYSTOMIS F.4508.14(FNRS)PDR T.1110.14F(FNRS)ARC AUWB-2012-12/17-ULB1-IAPAS
文摘In this paper, the authors prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R^N, as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. The authors also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities.
