We fabricate a three-layer metamaterial of metal patterns/dielectric/metal films. The optical properties associated with Fano resonance of the metamaterials are investigated experimentally and theoretically. The resul...We fabricate a three-layer metamaterial of metal patterns/dielectric/metal films. The optical properties associated with Fano resonance of the metamaterials are investigated experimentally and theoretically. The results indicate that the introduction of Fano resonance due to symmetry breaking leads to a much wider absorption range. Furthermore, the amplitude and phase of reflection can be modulated effectively by adjusting various free parameters using the proposed structure.展开更多
Let ：T2k＋1 be the set of trees on 2k＋ 1 vertices with nearly perfect matchings, and let S2k＋2 be the set of trees on 2k ＋ 2 vertices with perfect matchings. The largest Laplacian spectral radii of trees in ：T2k...Let ：T2k＋1 be the set of trees on 2k＋ 1 vertices with nearly perfect matchings, and let S2k＋2 be the set of trees on 2k ＋ 2 vertices with perfect matchings. The largest Laplacian spectral radii of trees in ：T2k＋l and S2k＋2 and the corresponding trees were given by Guo （2003）. In this paper, the authors determine the second to the sixth largest Laplacian spectral radii among all trees in T2k＋1 and give the corresponding trees.展开更多
Let T2k＋1 be the set of trees on 2k＋1 vertices with nearly perfect matchings and α（T） be the algebraic connectivity of a tree T. The authors determine the largest twelve values of the algebraic connectivity of th...Let T2k＋1 be the set of trees on 2k＋1 vertices with nearly perfect matchings and α（T） be the algebraic connectivity of a tree T. The authors determine the largest twelve values of the algebraic connectivity of the trees in T2k＋1. Specifically, 10 trees T2,T3,... ,T11 and two classes of trees T（1） and T（12） in T2k＋1 are introduced. It is shown in this paper that for each tree T^′1,T^″1∈T（1）and T^′12,T^″12∈T（12） and each i,j with 2≤i〈j≤11,α（T^′1）=α（T^″1）〉α（Tj）〉α（T^′12）=α（T^″12）.It is also shown that for each tree T with T∈T2k＋1／（T（1）∪{T2,T3,…,T11}∪T（12））,α（T^′12）〉α（T）.展开更多
An unsplit-field higher order nearly perfectly matched layer(NPML)based on the auxiliary differential equation approach is introduced in three-dimensional finite-difference timedomain lattices.The proposed scheme has ...An unsplit-field higher order nearly perfectly matched layer(NPML)based on the auxiliary differential equation approach is introduced in three-dimensional finite-difference timedomain lattices.The proposed scheme has the advantage of both the NPML scheme and the higher order concept in terms of the improved absorbing performance and considerable computational efficiency.By incorporating with the generalized material independent concept,the proposed implementation is indepen dent of the material’s type.Thus,it has the advantages of terminating arbitrary media without changing the updated equations in the PML regions.Its effectiveness and efficiency is further demonstrated through numerical examples.展开更多
By incorporating the higher order concept,the piecewise linear recursive convolution(PLRC)method and CrankNicolson Douglas-Gunn(CNDG)algorithm,the unconditionally stable complex frequency shifted nearly perfectly matc...By incorporating the higher order concept,the piecewise linear recursive convolution(PLRC)method and CrankNicolson Douglas-Gunn(CNDG)algorithm,the unconditionally stable complex frequency shifted nearly perfectly matched layer(CFS-NPML)is proposed to terminate the left-handed material(LHM)domain.The proposed scheme takes advantages of CFSNPML formulation,the higher order concept PLRC method and the unconditionally stable CNDG algorithm in terms of absorbing performance,computational efficiency,calculation accuracy and convenient implementation.A numerical example is carried out to demonstrate the effectiveness and efficiency of the proposed scheme.The results indicate that the proposed scheme can not only have considerable absorbing performance but also maintain the unconditional stability of the algorithm with the enlargement of time steps.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 11304002the Natural Science Foundation of Education Bureau of Anhui Province under Grant No KJ2013A136the Natural Science Foundation of Anhui Province under Grant No 1208085MA07
文摘We fabricate a three-layer metamaterial of metal patterns/dielectric/metal films. The optical properties associated with Fano resonance of the metamaterials are investigated experimentally and theoretically. The results indicate that the introduction of Fano resonance due to symmetry breaking leads to a much wider absorption range. Furthermore, the amplitude and phase of reflection can be modulated effectively by adjusting various free parameters using the proposed structure.
基金supported by the National Natural Science Foundation of China under Grant No. 10331020.
文摘Let ：T2k＋1 be the set of trees on 2k＋ 1 vertices with nearly perfect matchings, and let S2k＋2 be the set of trees on 2k ＋ 2 vertices with perfect matchings. The largest Laplacian spectral radii of trees in ：T2k＋l and S2k＋2 and the corresponding trees were given by Guo （2003）. In this paper, the authors determine the second to the sixth largest Laplacian spectral radii among all trees in T2k＋1 and give the corresponding trees.
文摘Let T2k＋1 be the set of trees on 2k＋1 vertices with nearly perfect matchings and α（T） be the algebraic connectivity of a tree T. The authors determine the largest twelve values of the algebraic connectivity of the trees in T2k＋1. Specifically, 10 trees T2,T3,... ,T11 and two classes of trees T（1） and T（12） in T2k＋1 are introduced. It is shown in this paper that for each tree T^′1,T^″1∈T（1）and T^′12,T^″12∈T（12） and each i,j with 2≤i〈j≤11,α（T^′1）=α（T^″1）〉α（Tj）〉α（T^′12）=α（T^″12）.It is also shown that for each tree T with T∈T2k＋1／（T（1）∪{T2,T3,…,T11}∪T（12））,α（T^′12）〉α（T）.
基金This work was supported by the National Natural Science Foundation of China(6157102261971022).
文摘An unsplit-field higher order nearly perfectly matched layer(NPML)based on the auxiliary differential equation approach is introduced in three-dimensional finite-difference timedomain lattices.The proposed scheme has the advantage of both the NPML scheme and the higher order concept in terms of the improved absorbing performance and considerable computational efficiency.By incorporating with the generalized material independent concept,the proposed implementation is indepen dent of the material’s type.Thus,it has the advantages of terminating arbitrary media without changing the updated equations in the PML regions.Its effectiveness and efficiency is further demonstrated through numerical examples.
文摘By incorporating the higher order concept,the piecewise linear recursive convolution(PLRC)method and CrankNicolson Douglas-Gunn(CNDG)algorithm,the unconditionally stable complex frequency shifted nearly perfectly matched layer(CFS-NPML)is proposed to terminate the left-handed material(LHM)domain.The proposed scheme takes advantages of CFSNPML formulation,the higher order concept PLRC method and the unconditionally stable CNDG algorithm in terms of absorbing performance,computational efficiency,calculation accuracy and convenient implementation.A numerical example is carried out to demonstrate the effectiveness and efficiency of the proposed scheme.The results indicate that the proposed scheme can not only have considerable absorbing performance but also maintain the unconditional stability of the algorithm with the enlargement of time steps.
