We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator fun...We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.展开更多
For a photonic crystal （PhC） of finite size, it is important to calculate its transmission and reflection spectra. For two-dimensional （2-D） PhCs composed of a square lattice of circular cylinders, the problem can...For a photonic crystal （PhC） of finite size, it is important to calculate its transmission and reflection spectra. For two-dimensional （2-D） PhCs composed of a square lattice of circular cylinders, the problem can be solved by an efficient method based on the Dirichlet-to-Neumann （DtN） map of the unit cell and a marching scheme using a pair of operators. In this paper, the DtN operator marching method is extended to handle 2-D PhCs with complex unit cells and arbitrary lattice structures.展开更多
A problem of nanocatalyst improvement is considered. The existence of irregularities at the surface of nanoparticle leads to the increasing of the surface/volume ratio and, correspondingly, to the improvement of the c...A problem of nanocatalyst improvement is considered. The existence of irregularities at the surface of nanoparticle leads to the increasing of the surface/volume ratio and, correspondingly, to the improvement of the catalytic activity. But this impurity gives one an additional effect due to the change of the electronic density at the surface. We suggest simple model for the description of this effect. The model allows one to find the discrete spectrum of the Schrdinger operator for nanoparticle. Due to this impurity induced bound states the electron density increases near the surface. It leads to the increase of the catalytic activity of nanoparticles with surface impurities.展开更多
基金China Postdoctoral Science Foundation Grant 2019M650460the NSF grant DMS-2011148.The research of J.Sun is supported partially by the Simons Foundation Grant 711922.
文摘We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.
基金This research was partially supported by a City University of Hong Kong research grant(Project No.7001862).
文摘For a photonic crystal （PhC） of finite size, it is important to calculate its transmission and reflection spectra. For two-dimensional （2-D） PhCs composed of a square lattice of circular cylinders, the problem can be solved by an efficient method based on the Dirichlet-to-Neumann （DtN） map of the unit cell and a marching scheme using a pair of operators. In this paper, the DtN operator marching method is extended to handle 2-D PhCs with complex unit cells and arbitrary lattice structures.
基金Supported by Federal Targeted Program "Scientific and Educational Human Resources for Innovation-Driven Russia" (contracts P689NK-526P, 14.740.11.0879, and 16.740.11.0030) and grant 11-08-00267 of Russian Foundation for Basic Researchesstate contract SC16.516.11.6073 and by Federal Targeted Program "Researches and Development in the Prioring Directions Developments of a Scientific and Technological Complex of Russia 2007-2013" (state contract 07.514.11.4146)
文摘A problem of nanocatalyst improvement is considered. The existence of irregularities at the surface of nanoparticle leads to the increasing of the surface/volume ratio and, correspondingly, to the improvement of the catalytic activity. But this impurity gives one an additional effect due to the change of the electronic density at the surface. We suggest simple model for the description of this effect. The model allows one to find the discrete spectrum of the Schrdinger operator for nanoparticle. Due to this impurity induced bound states the electron density increases near the surface. It leads to the increase of the catalytic activity of nanoparticles with surface impurities.
