相关论文: Solving Three Dimensional Maxwell Eigenvalue Probl…
There are many numerical methods for simulate three-dimensional photonic crystals, after comparison, we choose Yee's scheme to be our discrete method. So far, this method can only be applied to simple cubic lattice and face-centered cubic…
Our goal is to predict the band structure of photonic crystals. This task requires us to compute a number of the smallest non-zero eigenvalues of the time-harmonic Maxwell operator depending on the chosen Bloch boundary conditions. We…
In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue…
We consider the calculation of the band structure of frequency dependent photonic crystals. The associated eigenvalue problem is nonlinear and it is challenging to develop effective convergent numerical methods. In this paper, the band…
We propose a new method to compute band structures of dispersive photonic crystals. It can treat arbitrarily frequency-dependent, lossy or lossless materials. The band structure problem is first formulated as the eigenvalue problem of an…
We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc…
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
In this paper we describe an application of the finite difference method to obtain the transverse magnetic photonic band gap diagram of a photonic crystal. The strategy of this method is to formulate the Maxwell equations in finite…
In the band theory for non-Hermitian systems, the energy eigenvalues, which are complex, can exhibit non-trivial topology which is not present in Hermitian systems. In one dimension, it was recently noted theoretically and demonstrated…
Bravais lattices are the most fundamental building blocks of crystallography. They are classified into groups according to their translational, rotational, and inversion symmetries. In computational analysis of Bravais lattices, fulfilment…
In this work we investigate the computation of dispersion relation (i.e., band functions) for three-dimensional photonic crystals, formulated as a parameterized Maxwell eigenvalue problem, using a novel hp-adaptive sampling algorithm. We…
The article is devoted to the discussion of the high-throughput approach to band structures calculations. We present scientific and computational challenges as well as solutions relying on the developed framework (Automatic Flow,…
Motivated by recent experiments demonstrating the creation of atomically sharp interfaces between hexagonal sapphire and cubic SrTiO$_3$ with finite twist, we here develop and study a general electronic band theory for this novel class of…
The structural solution problem can be a daunting and time consuming task. Especially in the presence of impurity phases, current methods such as indexing become more unstable. In this work, we apply the novel approach of semi-supervised…
The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the…
Complex bands $\vec{k}^{\perp}(E)$ in a semiconductor crystal, along a general direction $\vec{n}$, can be computed by casting Schr\"odinger's equation as a generalized polynomial eigenvalue problem. When working with primitive lattice…
Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of 2D hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-particle…
We have performed a numerical solution for band structure of an Abrikosov vortex lattice in type-II superconductors forming a periodic array in two dimensions for applications of incorporating the photonic crystals concept into…