scholarly journals Dynamic homogenisation of Maxwell’s equations with applications to photonic crystals and localised waveforms on gratings

Wave Motion ◽  
2017 ◽  
Vol 69 ◽  
pp. 35-49 ◽  
Author(s):  
B. Maling ◽  
D.J. Colquitt ◽  
R.V. Craster
Keyword(s):  
Photonic Crystals ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

FAME

2021 ◽  
Vol 47 (3) ◽  
pp. 1-24
Author(s):  
Xing-long Lyu ◽  
Tiexiang Li ◽  
Tsung-ming Huang ◽  
Jia-wei Lin ◽  
Wen-wei Lin ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Maxwell’S Equations ◽  
Large Scale ◽  
Maxwell's Equations ◽  
Eigenvalue Problems ◽  
Null Space ◽  
Three Dimensional ◽  
Coefficient Matrix ◽  
Generalized Eigenvalue Problems ◽  
Matrix Vector

In this article, we propose the Fast Algorithms for Maxwell’s Equations (FAME) package for solving Maxwell’s equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee’s discretization. The GEPs are transformed into a null-space free standard eigenvalue problem with a Hermitian positive-definite coefficient matrix. The computation times for FFT-based matrix-vector multiplications with matrices of dimension 7 million are only 0.33 and 3.6 × 10 − 3 seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with matrices of dimension more than 19 million, in 127 to 191 seconds per problem. These results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.

scholarly journals Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Zhongfei Xiong ◽  
Ruo-Yang Zhang ◽  
Rui Yu ◽  
C. T. Chan ◽  
Yuntian Chen
Keyword(s):  
Photonic Crystals ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Nodal Line ◽  
Rotation Symmetry ◽  
Hidden Symmetries ◽  
Space Groups ◽  
Nodal Lines ◽  
Hidden Symmetry ◽  
Photonic Band

Abstract It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell’s equations. The bands with a constant kz and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone, giving rise to exotic transport features of light at the nexus point. We show that spin-1 conical diffraction occurs at the nexus point, which can be used to manipulate the charges of optical vortices. Our work reveals that Maxwell’s equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.

scholarly journals Not every dipole is the same: the hidden patterns of dipolar near fields

2018 ◽  
Vol 49 (4) ◽  
pp. 14-18 ◽  
Author(s):  
Michela F. Picardi ◽  
Anatoly V Zayats ◽  
Francisco J. Rodríguez-Fortuño
Keyword(s):  
Photonic Crystals ◽  
Quantum Optics ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Scientific Field ◽  
Modern Physics ◽  
Hidden Patterns

Nanophotonics is a fast-evolving scientific field studying light at the nanoscale. Its fascinating advances typically stem from concepts in modern physics, such as quantum optics, photonic crystals and optomechanics [1]. Occasionally, new insights appear even from the classical Maxwell’s equations of electromagnetism themselves [2].

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

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