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In this paper we consider the free-form optimization of eigenvalues in electromagnetic systems by means of shape-variations with respect to small deformations. The objective is to optimize a particular eigenvalue to a target value. We…

Optimization and Control · Mathematics 2026-05-19 Christine Herter , Sebastian Schöps , Winnifried Wollner

This paper presents a point-wise divergence-free projection method for numerical approximations of photonic quasicrystals problems. The original three-dimensional quasiperiodic Maxwell's system is transformed into a periodic one in higher…

Numerical Analysis · Mathematics 2024-09-10 Zixuan Gao , Zhenli Xu , Zhiguo Yang

We present a kernel compensation method for Maxwell eigenproblem for photonic crystals to avoid the infinite-dimensional kernels that cause many difficulties in the calculation of energy gaps. The quasi-periodic problem is first transformed…

Numerical Analysis · Mathematics 2025-03-26 Chenhao Jin , Yinhua Xia , Yan Xu

We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous…

This paper gives an overview of recent work on three-dimensional (3D) photonic crystals with a "full and complete" 3D photonic band gap. We review five main aspects: 1) spontaneous emission inhibition, 2) spatial localization of light…

Quantum Physics · Physics 2015-04-28 W. L. Vos , L. A. Woldering

In this study, a variational method for the inverse problem of self-assembly, i.e., a reconstruction of the interparticle interaction potential of a given structure, is applied to three-dimensional crystals. According to the method, the…

Soft Condensed Matter · Physics 2021-01-22 Masashi Torikai

We present a finite-element simulation tool for calculating light fields in 3D nano-optical devices. This allows to solve challenging problems on a standard personal computer. We present solutions to eigenvalue problems, like Bloch-type…

Optics · Physics 2009-05-28 S. Burger , R. Klose , A. Schaedle , F. Schmidt , L. Zschiedrich

In ab-initio indexing, for a given diffraction/scattering pattern, the unit-cell parameters and the Miller indices assigned to reflections in the pattern are determined simultaneously. "Ab-initio" means a process performed without any good…

Materials Science · Physics 2024-04-23 R. Oishi-Tomiyasu

This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…

Spectral Theory · Mathematics 2021-01-26 Biagio Cassano , Lucrezia Cossetti , Luca Fanelli

The topology, the symmetry involving the shape of dielectric cylinders, and the lattice structure are among the most important ingredients in the architecture of photonic crystals. In this paper, we present a systematic derivation of the…

Condensed Matter · Physics 2007-05-23 Pi-Gang Luan , Zhen Ye

We derive a framework for classifying topological bands in three-dimensional photonic band structures, where the zero frequency polarization singularity implied by Maxwell's equations complicates the direct application of existing…

We propose a new method based on variational principle for analysis of photonic crystal (PC) slabs. Most of the methods used today treat PC slab as a three-dimensional (3D) crystal and this makes them very time and/or memory consuming. In…

Mesoscale and Nanoscale Physics · Physics 2015-05-04 Mohammad Hasan Aram , Sina Khorasani

Tight-binding models can accurately replicate the band structure and topology of crystalline systems. They have been widely used in solid-state physics due to their versatility and low computational cost. It is straightforward to build an…

We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretisation, outline the implementation, and showcase numerical examples.

Computational Engineering, Finance, and Science · Computer Science 2021-06-03 Stefan Kurz , Sebastian Schöps , Gerhard Unger , Felix Wolf

We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes…

Optics · Physics 2011-02-21 Vincenzo Savona

We consider photonic crystal fibres (PCFs) made from arbitrary base materials and introduce a short-wavelength approximation which allows for a mapping of the Maxwell's equations onto a dimensionless eigenvalue equations which has the form…

Optics · Physics 2007-05-23 Niels Asger Mortensen

Key words : The Maxwell equations, band structure calculations, Kohn-Korringa-Rostocker method, and multiple-scattering theory for photons. For those who are interested in how to prepare perfect mirror from a purely transparent material.…

Condensed Matter · Physics 2008-02-03 Alexander MOROZ

Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the…

We study photonic band structure of two- and three-dimensional magnetophotonic crystals and the polarization properties of their eigenmodes using a plane wave expansion method. The alteration of the photonic band structure and eigenmodes by…

Optics · Physics 2009-07-07 A. B. Khanikaev , K. Yayoi , M. J. Steel , A. V. Baryshev , M. Inoue

We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue problem becomes nonlinear. In the lossless case, linearization…

Numerical Analysis · Mathematics 2019-12-03 Robert Altmann , Marine Froidevaux