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In this paper we address the question how to design photonic crystals that have photonic band gaps around a finite number of given frequencies. In such materials electromagnetic waves with these frequencies can not propagate; this makes…

Spectral Theory · Mathematics 2019-03-07 Markus Holzmann , Vladimir Lotoreichik

In photonic crystals the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatially strictly periodic…

We investigate non-Hermitian photonic crystals in which the lossy and lossless constituents share the same real permittivity and differ only in their imaginary part. We characterize the complex band structure and reflection response of both…

Optics · Physics 2026-04-08 Jin Xu , Daniel Cui , Aaswath P. Raman

Photonic crystals with a sufficiently high refractive index contrast display partial or full band gaps. However, imperfections in the metamaterial cause light scattering and extinction of the interfering propagating waves. Positive as well…

Optics · Physics 2022-02-02 Stefan Aeby , Geoffroy J. Aubry , Nicolas Muller , Frank Scheffold

It is well known that waves incident upon a crystal are transported only over a limited distance - the Bragg length - before being reflected by Bragg interference. Here, we demonstrate how to send waves much deeper into crystals, by…

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly…

The photonic band structures in certain two- and three-dimensional periodic networks made of one-dimensional waveguides are studied by using the Floquet-Bloch theorem. We find that photonic band gaps exist only in those structures where the…

Disordered Systems and Neural Networks · Physics 2007-05-23 S. K. Cheung , T. L. Chan , Z. Q. Zhang , C. T. Chan

The band gap, a key concept in solid-state physics, is traditionally explained by the Bragg diffraction of electron waves in the periodic potential of a crystal. Although widely accepted, this framework raises fundamental issues in…

Materials Science · Physics 2025-08-28 Koichi Kajiyama

Quasicrystals, realized in metal alloys, are a class of lattices exhibiting symmetries that fall outside the usual classification for periodic crystals. They do not have translational symmetry and yet the lattice points are well ordered.…

Optics · Physics 2009-11-13 Jun Xu , Rui Ma , Xia Wang , Wing Yim Tam

A phoxonic crystal waveguide with the glide symmetry is designed, in which both electromagnetic and elastic waves can propagate along the glide plane at the same time. Due to the band-sticking effect, super-cell bands of the waveguide…

Optics · Physics 2023-10-27 Linlin Lei , Lingjuan He , Qinghua Liao , Wenxing Liu , Tianbao Yu

We consider a model for a one-dimensional photonic crystal formed by a succession of Kerr-type equidistant spaceless interfaces immersed in a linear medium. We calculate the band structure and reflectance of this structure as a function of…

Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator for a joint optical structure formed by connecting together…

Optimization and Control · Mathematics 2024-07-30 Chiu-Yen Kao , Junshan Lin , Braxton Osting

2D dielectric photonic quasicrystals can be designed to show isotropic band gaps. The system here studied is a quasiperiodic lattice made of silicon dielectric cylinders arranged as periodic unit cell based on a decagonal approximant of a…

Optics · Physics 2021-07-21 Angel Andueza , Joaquin Sevilla , Jesus Perez-Conde , Kang Wang

We consider a quantum particle in a waveguide which consists of an infinite straight Dirichlet strip divided by a thin semitransparent barrier on a line parallel to the walls which is modeled by a $\delta$ potential. We show that if the…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 P. Exner , D. Krejcirik

Coupled electromagnetic waves propagating in a waveguide array are discussed. This waveguide array can be considered as one dimensional photon crystal composed from the unit cell containing three different waveguides, namely, two positive…

Pattern Formation and Solitons · Physics 2015-05-20 Andrei Maimistov

A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial…

Quantum Gases · Physics 2022-03-08 Lingzhen Guo , Michael Marthaler , Gerd Schön

We analytically model a one-dimensional lattice with periodic impurities representing a photonic crystal from first principles. We then investigate bound states in the continuum by computing the transmission and reflection coefficients. It…

Quantum Physics · Physics 2024-10-10 Benjamin Rempfer , Gonzalo Ordonez

Two well-known methods for the design of quasicrystal models are used to create novel nonlinear optical devices. These devices are useful for efficient three-wave mixing of several different processes, and therefore offer greater…

Materials Science · Physics 2009-11-13 Alon Bahabad , Ron Lifshitz , Noa Voloch , Ady Arie

The great interest to the two and three dimensionally periodic structures, called photonic crystals (PCs), has begun with the pioneer works of Yablonovitch and John as one can efficiently control the propagation of the electromagnetic (EM)…

Optics · Physics 2016-02-19 Mirbek Turduev

The recent development of subwavelength photonic and phononic crystals shows the possibility of controlling wave propagation at deep subwavelength scales. Subwavelength bandgap phononic crystals are typically created using a periodic…

Analysis of PDEs · Mathematics 2019-04-10 Habib Ammari , Erik Orvehed Hiltunen , Sanghyeon Yu