scholarly journals Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory

Materials ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1475 ◽  
Author(s):  
J. Flores Méndez ◽  
A. C. Piñón Reyes ◽  
M. Moreno Moreno ◽  
A. Morales-Sánchez ◽  
Gustavo M. Minquiz ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Displacement Vector ◽  
Effective Permittivity ◽  
Homogenization Theory ◽  
Effective Parameters ◽  
Good Correspondence ◽  
Filling Fraction ◽  
Coherent Wave ◽  
Electric And Magnetic Fields ◽  
Magnetic Inclusions

A homogenization theory that can go beyond the regime of long wavelengths is proposed, namely, a theory that is still valid for vectors of waves near the edge of the first zone of Brillouin. In this paper, we consider that the displacement vector and the magnetic induction fields have averages in the volume of the cell associated with the values of the electric and magnetic fields in the edges of the cell, so they satisfy Maxwell’s equations. Applying Fourier formalism, explicit expressions were obtained for the case of a photonic crystal with arbitrary periodicity. In the case of one-dimensional (1D) photonic crystals, the expressions for the tensor of the effective bianisotropic response (effective permittivity, permeability and crossed magneto-electric tensors) are remarkably simplified. Specifically, the effective permittivity and permeability tensors are calculated for the case of 1D photonic crystals with isotropic and anisotropic magnetic inclusions. Through a numerical calculation, the dependence of these effective tensors upon the filling fraction of the magnetic inclusion is shown and analyzed. Our results show good correspondence with the approach solution of Rytov’s effective medium. The derived formulas can be very useful for the design of anisotropic systems with specific optical properties that exhibit metamaterial behavior.

scholarly journals Erratum: Flores, J., et al. Effective Parameters for 1D Photonic Crystals with Isotropic and Anisotropic Magnetic Inclusions: Coherent Wave Homogenization Theory. Materials 2020, 13, 1475

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3053
Author(s):  
J. Flores Méndez ◽  
A. C. Piñón Reyes ◽  
M. Moreno Moreno ◽  
A. Morales-Sánchez ◽  
Gustavo M. Minquiz ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Homogenization Theory ◽  
Effective Parameters ◽  
Coherent Wave ◽  
Magnetic Inclusions

The authors wish to make the following corrections to this paper [1]: replace: (37) 1 ε z = f ε m = 1 − f ε d and (39) 1 μ z = f μ m = 1 − f μ d with the correct expressions: (37) 1 ε z = f ε m + 1 − f ε d and (39) 1 μ z = f μ m + 1 − f μ d [...]

Controlling the amount of acoustic absorption by using clusters of hard cylinders

2021 ◽  
Vol 263 (2) ◽  
pp. 4608-4614
Author(s):  
Vicente Cutanda Henriquez ◽  
José Sánchez-Dehesa
Keyword(s):  
Boundary Element Method ◽  
Numerical Experiments ◽  
Hexagonal Lattice ◽  
Filling Ratio ◽  
Homogenization Theory ◽  
Acoustic Absorption ◽  
Effective Parameters ◽  
Filling Fraction ◽  
Homogenization Approach ◽  
Comprehensive Study

The viscothermal absorption of a cluster of hard cylinders periodically arranged in air is directly related with the filling fraction of the underlying lattice. In this work, we present a comprehensive study of the viscous absorption of clusters with circular external shape. The study has been performed by using a homogenization theory in which the clusters have been represented by a single fluid-like cylinder with effective parameters. The validity of the homogenization approach has been supported with numerical experiments in which the viscosity of the actual cluster is calculated with an improved version of the boundary element method. The simulations have been performed by embedding the clusters in a multimode impedance tube. For example, for a circular cluster containing 817 hard cylinders distributed in a hexagonal lattice with filling ratio of 0.836, the absorptive factor calculated with the homogenization approach is 41.5%, which underestimates by about 1% the value obtained with the complete cluster.

Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

1990 ◽  
Vol 48 (2) ◽  
pp. 110-111 ◽  
Author(s):  
F. Hasselbach ◽  
A. Schäfer
Keyword(s):  
Group Velocity ◽  
Wave Packets ◽  
Index Of Refraction ◽  
Electron Wave ◽  
Fringe Contrast ◽  
Faraday Cage ◽  
Optical Index ◽  
Wien Filter ◽  
Coherent Wave ◽  
Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

scholarly journals Magnetodielectric and Metalomagnetic 1D Photonic Crystals Homogenization:ε-μLocal Behavior

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
J. I. Rodríguez Mora ◽  
J. Flores Méndez ◽  
B. Zenteno Mateo ◽  
F. Severiano Carrillo ◽  
R. C. Ambrosio Lázaro
Keyword(s):  
Magnetic Field ◽  
Photonic Crystals ◽  
Electromagnetic Fields ◽  
Magnetic Induction ◽  
Bravais Lattice ◽  
Arbitrary Form ◽  
Permittivity And Permeability ◽  
Induction Components ◽  
Homogenous Medium ◽  
Magnetic Inclusions

A theory for calculating the effective optic response of photonic crystals with metallic and magnetic inclusions is reported, for the case when the wavelength of the electromagnetic fields is much larger than the lattice constant. The theory is valid for any type of Bravais lattice and arbitrary form of inclusions in the unitary cell. An equations system is obtained for macroscopic magnetic field and magnetic induction components expanding microscopic electromagnetic fields in Bloch waves. Permittivity and permeability effective tensors are obtained comparing the equations system with an anisotropic nonlocal homogenous medium. In comparison with other homogenization theories, this work uses only two tensors: nonlocal permeability and permittivity. The proposal showed here is based on the use of permeability equations, which are exact and very simple. We present the explicit form of these tensors in the case of binary 1D photonic crystals.

scholarly journals Pulse Reshaping in Double-zero-index Photonic Crystals with Dirac-like-cone Dispersion

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Tao Xu ◽  
Dejun Zhu ◽  
Zhi Hong Hang
Keyword(s):  
Photonic Crystals ◽  
Numerical Simulations ◽  
Group Velocity ◽  
Brillouin Zone ◽  
Flat Band ◽  
Effective Parameters ◽  
Double Zero ◽  
Linear Dispersion ◽  
Frequency Components ◽  
Zero Index

Abstract Triply-degenerate Dirac-like cone at the Brillouin zone center attracts much research interest in recent years. Whether the linear dispersion in such a Dirac-like cone reflects the same physics to Dirac cones at the Brillouin zone boundaries is still under investigation. In this manuscript, through microwave experiments and numerical simulations, we observe intriguing pulse reshaping phenomena in double-zero-index photonic crystals, which cannot be fully understood from their close-to-zero effective parameters. A reshaped pulse, with frequency components close to the Dirac frequency filtered, is propagating at a constant group velocity while part of these filtered frequencies appears at a much later time. In time domain measurements, we find a way to separate the effect between the linear dispersion and the extra flat band in Dirac-like cone to have a better understanding of the underneath physics. We succeed in obtaining the group velocity inside a double-zero-index photonic crystal and good consistence can be found between experiments, numerical simulations and band diagram calculations.

Efficient Effective Permittivity Treatment for the 2D-FDTD Simulation of Photonic Crystals

2007 ◽  
Vol 4 (3) ◽  
pp. 644-648 ◽  
Author(s):  
T. Jalali ◽  
K. Rauscher ◽  
A. Mohammadi ◽  
D. Erni ◽  
Ch. Hafner ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Effective Permittivity ◽  
Fdtd Simulation ◽  
2D Fdtd

Calculation of Electromagnetic Constitutive Parameters of Insulating Magnetic Materials with Conducting Inclusions

1995 ◽  
Vol 408 ◽  
Author(s):  
Drs. Eric Kuster ◽  
Rick Moore ◽  
Lisa Lust ◽  
Paul Kemper
Keyword(s):  
Magnetic Properties ◽  
Correlation Length ◽  
Method Of Moments ◽  
Effective Permittivity ◽  
Frequency Dispersion ◽  
Effective Parameters ◽  
Electromagnetic Model ◽  
Permittivity And Permeability ◽  
The Matrix ◽  
Constitutive Parameters

AbstractA Method of Moments (MoM) electromagnetic model of percolating conducting films was applied to calculate the effective parameters of the composite formed by conducting inclusions placed within a dispersive magnetic but nondispersive dielectric matrix. The MoM calculations demonstrate a coupling between the magnetic properties of the matrix and the effective composite permittivity and frequency dispersion of the composite. The coupling of permittivity and permeability is observed near the percolation threshold of the composite and for high conductivity inclusions. The prediction agrees with physical expectations since near percolation the conduction correlation length dominates the effective permittivity of the composite and this correlation length is determined by both the permittivity and permeability of the composite.

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