Table Of ContentWaves in Nonlinear Layered
Metamaterials, Gyrotropic and
Plasma Media
Online at: https://doi.org/10.1088/978-0-7503-2336-9
Waves in Nonlinear Layered
Metamaterials, Gyrotropic and
Plasma Media
Yuriy Rapoport
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
and
University of Warmia and Mazury in Olsztyn, Poland
Vladimir Grimalsky
Autonomous University of State Morelos, Cuernavaca, Morelos, Mexico
IOP Publishing, Bristol, UK
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ISBN 978-0-7503-2336-9(ebook)
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DOI 10.1088/978-0-7503-2336-9
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Contents
Preface xiv
Author biographies xx
Page dedicated to Professor Allan D Boardman xxii
Selected publications of the authors xxiv
1 Introductory chapter 1-1
1.1 Metamaterials: the discovery of 2000th 1-1
1.2 Characteristic features of the media and wave phenomena in 1-1
metamaterials and the main approaches to their modeling
1.2.1 Typical properties of metamaterials 1-1
1.2.2 Bi-anisotropy (gyrotropy), non-reciprocity and controllability of 1-3
environments of the metamaterial media
1.2.3 Graphene as a metamaterial chiral medium 1-6
1.2.4 Nonlinearity in layered media. Wave beams and packets with a 1-6
moderate spectrum width. Spatial and temporal solitons
and magnetooptical control of solitons. Control of wave
structures in inhomogeneous and non-stationary gyrotropic
and metamaterial media
1.2.5 Active metamaterials. Problems of spatial amplification 1-10
and convective instability
1.2.6 Field concentration, transformation optics, strong and resonant 1-11
nonlinearities, nonlocality and spatial dispersion in layered media
1.2.7 Hyperbolic metamaterials 1-13
1.2.8 Wave processes in layered media of different physical nature 1-14
in the presence of both volume and surface nonlinearities
1.2.9 Metamaterial approach 1-17
1.3 Purpose, tasks, and structure of the book 1-19
List of abbreviations 1-20
References 1-20
2 Metamaterials with active metaparticles. Absolute and 2-1
convective instability in the active metamaterials
2.1 Artificial molecules (AMs) and their individual polarizations 2-1
2.1.1 Individual polarizations of Ω-particles 2-3
2.1.2 Individual polarizations of the ring resonators with the gap. 2-4
The necessary conditions for the change of the sign of the losses
v
WavesinNonlinearLayeredMetamaterials,GyrotropicandPlasmaMedia
2.1.3 Principles of linear and nonlinear homogenization based on the 2-6
method of perturbations
2.2 Possibility of the existence of active metamaterials with spatial 2-13
amplification and negative phase behavior
2.2.1 Simplified consideration based on the approximation of the 2-13
frequency-independent conductivity of the active loading
2.2.2 Qualitative estimations of the possibility of creating an active 2-17
metamaterial with negative phase behavior on the basis of
periodic infinite structures. Taking into account the
frequency dependence of the active loads of metaparticles
2.2.3 A general approach to the problem of stability of resonant 2-23
negative metamaterials
2.3 Nonlinear homogenization out of the frames of the perturbation 2-27
method and constitutional (material) nonlinear relationships
2.4 Conclusions 2-32
Problems to chapter 2 2-33
Problem 2.1 2-33
Problem 2.2 2-33
Problem 2.3 2-33
List of abbreviations 2-33
References 2-45
3 General method of the derivation of nonlinear evolution 3-1
equations for layered structures (NEELS) with the volume
and surface nonlinearities
3.1 A method for the derivation of the nonlinear evolution equations for 3-2
the waves in layered structures with bi-anisotropic metamaterials
3.1.1 Formulation of the problem for the media with weak 3-2
nonlinearity and weak losses/gain. NEELS in a differential form
3.1.2 Equations for the slowly varying envelope amplitude of a wave 3-5
packet in unbounded media with a spatial dispersion
3.1.3 EquationsfortheenvelopeamplitudesNEELSintheintegralform 3-7
3.2 Method NEELS for the giant resonance generation of the second 3-10
harmonic of surface plasmons and the contribution of the surface
and volume nonlinearities
3.3 Method NEELS for nonlinear electromagnetic and MSWs in the 3-11
layered dielectric-ferromagnetic media with spatial dispersion and
auxiliary boundary conditions
3.3.1 BVMSWs in longitudinally magnetized ferrite films 3-11
vi
WavesinNonlinearLayeredMetamaterials,GyrotropicandPlasmaMedia
3.3.2 Developing NEELS method for the case of nonlinear pulses 3-16
with the moderate spectrum in gyrotropic layered structures.
Magnetized gyrotropic and dielectric structures with spatial
dispersion and auxiliary nonlinear boundary conditions
3.3.3 Magnetized gyrotropic and dielectric structures with spatial 3-19
dispersion and auxiliary nonlinear boundary conditions
3.3.4 Development of the NEELS method for space-time modeling 3-23
solitons and nonlinear wave structures in controlled and
active nonlinear gyrotropic and metamaterial waveguides:
from microwave to the optical ranges
3.4 Conclusions to chapter 3 3-23
Problems to chapter 3 3-24
Problem 3.1 3-24
Problem 3.2 3-24
Problem 3.3 3-25
Problem 3.4 3-26
List of abbreviations 3-26
References 3-41
4 Application of the nonlinear evolution equations for layered 4-1
structures (NEELS) method to the layered nonlinear passive
gyrotropic and plasma-like structures with volume
and surface nonlinearities
4.1 Application of method NEELS for the giant resonance generation 4-1
of the second harmonic of surface plasmons and contribution of the
surface and volume nonlinearities
4.2 Vortex structures on the backward volume magnetostatic waves 4-3
in ferrite films
4.2.1 Excitation by a circular antenna of linear stationary FVMSW 4-4
structures possessing phase defects
4.2.2 Formulation of the problem of non-stationary pulse interaction 4-8
and main relations
4.2.3 Numerical simulations 4-9
4.2.4 Conclusions to section 4.2 4-13
4.3 Formation and propagation of the bullets in the gyrotropic 4-13
waveguides accounting for higher-order nonlinearities
4.4 Application of the method NEELS for the propagation of the waves 4-16
in the linear waveguide Earth-Ionosphere
4.5 Conclusions to chapter 4 4-17
vii
WavesinNonlinearLayeredMetamaterials,GyrotropicandPlasmaMedia
Problems to chapter 4 4-18
Problem 4.1 4-18
Problem 4.2 4-18
Problem 4.3 4-19
Problem 4.4 4-21
Problem 4.5 4-22
List of abbreviations 4-23
References 4-23
5 Controllable propagation and reflection of electromangetic 5-1
waves in layered gyrotropic metamaterial media
5.1 The problems under consideration 5-1
5.2 The magnetooptic control of spatial and spatio-temporal solitons in 5-3
metamaterial waveguides
5.3 Stationary equations and spatial solitons in the presence of the 5-3
higher-order effect: nonlinear diffraction
5.4 Non-stationary equations and spatial-temporal solitons in the presence 5-8
of higher-order effects: nonlinear diffraction and dispersion,
Raman interaction, and linear third-order dispersion. Generalization
of NEELS method
5.4.1 Evolution equations for temporary solitons with higher-order 5-8
effects
5.4.2 The principle of magnetooptical control of time solitons in a 5-10
non-stationary metamaterial medium
5.4.3 Lagrangian dynamics and magnetooptical control of time 5-13
solitons with higher-order effects
5.5 New types of surface magnetic polaritons and reflection of electro- 5-15
magnetic waves in metamaterial–dielectric systems
5.5.1 Equations for surface polaritons at the boundary of semi-infinite 5-16
layered gyrotropic and metamaterial media
5.5.2 New types of surface magnetic polaritons in the ferromagnetic 5-18
system—metamaterial
5.5.3 Shift of electromagnetic pulses upon reflection from the system 5-20
‘semi-infinite dielectric–dielectric layer-semi-infinite
metamaterial with negative ε, μ’
5.6 Conclusions 5-23
Problems to chapter 5 5-34
Problem 5.1 5-34
Problem 5.2 5-35
viii
WavesinNonlinearLayeredMetamaterials,GyrotropicandPlasmaMedia
Problem 5.3 5-36
List of abbreviations 5-36
References 5-36
6 Parametric interactions of the nonlinear waves in active 6-1
layered metamaterials and gyrotropic structures
6.1 Wave structures in layered active gyrotropic media with parametric 6-2
interaction
6.1.1 Formulation of the problem 6-2
6.1.2 Investigations of the three-wave parametric interaction of 6-4
MSW in gyrotropic layered structures by NEELS method
6.1.3 Results on the formation of nonlinear active structures in 6-6
parametric interaction in a gyrotropic medium
6.2 Nonlinear waves in the layered bi-anisotropic metamaterials 6-9
6.3 Parametric interactions and phase conjugation on active 6-11
two-dimensional chiral metamaterial surfaces with linear and
nonlinear Huygens sources
6.3.1 Justification and formulation of the problem 6-12
6.3.2 Conditions of phase conjugation without reflection 6-12
6.3.3 Simulation results 6-14
6.4 Conclusions to chapter 6 6-15
Problems to chapter 6 6-21
List of abbreviations 6-24
References 6-24
7 Formation propagation, and control of bullets in metamaterial 7-1
waveguides with higher-order nonlinear effects and
magnetooptic interaction
7.1 Introduction 7-1
7.2 Instabilities of bullets in the metamaterial waveguides with the 7-2
influence of the higher-order nonlinear effects
7.3 Stabilization of bullets in periodical and magnetooptic metamaterial 7-5
waveguides
7.4 Conclusions for chapter 7 7-8
Problems to chapter 7 7-12
Problems to section 7.1 7-12
Problem 7.1 7-12
Problem 7.2 7-12
ix
