Electromagnetic Waves in Nonlinear Metamaterials: Gyrotropic, Plasmonic and Layered Media

PRELIMS.pdf
Preface
Author biographies
Yuriy Rapoport
Volodymyr Grimalsky
Page dedicated to Professor Allan D Boardman
Outline placeholder
Professor Allan D Boardman
Selected publications of the authors
Journal papers
Monographs/chapters in the monographs
Textbook
CH001.pdf
Chapter 1 Introductory chapter
1.1 Metamaterials: the discovery of 2000th
1.2 Characteristic features of the media and wave phenomena in metamaterials and the main approaches to their modeling
1.2.1 Typical properties of metamaterials
1.2.2 Bi-anisotropy (gyrotropy), non-reciprocity and controllability of environments of the metamaterial media
1.2.3 Graphene as a metamaterial chiral medium
1.2.4 Nonlinearity in layered media. Wave beams and packets with a 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 and convective instability
1.2.6 Field concentration, transformation optics, strong and resonant nonlinearities, nonlocality and spatial dispersion in layered media
1.2.7 Hyperbolic metamaterials
1.2.8 Wave processes in layered media of different physical nature in the presence of both volume and surface nonlinearities
1.2.9 Metamaterial approach
1.3 Purpose, tasks, and structure of the book
List of abbreviations
References
CH002.pdf
Chapter 2 Metamaterials with active metaparticles. Absolute and convective instability in the active metamaterials
2.1 Artificial molecules (AMs) and their individual polarizations
2.1.1 Individual polarizations of Ω-particles
2.1.2 Individual polarizations of the ring resonators with the gap. The necessary conditions for the change of the sign of the losses
2.1.3 Principles of linear and nonlinear homogenization based on the method of perturbations
2.2 Possibility of the existence of active metamaterials with spatial amplification and negative phase behavior
2.2.1 Simplified consideration based on the approximation of the frequency-independent conductivity of the active loading
2.2.2 Qualitative estimations of the possibility of creating an active 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 negative metamaterials
2.3 Nonlinear homogenization out of the frames of the perturbation method and constitutional (material) nonlinear relationships
2.4 Conclusions
Problems to chapter 2
Problem 2.1
Problem 2.2
Problem 2.3
List of abbreviations
Appendix A
A.1 Model of a new active bi-anisotropic metamaterial
A.2 To the characterization of metamolecules of bi-anisotropic metamaterial
A.3 Homogenization for linear metamaterials with MC in the form of ‘Ω-particles’. The principle of nonlinear homogenization of metamaterial by perturbation method
A.4 Possibility of simultaneous amplification of EMW and negative signs of real parts of dielectric ε ‘and magnetic μ’ permeability of metamaterial based on split rings with active diodes. Estimation of the ‘effective length’ of spatial amplification of EMW in active metamaterial
A.5 Simplified analysis of the possibility of creating an active metamaterial environment with spatial amplification: approximation of frequency-independent conductivities of ‘active loads’ of the metaparticles
A.6 The stability problem related to the roots and poles of the dispersion relation
A.7 Conditions for the absence of AI associated with the effects of the finiteness of the structure period
A.8 Homogenization and nonlinear constitutional equations for the bi-anisotropic metamaterial
References
CH003.pdf
Chapter 3 General method of the derivation of nonlinear evolution equations for layered structures (NEELS) with the volume and surface nonlinearities
3.1 A method for the derivation of the nonlinear evolution equations for the waves in layered structures with bi-anisotropic metamaterials
3.1.1 Formulation of the problem for the media with weak nonlinearity and weak losses/gain. NEELS in a differential form
3.1.2 Equations for the slowly varying envelope amplitude of a wave packet in unbounded media with a spatial dispersion
3.1.3 Equations for the envelope amplitudes NEELS in the integral form
3.2 Method NEELS for the giant resonance generation of the second harmonic of surface plasmons and the contribution of the surface and volume nonlinearities
3.3 Method NEELS for nonlinear electromagnetic and MSWs in the layered dielectric-ferromagnetic media with spatial dispersion and auxiliary boundary conditions
3.3.1 BVMSWs in longitudinally magnetized ferrite films
3.3.2 Developing NEELS method for the case of nonlinear pulses 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 dispersion and auxiliary nonlinear boundary conditions
3.3.4 Development of the NEELS method for space-time modeling 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
Problems to chapter 3
Problem 3.1
Problem 3.2
Problem 3.3
Problem 3.4
List of abbreviations
Appendix B to Chapter 3
Appendix B.1 Application of the method NEELS for the nonlinear waves in the homogeneous and layered magnetodielectric media. Shifts of frequency and wavenumbers due to a presence of volume nonlinearity
Appendix B.2 The method of derivation of nonlinear evolution equations for nonlinear plasmons in layered media by the method NEELS in the integral form
Appendix B.2.1 Linear motion of the charges
Appendix B.2.2 The general method NEELS. The nonlinearity accounting for motion of surface charges
Appendix B.2.3 Resonance of the second harmonic
Appendix B.2.4 A set of equations for the coupled fundamental and resonant second harmonics
Appendix B2.5 Equation of the method NEELS in the integral form and surface nonlinearity in the electrostatic approximation
Appendix B.3 Quasi-solitons on surface plasmons with a second harmonic close to resonance
Appendix B.4 Estimation of conditions necessary for observation of nonlinear effects in layered plasmon structures from microwave to optical ranges
Appendix B.5 Relationships of the method NEELS for the surface plasmons as a particular case of bi-anisotropic metamaterials
Appendix B.6 Equations of the NEELS method in integral and differential form taking into account nonlinearity in auxiliary boundary conditions associated with spatial dispersion
Appendix B.7 Details of the derivation of the nonlinear evolution eauations for BVMSW by means of method NEELS
Appendix B.7.1 The contribution of terms with harmonics of second order in the nonlinear term for the BVMSW
Appendix B.7.2 Evaluations of the contributions of the terms with higher harmonics in the nonlinear term for the BVMSW
Appendix B.7.3 Coefficients in the evolution equations for the envelope amplitude with higher linear and nonlinear terms
Appendix B.7.4 Comparison of the nonlinear coefficient for the BVMSW with the coefficient obtained in Slavin and Rojdestvenski (1994) and Leblond (2001)
References
CH004.pdf
Chapter 4 Application of the nonlinear evolution equations for layered 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 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 in ferrite films
4.2.1 Excitation by a circular antenna of linear stationary FVMSW structures possessing phase defects
4.2.2 Formulation of the problem of non-stationary pulse interaction and main relations
4.2.3 Numerical simulations
4.2.4 Conclusions to section 4.2
4.3 Formation and propagation of the bullets in the gyrotropic waveguides accounting for higher-order nonlinearities
4.4 Application of the method NEELS for the propagation of the waves in the linear waveguide Earth-Ionosphere
4.5 Conclusions to chapter 4
Problems to chapter 4
Problem 4.1
Problem 4.2
Problem 4.3
Problem 4.4
Problem 4.5
List of abbreviations
References
CH005.pdf
Chapter 5 Controllable propagation and reflection of electromangetic waves in layered gyrotropic metamaterial media
5.1 The problems under consideration
5.2 The magnetooptic control of spatial and spatio-temporal solitons in metamaterial waveguides
5.3 Stationary equations and spatial solitons in the presence of the higher-order effect: nonlinear diffraction
5.4 Non-stationary equations and spatial-temporal solitons in the presence 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 effects
5.4.2 The principle of magnetooptical control of time solitons in a non-stationary metamaterial medium
5.4.3 Lagrangian dynamics and magnetooptical control of time solitons with higher-order effects
5.5 New types of surface magnetic polaritons and reflection of electromagnetic waves in metamaterial–dielectric systems
5.5.1 Equations for surface polaritons at the boundary of semi-infinite layered gyrotropic and metamaterial media
5.5.2 New types of surface magnetic polaritons in the ferromagnetic system—metamaterial
5.5.3 Shift of electromagnetic pulses upon reflection from the system ‘semi-infinite dielectric–dielectric layer-semi-infinite metamaterial with negative ε, μ’
5.6 Conclusions
Appendix C
Appendix C.1 Derivation of evolutionary equation for time domain and layered metamaterial medium with linear and nonlinear effects of higher orders and magnetooptic control
Appendix C.2 Details of the Lagrange formalism method for qualitative description of magnetooptic control of the purpose of material solitons
Appendix C.3 Detailed consideration of dispersion for new types of surface magnetic polaritons in the system ‘ferromagnetic-metamaterial’ and the ‘magnetostatic boundary case’
Appendix C.4 Derivation of equations for the shift of the electromagnetic pulse when reflected from the system ‘semi-infinite dielectric layer-semi-infinite metamaterial with negative ε, μ’
Problems to chapter 5
Problem 5.1
Problem 5.2
Problem 5.3
List of abbreviations
References
CH006.pdf
Chapter 6 Parametric interactions of the nonlinear waves in active layered metamaterials and gyrotropic structures
6.1 Wave structures in layered active gyrotropic media with parametric interaction
6.1.1 Formulation of the problem
6.1.2 Investigations of the three-wave parametric interaction of MSW in gyrotropic layered structures by NEELS method
6.1.3 Results on the formation of nonlinear active structures in parametric interaction in a gyrotropic medium
6.2 Nonlinear waves in the layered bi-anisotropic metamaterials
6.3 Parametric interactions and phase conjugation on active two-dimensional chiral metamaterial surfaces with linear and nonlinear Huygens sources
6.3.1 Justification and formulation of the problem
6.3.2 Conditions of phase conjugation without reflection
6.3.3 Simulation results
6.4 Conclusions to chapter 6
Appendix D.1 Formation of nonlinear structures in ‘wide’ film and ‘narrow’ active gyrotropic wave
Appendix D.2 Splitting of the peak of the ‘idle’ pulse in the transverse direction during parametric interaction
Appendix D.3 The tendency to equalize the integral amplitudes of the signal and the ‘idle’ pulse at relatively small values of the amplitude of the input pulse and large values of the pump amplitude in the ‘narrow’ FF
Appendix D.4 Almost reflectionless phase conjugation and Huygence sources
Problems to chapter 6
List of abbreviations
References
CH007.pdf
Chapter 7 Formation propagation, and control of bullets in metamaterial waveguides with higher-order nonlinear effects and magnetooptic interaction
7.1 Introduction
7.2 Instabilities of bullets in the metamaterial waveguides with the influence of the higher-order nonlinear effects
7.3 Stabilization of bullets in periodical and magnetooptic metamaterial waveguides
7.4 Conclusions for chapter 7
Appendix E Results of the modeling formation and propagation of the bullets in metamaterial waveguides accounting for influence of higher-order nonlinearities
Problems to chapter 7
Problem 7.1
Problem 7.2
Problem to section 7.2
Problem 7.3.
List of abbreviations
References
CH008.pdf
Chapter 8 Giant double-resonant second harmonic generation in the multilayered dielectric–graphene metamaterials
8.1 Introduction
8.2 Basic equations
8.2.1 Kinetic approach
8.2.2 Hydrodynamic approach
8.2.3 Boundary conditions at the graphene sheets
8.3 Double resonant reflection and nonlinear scattering into second harmonic: simulations
8.4 Discussion and conclusions
List of abbreviations
Problems to chapter 8
References
CH009.pdf
Chapter 9 Nonlinear transformation optics and field concentration
9.1 Introduction to metamaterial transformations and geometrical optics mapping onto full-wave nonlinear solutions. Impact of nonlinear wave transformations on the design of realistic devices
9.2 Inhomogeneous dielectric permittivity and the wave equation
9.3 ‘Ordinary’ geometrical optics
9.4 New CGO techniques
9.5 Formulas of CGO for the particular system shown in figure 9.1
9.6 Electromagnetic field inside an internal nonlinear region r⩽Rc
9.7 Matching ‘full-wave’ and ‘CGO’ solutions and possible applications
9.8 Superfocusing combining linear and nonlinear media to create new forms of energy capture and field concentration
9.9 Conclusions
List of abbreviations
Problems to chapter 9
Problem 9.1
Problem 9.2
Problem 9.3
References
CH010.pdf
Chapter 10 Wave processes in controlled and active metamaterials and plasma-like media in the presence of resonance and strong nonlinearity
10.1 Conditions for transition to the mode of strong nonlinearity during the generation of a giant localized surface plasmonic second harmonic
10.2 Nonlinear electromagnetic waves in metamaterial field concentrators
10.3 Nonlinear switching effect when electromagnetic waves pass through a multilayer resonant system ‘dielectric–graphene’
10.4 Conclusions
Problems to chapter 10
Problem 10.1
Problem 10.2
Problem 10.3
List of abbreviation
References
CH011.pdf
Chapter 11 Nonlinear stationary and non-stationary diffraction in active planar anisotropic hyperbolic metamaterial
11.1 Introduction
11.2 Basic equations. Two approaches: with and without an averaging
11.3 Details of the structure and requirements for materials
11.3.1 Details of the structure
11.3.2 Requirements for materials
11.4 Results of simulations
11.5 The limiting case of the stationary NSE
11.6 The discussion and main results
Problems to chapter 11
Problem 11.1
Problem 11.2
Problem 11.3
References
CH012.pdf
Chapter 12 Analytical models of formation of nonlinear dissipative wave structures in active quantum hyperbolic planar resonant metamaterials in IR range
12.1 General description of the problem
12.1.1 Relevance of metamaterials, and in particular hyperbolic metamaterials, for modern photonics and the role of metamaterials in modern research projects
12.1.2 The importance of nonlinear wave processes in active hyperbolic metamaterials
12.1.3 Modern hyperbolic metamaterials
12.2 Theoretical approach to modeling of modern nonlinear active hyperbolic metamaterials. Ginzburg–Landau equation
12.3 Details of the structure of the active hyperbolic metamaterial
12.3.1 Evolutionary equation for nonlinear momentum propagation at an arbitrary angle to the optical axis in the laboratory coordinate frame in the ‘time representation’ and coordinate representation
12.3.2 Evolution equation written with respect to the laboratory coordinate frame XYZ
12.3.3 Evolutionary equation for nonlinear propagation of a pulse at an arbitrary angle to the optical axis in the coordinate frame X′Y′Z′, where the group velocity is directed along z′, in the spatial representation
12.4 The model of a two-level active medium and equations for nonlinear EMW in planar active resonant hyperbolic medium
12.5 Example of numerical modeling
12.6 Conclusions
Problems to chapter 12
Problem 12.1
Problem 12.2
Problem 12.3
Problem 12.4
List of abbreviations
References
CH013.pdf
Chapter 13 Rogue waves in metamaterial waveguides
13.1 Introduction
13.2 Simulations
13.3 Conclusions to chapter 13 and future trends
Problems to chapter 13
References
CH014.pdf
Chapter 14 Waves in nonlinear layered metamaterials, gyrotropic and plasma media. The main results of the book and the proposed directions for future research
14.1 The main results obtained in the previous chapters
List of abbreviations
References