Fano Resonances in Optics and Microwaves: Physics and Applications

Fano Resonances in Optics and Microwaves: Physics and Applications

Hardcover(1st ed. 2018)

$179.99
Choose Expedited Shipping at checkout for guaranteed delivery by Thursday, January 24

Product Details

ISBN-13: 9783319997308
Publisher: Springer International Publishing
Publication date: 11/20/2018
Series: Springer Series in Optical Sciences , #219
Edition description: 1st ed. 2018
Pages: 582
Product dimensions: 6.10(w) x 9.25(h) x (d)

About the Author

Dr. EUGENE O. KAMENETSKII received his diploma of Engineer in Electrical Engineering and the PhD degree in Physics and Mathematics from the Electrical Engineering Institute, St. Petersburg, Russia, in 1969 and 1986, respectively. He is presently with Ben Gurion University of Negev, Israel as a Head of Microwave Magnetic Laboratory. He is an author (co-author) of 150 refereed journal and conference papers. He was an Editor of the Review Book: "Electromagnetic, magnetostatic, and exchange-interaction vortices in confined magnetic structures", Research Signpost Publisher, Kerala, 2008. He is a Fellow of the Electromagnetics Academy (USA) since 2007. His special fields of scientific interests are magnetic waves and oscillations, spectral theory of artificial atomic structures, metamaterials for microwave and optics applications, microwave microscopy, and microwave biosensing.

Prof. ALMAS SADREEV, graduated Kazan State University in 1971 in Theoretical Physics, received the First Doctor degree in 1974 in Kazan State University. Since 1994 he is the head of Lab. of Theory of Nonlinear Processes, Kirensky Institute of Physics, Federal Research Center KSC SB RAS. Got Honorous Causa Doctor 2002 Linkoping University, Sweden.

A/Prof ANDREY MIROSHNICHENKO obtained his PhD in 2003 from the Max-Planck Institute for Physics of Complex Systems in Dresden, Germany. In 2004 he moved to Australia to join the Nonlinear Physics Centre at ANU. During this time A/Prof Miroshnichenko made fundamentally important contributions to the field of photonic crystals and bringing the concept of the Fano resonances to photonics. In 2007 A/Prof Miroshnichenko was awarded by Australian Postdoctoral Fellowship from the Australian Research Council. It allowed him to initiate the research on a new class of tunable photonic structures infiltrated with liquid crystals. Later, in 2011 he was awarded by Future Fellowship from the Australian Research Council. During this period he pioneered the research of high-index dielectric nanoparticles in the visible range, including one of the first demonstrations of the optically induced magnetic response in silicon nanoparticles. In 2017 he has moved to the University of New South Wales Canberra and got very prestigious Scientia Fellowship. The current topics of his research are nonlinear nanophotonics, topologiccal photonics, and resonant interaction of light with nanoclusters, including optical nanoantennas and metamaterials.

Table of Contents

1. LINEAR AND NONLINEAR DYNAMICS OF FANO RESONANCES IN PLASMONIC STRUCTURES COUPLED TO QUANTUM EMITTERS

Mehmet Emre Tasgin

Institute of Nuclear Sciences, Hacettepe University, 06800 Ankara, Turkey

metasgin@hacettepe.edu.tr

Fano resonances manifest novel phenomena both in linear and nonlinear response of plasmonicnano-materials. They can extend the lifetime of plasmonic excitations, enabling the operation nanolasers, or they can increase the fluorescence of quantum emitters. They also provide control over nonlinear optical processes such as second harmonic generation and four-wave mixing. Fano resonances can both enhance or suppress nonlinear response. Interference of two or more absorption/conversion paths is responsible for the appearance of these effects. In this Chapter, we demonstrate explicitly -on a single equation- how path interference takes part in linear and nonlinear Fano resonances.

Keywords: L

ifetime, second harmonic generation, four-wave mixing

2. FANO-RESONANT EXCITATIONS OF GENERALIZED OPTICAL SPIN WAVES

Xianji Piao*, Sunkyu Yu, Minpyo Lee, and Namkyoo Park

Photonic Systems Laboratory, Department of ECE, Seoul National University, Seoul 08826, Korea

* xjpiao227@gmail.com

While chiral or gyrotropic materials possess spinor ‘wavefunctions’ as their eigenvectors, optical spin ‘observables’ cannot be obtained in those materials due to the lack of spinor impedances. Additional non-conservative functions are thus required for deriving spin observables, such as circular dichroism or magneto-optical effects. In this chapter, a conservative approach for achieving optical spin will be described, by exploiting Fano spectral-separation of optical spins. Starting from spinor temporal coupled mode theory for 2D/3D chiral resonances, the origin of spin-Fano interactions is demonstrated: the link

between spinor eigenvectors in the polarization domain and anti-symmetric Fano resonances in the spectral domain. Compared with chiral, gyrotropic, and birefringent materials, novel applications of this spin-Fano resonance are discussed toward optical spintronics: including highly-selective spin switching and unpolarized operations.

Keywords: optical spin, anti-symmetric Fano resonance, optical spintronics

3. MUELLER MATRIX APPROACH FOR ENGINEERING ASYMMETRIC FANO-RESONANCE LINE SHAPE IN AN ANISOTROPIC OPTICAL SYSTEM

S.K. Ray, S. Chandel, A.K. Singh, P. Mitra, and N. Ghosh*

Indian Institute of Science Education and Research (IISER) Kolkata, India - 741246

*nghosh@iiserkol.ac.in

The asymmetric Fano resonance originating from the interference of a narrow resonance with a broad spectral line or continuum of states is a universal phenomenon, observed in diverse quantum and classical sy

stems. The Fano resonances observed in micro and nano optical systems have received particular attention due to their numerous potential applications like in sensing, switching, lasing, filters and robust color display, nonlinear and slow-light devices, invisibility cloaking, and so forth. Most of the aforementioned applications are known to critically depend upon the ability to control or modulate the asymmetry of the spectral line shape by external means. Thus, tuning the Fano resonance via some experimentally accessible parameters are highly desirable for realistic applications. In this chapter, we discuss a new concept based on polarization Mueller matrix analysis for tuning the Fano interference effect and the resulting asymmetric spectral line shape in anisotropic optical system. The approach is founded on a generalized model of anisotropic Fano resonance and exploits the different polarization response (anisotropy) of the two interfering modes to achieve unprecedented control over Fano resonance. Illustrative results on the use of the model for tuning Fano resonance in waveguidedplasmonic crystals are presented. In this context, the fundamentals of polarized light and the mathematical framework of Stokes-Mueller formalism are discussed. The specifics of a novel dark field Mueller matrix spectroscopy system and its use for studying the Fano resonance in plasmonic systems is illustrated with selected examples. The chapter concludes with an outlook on the prospects of the polarization-optimized anisotropic Fano resonant systems for applications involving control and manipulation of electromagnetic waves at the nano scale.

Keywords:Fano resonance, polarization, anisotropy, Mueller matrix, plasmonic crystal

4. FANO RESONANCE AND BOUND STATES IN THE CONTINUUM IN EVANESCENTLY-COUPLED OPTICAL STRUCTURES

Stefano Longhi

Departimeto di Fisica, Politecnico di Milano, Italy

stefano.longhi@polimi.it

In this chapter I will review some recent theoretical and experimental advances in the field of Fano resonances and bound states in the continuum for light transport in evanescently-coupled optical structures, including arrays of dielectric optical waveguides and coupled resonator optical waveguides. The review will be focused on the occurrence of Fano resonances and bound states in static photonic structures, the role of particle (photon) statistics, dynamical control of Fano resonances, and Fano resonances in non-Hermitian optical structures.

Keywords: Fano resonance in photonics, bound states in the continuum, optical waveguides

5. MODELS OF COUPLED OSCILLATOR FOR FANO RESONANCES

Benjamin Gallinet

CSEM SA, Thin Film Optics, Muttenz, 4132, Switzerland

Benjamin.GALLINET@csem.ch

Fano resonances can be modeled with systems of weakly or strongly coupled

mechanical oscillators, providing insight into the dynamics of subradiant and superradiant modes. In particular, a resonance formula for Fano-like resonances in lossy systems can be derived. The application of these oscillator models to experimental measurements is reviewed, with applications in refractive index sensing, nanoscale rulers or non-linear optics.

Keywords:mechanical oscillator model, weak coupling, strong coupling

6. DYNAMICAL CONTROL OF EIT-LIKE EFFECT IN METAMATERIALS FOR STORAGE AND RETRIEVAL OF ELECTROMAGNETIC WAVES

T. Nakanishi*, S. Tohi, and M. Kitano

Department of Electronic Science and Engineering, Kyoto University, Kyoto, 615-8510 Japan

* t-naka@kuee.kyoto-u.ac.jp

We introduce dynamically tunable metamaterials in analogy with electromagnetically induced transparency (EIT) effect in atomic physics.The metamaterials can not only modulate the tra

nsmission and group velocity of electromagnetic waves but also store electromagnetic waves coherently.

Keywords:electromagnetically induced transparency effect, tunable metamaterial, slow and storage of light.

7. TEMPORAL COUPLED-MODE THEORY FOR LIGHT SCATTERING AND ABSORPTION BY NANOSTRUCTURES

Zhichao Ruan

Department of Physics, Zhejiang University, and State Key Laboratory of Modern Optical Instrumentation Hangzhou 310027, China

zhichao@zju.edu.cn

Nanostructures usually can be viewed as optical cavities supporting resonances. The presence of resonances consequently influences the scattering and absorption properties profoundly. Temporal coupled-mode theory (TCMT) was initially developed and applied for analyzing waveguide-resonator interactions in integrated optics. In this chapter, we develop the TCMT formalism to describe the coupling process and the interference effect involved with opti

cal resonances in single nanoparticles. We first derive the temporal coupled-mode theory based on the consideration of energy conservation and time-reversal symmetry and validate the theory with numerical simulations. Based on the theory, we then show that the Fano interference effect can be modeled by a simple temporal coupled-mode equation, which provides a line shape formula for scattering and absorption cross section. Next we discuss the super-scattering effect of a single subwavelength particle, where an arbitrarily large total scattering cross section can be achieved provided that one maximizes contributions from a sufficiently large number of resonances. Last we investigate the upper limit of absorption cross section of a single particle over all incident angles, which plays a key role in the efficiency enhancement of solar cells and photodetectors.

Keywords: coupled-mode theory, Fano resonance, super-scattering

8. A FULL-R

ETARDED SPECTRAL TECHNIQUE FOR THE FANO-RESONANCE ANALYSIS IN SPHERICAL NANOPARTICLES

C. Forestiere*, M. Pascale, R. Tricarico, and G. Miano

Department of Electrical Engineering and Information Technology, Universita degli Studi di Napoli Federico II, via Claudio 21, Napoli, 80125, Italy

* carlo.forestiere@unina.it

Spherical nanoparticles have represented a fertile framework for the investigation of Fano-resonances in the electromagnetic scattering. Here, we introduce a full-retarded representation of the electromagnetic field scattered by a homogeneous sphere, in terms of a set of modes independent of its permittivity. We use this theory to unveil the origin of asymmetric scattering line-shapes in spherical nanoparticles, by identifying the interfering modes responsible for the corresponding peaks and the dips. Eventually, we discuss the role played by the material properties in enabling or preventing the interference effects behind Fano-resonances.

Keywords:Fano-resonance, Mie scattering, material independent modes

9. DARK-MODE CHARACTERISTICS OF METASURFACES ENGINEERED BY SYMMETRY MATCHING OF RESONANT ELEMENTS AND ELECTROMAGNETIC FIELDS

A. Lupu1*, E. Bochkova1, S. N. Burokur2, and A. de Lustrac1,3

1Centre de Nanosciences et de Nanotechnologies, CNRS, Univ. Paris-Sud, Université Paris-Saclay, C2N – Orsay, 91405 Orsaycedex, France

2LEME, EA 4416, Université Paris Nanterre, 92410 Ville d’Avray, France

3Université Paris Nanterre, 92410 Ville d’Avray, France

* anatole.lupu@c2n.upsaclay.fr

We revisit the engineering of metasurfaces displaying sharp spectral features and conventionally relying on electromagnetically induced transparency resulting from Fano-type interference between dark and bright resonant elements. The aim of the developed approach based on sym

metry considerations is to show that electromagnetically induced transparency and dark mode excitation are not necessarily associated. We bring theoretical and experimental evidence in the microwave domain that electromagnetically induced transparency and dark mode excitation can be achieved in an independent manner by using distinctly different mechanisms. The use of these distinctly different mechanisms provides higher flexibility for metasurfaces engineering and results in a great improvement of their spectral performances.

Keywords: dark modes, metasurfaces, electromagnetically induced transparency

10. LIGHT-TUNABLE FANO RESONANCES IN METAL-DIELECTRIC MULTILAYER STRUCTURES.

Shinji Hayashi

Department of Electrical and Electronic Engineering, Graduate School of Engineering,

Kobe University, Japan

s.hayashi@dragon.kobe-u.ac.jp , shin3haya4@gmail.com

Multilayer structures composed of a metallic l

ayer and three dielectric layers (MIII structures) exhibit sharp Fano resonances in their attenuated total reflection spectra, when the thicknesses and dielectric constants of the layers are appropriately chosen. The Fano resonances originate from the interaction between surface plasmonpolaritons at the MI interface and waveguide modes supported by III structures. When photofunctional molecules are incorporated into one of the dielectric layers, it is possible to modulate the Fano resonances by light irradiation. Phototuning of the Fano resonance based on the photoisomerization of azo-dye molecules doped into the waveguide layer is discussed in depth.

Keywords:SPP mode, waveguide mode, dye molecules

11. STUDY OF FANO RESONANCE IN THE CORE-LEVEL ABSORPTION SPECTRUM OF AN IMPURITY IN ONE-DIMENSIONAL SUPERLATTICE IN TERMS OF COMPLEX SPECTRAL ANALYSIS

Satoshi Tanaka1*, Taku Fukuta1, and Tomio Petrosky2;3

1Department of Physical Science, Osaka Prefecture University, Japan

2Center for Complex Quantum Systems, University of Texas at Austin, USA

3Institute of Industrial Science, University of Tokyo, Japan

* stanaka@p.s.osakafu-u.ac.jp

Core absorption spectrum of an impurity embedded in a one-dimensional tight-binding chain is theoretically investigated in terms of complex spectral analysis.

The spectrum shows a distinct Fano-profile only with a single intra-atomic transition.

The asymmetric Fano absorption profile is attributed to the complex oscillator strength of the transitions to the discrete resonance states belonging to the extended Hilbert space.

Nonlinear nature of the effective non-Hermitian Hamiltonian enhances the asymmetric Fano profile of the absorption spectrum.

Keywords:Fano resonance, Complex spectral analysis, Non-Hermitian Hamiltonian

12.&nbs

p; FANO-RESONANCES FOR DIRECTIONAL SCATTERING IN DIELECTRIC NANOWIRES

P. R. Wiecha1*,A. Cuche1, A. Arbouet1, C. Girard1, G. Colas des Francs2, A.Lecestre3, G. Larrieu3, F. Fournel4, V. Larrey4, T. Baron5, and V. Paillard1**

1CEMES-CNRS, Universite de Toulouse, CNRS, UPS, Toulouse, France

2ICB, UMR 6303 CNRS - Universite de Bourgogne-Franche Comte, Dijon, France

3LAAS-CNRS, Universite de Toulouse, CNRS, INP, Toulouse, France

4CEA-LETI/MINATEC, CEA, Grenoble, France

5CNRS, LTM, Universite de Grenoble-Alpes, Grenoble, France

*peter.wiecha@cemes.fr;**vincent.paillard@cemes.fr

High refractive-index dielectric nanostructures provide original optical properties thanks to the occurrence of size- andshape-dependent optical resonances. Recently, such nano

structures attracted increasing interest as possible low-loss alternativesto plasmonic particles. A peculiarity of dielectric nanostructures is the spectrally overlapping occurrence of broad, loworder modes and much narrower, higher order modes. The latter areare usually characterized by a rapidly varying frequencydependent phase, which – in superposition with the lower order mode of approximately constant phase – leads to typicalspectral features known as Fano-resonances.Surprisingly, such Fano-resonances occur in dielectric nanostructures of the simplest geometries. In nanospheres, interferencebetween broad magnetic dipole and narrower electric dipole modes can be observed. In high aspect-ratio structures likedielectric nanowires, either the electric or the magnetic dipolar mode (depending on the illumination conditions) interfereswith higher order multipole contributions.Using Mie theory we analyze the apparition of Fano-resonances in dielectric nanowires and discuss their consequences likeuni-directional scattering. By means of numerical simulations we furthermore investigate the impact of other than cylindricalnanowire cross-sections, of a substrate and of coupled nanowires on those Fano-resonances.

Keywords:Mie theory, high-index dielectric nanowires, directional scattering

13. FANO RESONANCES IN FLAT BAND NETWORKS

Ajith Ramachandran*, Carlo Danieli, and Sergej Flach

Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, South Korea

* ajithstcp@pcs.ibs.re.kr

Linear wave equations on lattices with translational invariance are characterized by an eigenvalue band structure in reciprocal space. Flat band lattices have at least one of the bands completely dispersionless. Such bands are coined flat bands. Flat bands occur in fine-tuned networks, and in networks protected by chiral symmetries. Recently a number of such systems were realized in structure

d optical systems, exciton-polariton condensates, and ultracold atomic gases. Short range hopping leads to the existence of compact localized modes. We will show how local defects couple these compact modes todispersive states and generate Fano resonances in the transmission. A finite density of Fano defects, which is equivalent to introducing a disorderpotential, leads to novel scaling laws in the localization length of disordered dispersive states.Nonlinearities allow to keep the compact state of flat band modes, while renormalizing their frequencies. These strictly compact nonlinearexcitations induce Fano resonances in the wave propagation through the system.

Keywords:flat bands, compact localized states, defects, disorder, nonlinearity

14. MULTIPLE-RESONANCE INTERFERENCE IN METALLIC NANOHOLE ARRAYS

M. Nishida* and Y. Kadoya

Graduate School of Advanced Science of Matter, Hiroshima University, Higashi-Hiroshima, 7

39-8530, Japan

* mnishida@hiroshima-u.ac.jp

In metallic nanohole arrays, the surface plasmonpolaritons on the metal surfaces and the waveguide modes in the nanoholes are combined to form multipole surface plasmons. If these surface bound modes appear in a narrow frequency range, interference between multiple resonances causes so-called Fano-Feshbach resonances and yields various resonant peak-dip structures in transmission, reflection and absorption spectra. In this chapter, we discuss the theoretical details of the mechanism of the multiple-resonance interferences in metallic nanohole array systems.

Keywords: metallic nanohole array, multipole surface plasmon, Fano-Feshbach resonance

15. RESONANT-STATE EXPANSION OF THE FANO PEAK IN OPEN QUANTUM SYSTEMS

Naomichi Hatano1* and Gonzalo Ordonez2**

1Institute of Industrial Science, University of Tokyo, 5-1-5 Kashiwanoh

a, Kashiwa, Chiba 277-8574, Japan

2Department of Physics and Astronomy, Butler University, 4600 Sunset Avenue, Indianapolis, Indiana 46208, U.S.A.

*hatano@iis.u-tokyo.ac.jp;**gordonez@butler.edu

We first introduce a novel complete set that spans the Hilbert space of the central part of an open quantum-dot system. This complete set contains all states of point spectra including not only bound states but also resonant states with complex eigenvalues, while it does not contain any states of continuous spectra.We thereby analytically expand the conductance of the dot in terms of all discrete states without any background integrals. We then explain the Fano peak as an interference effect involving resonant states. We find that there are three types ofFano asymmetry according to their origins: the interference between a resonant state and an anti-resonant state, that between a resonant state and a bound state, and that between two resonant states. We derive micro

scopic expressions of the Fano parameters that describe the three types of Fano asymmetry. We show that the last two types display the asymmetric energy dependence given by Fano, but the first one shows a slightly different form. We also reveal that the Fano parameter of the first type can become complex under an external magnetic field.

Keywords:Resonant state, open quantum system,Fano asymmetric parameter

16. MULTIPLE STATE FANO RESONANCES UNDER NON-EQUILIBRIUM CONDITIONS

J. Fransson1* and J. P. Bird2,

1Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden

2Department of Electrical Engineering, University at Buffalo, The State University of New York, Buffalo, USA

* Jonas.Fransson@physics.uu.se

While Fano resonances are typically associated with a two pathway scheme between reservoirs, in which one path provides a direct coupling between the

reservoirs whereas the second goes through an intermediate, often discrete, state. The phase mismatch between the wavefunctions traversing the two pathways is the origin of the Fano resonance. Here, we discuss set-ups in which additional intermediate states give rise to strong modifications of the regular Fano resonance profile. In particular, we show experimental results in conjunction with theoretical modeling what implications intruder intermediate states may have on the Fano interference.

Keywords: intruder states, non-equilibrium

17. FANO RESONANCES IN SLANTED HYPERBOLIC METAMATERIAL CAVITIES

F. Vaianella and B. Maes*

Micro- and Nanophotonic Materials Group, Faculty of Science, University of Mons, 20, place du Parc, B-7000 Mons, Belgium
* bjorn.maes@umons.ac.be

We present a general mechanism to excite Fano resonances inside slanted multilayered hyperbolic cavities. Fano resonances arise from the interference between a propagating and an evanescent mode inside the cavities, which can be as small as 5 nm because of the extremely high value of the effective indices inside these metamaterials.

Keywords: hyperbolic metamaterials, Fano resonances, plasmonics

18. ANTONIO BIANCONI

Antonio Bianconi

Rome International Center for Materials Science SuperstripesRICMASS, Italy

antonio.bianconi@ricmass.eu

19. BORIS LUKIYNCHUK

Boris Lukiyanchuk

Data StorageInstitute, Agency for Science,Technology and Research, Singapore

Boris_L@dsi.a-star.edu.sg

20. ALEXANDER KHANIKAEV

Alexander Khanikaev

Department of Electrical Engineering and Department of Physics, The City University of New York, New York

khanikaev@gmail.com

21. FANO RESONANCES IN LIGHT SCATTERING BY FINITE OBSTACLES

A. E. M

iroshnichenko

Nonlinear Physics Centre, The Australian National University, Australia

andrey.miroshnichenko@anu.edu.au

Light scattering by finite obstacles, either single particle or a number of particles in arbitrary configuration, exhibits various resonant effects. It turns out that almost any resonant response, either in directional or total scattering light scattering, can be efficiently described in terms of Fano resonance. One of the peculiar feature of the Fano resonance is complete destructive interference, which can be associated with radiationless excitations, such as nontrivial anapole modes.

Keywords: Fano resonance, Mie solution, nonradiating sources, all-dielectric nanostructure, anapole, optically induced magnetic response

22. TUNING OF FANO RESONANCES BY ROTATION OF CONTINUUM: WAVE FAUCET

A.F. Sadreev*, A.S. Pilipchuk, and A.A. Lyapina

Kirensky Institute of Physics, Federal R

esearch Center KSC SB RAS, 660036 Krasnoyarsk, Russia

* almas@tnp.krasn.ru

Fano resonances can be tuned by varying of either the eigenvalues of closed system or the coupling strengths of the eigenmodes with the continuum. We propose a new concept for tuning of Fano resonances via implementation the complex phase factors in the coupling matrix elements. Here we realize this concept in a non-axisymmetric waveguide which contains of cylindrical resonator and two semi-infinite cylindrical waveguides whose axes are shifted relative to each other by azimuthal angle On the example of acoustic transmission we show that change of crucially effects Fano resonances and creates an analog of a wave faucet opening and closing wave flux. Moreover there are discrete values of when bound state in the continuum occurs accompanying by the Fano resonance collapse.

Keywords: rotation of continuum, wave faucet, bound states in the continuum.

23. HELICAL BOUND STATES IN A MICROWAVE-FIELD CONTINUUM WITH AN EMBEDDED MDM FERRITE PARTICLE

E. O. Kamenetskii

Microwave Magnetic Laboratory, Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva, Israel

kmntsk@bgu.ac.il

Magnetic-dipolar modes (MDMs) in a quasi-2D ferrite disk are microwave energy-eigenstate oscillations with topologically distinct structures of rotating fields and unidirectional power-flow circulations. Quantized vortices in MDM oscillations manifest the long-range phase coherence of magnetic dipole-dipole interaction which are described by a complex-valued order parameter field – the magnetostatic-potential (MS-potential) scalar wave function. Because of strong spin–orbit interaction in magnetization dynamics, the MDMs in a quasi-2D ferrite disk are helical bound states in a microwave continuum. We consider the microwave transport properties of such a system including the a

ppearance of Fano resonances.

Keywords: magnetic dipolar oscillations, edge states, topological phases, magnetoelectric fields

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews