DOCSLIB.ORG

Imperfect Perfect Lens Vol

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Imperfect Perfect Lens Vol NANO LETTERS 2005 Imperfect Perfect Lens Vol. 5, No. 2 - Ivan A. Larkin and Mark I. Stockman* 339 343 Department of Physics and Astronomy, Georgia State UniVersity, Atlanta, Georgia 30303 Received December 9, 2004; Revised Manuscript Received January 12, 2005 ABSTRACT We have quantitatively established a fundamental limitation on the ultimate spatial resolution of the perfect lens (thin metal slab) in the near field. This limitation stems from the spatial dispersion of the dielectric response of the Fermi liquid of electrons with Coulomb interaction in the metal. We discuss possible applications in nanoimaging, nanophotolithography, and nanospectroscopy. The Veselago lens,1 that is a slab of a left-handed material We consider only near-field imaging and therefore use the with relative dielectric permittivity )-1 and magnetic quasistatic approximation, which does not include magnetic permeability µ )-1, builds a perfect image of a three- field. Therefore, the left-handedness of the material is dimensional object in the far-field zone. Such a lens was irrelevant. Consider a metal ( < 0) slab of thickness b experimentally confirmed in the microwave spectral region.2 parallel to the xy plane of the coordinate system, whose As shown by Pendry, the same slab builds also a perfect boundaries are at z ) 0 and z ) b. Let there be a unit charge three-dimensional image in the near field, deserving the name at a point (0, 0, - a). Then the electric potential to the right of perfect lens,3 as observed later in ref 4. In the near zone, of the slab (z > b) is given by8 the requirement for the permeability is lifted, and only the )- condition of 1 is important. -kr(z+a-2b) ∞ J (k r)e Actually, such a lens is only near-perfect,3 because its æ(r, z) ) 4∫ 0 r dk (1) 0 2 2k b 2 r spatial resolution is limited by the losses in the lens’s (1 + ) e r - (1 - ) material; in the visible range the best material is silver, having the lowest losses. One of the points of this letter is to suggest where is the metal permittivity relative to the host medium, that such losses can be minimized by using a high-index x 2 2 J0 is a Bessel function, r ) x +y is the radial coordinate, embedding dielectric that would shift the operational fre- and kr is a two-dimensional (2D) wave vector in the plane quency toward the red where the quality factor of silver is of the slab. For )-1 (i.e., for the frequency of the surface 5 much higher. Light amplification can also be used to plasmon resonance of the metal), behind the image plane of 6 compensate these losses. z g 2b - a, this potential is an ideal three-dimensional (3D) In this letter, we investigate a principal limitation on the image of the original single point charge resolution of the perfect lens stemming from the spatial dispersion (nonlocality) of the dielectric response of the ∞ - + - æ(r, z) ) ∫ J (k r)e kr(z a 2b) dk Fermi liquid of interacting electrons in the nanolens material. 0 0 r r Such dispersion leads to the aberrations of this lens in the 1 wave vector in the plane of the slab. This principally limits ) (2) the resolution of this lens, making it imperfect on the scale xr2 + (z - 2b + a)2 below ∼5 nanometers. This effect is independent from the known sources of the lens imperfection due to optical losses If is not exactly equal to -1, e.g., due to Im * 0, then in the metal and temporal dispersion that is related to these the image of eq 1 is not ideal, limited by the spatial resolution losses by Kramers-Kronig relations. Even if the absorption of δ ∼ b/(- ln| + 1|) g b/ln Q, where Q )-Re/Im is is reduced or compensated by the optical gain as in ref 6, the quality factor of the plasmon resonance of the metal. the spatial dispersion will remain and limit the resolution. The highest value of Q ∼ 100 for any natural material from The principal role of spatial dispersion of the surface polar- the near-infrared to ultraviolet region is for silver for light itons at high wavenumbers was pointed out two years ago frequency pω ≈ 1.2 eV. The surface plasmon resonance in preprint7 where it was considered for left-handed ( < 0 would have shifted to this frequency if the values of host and µ < 0) systems. Only a generic electromagnetic spectrum dielectric constant h ∼ 100 were available. However, it is was considered, and no quantitative limitations on the spatial not the case, and the realistic values of h ≈ 12 are typical 9 resolution were obtained, in contrast to the present letter. for wide-band semiconductors (e.g., Al0.2Ga0.8As) for pω 10.1021/nl047957a CCC: $30.25 © 2005 American Chemical Society Published on Web 01/22/2005 L R ) 2.2 eV. This choice provides the best possible suppression where E (kr) and E (kr) are the 2D Fourier transforms of L R of the absorption adverse effects. E⊥(x, y,0)andE⊥(x, y, b). Deriving eq 4, we have taken Now we consider a principally different source of the lens into account the cylindrical symmetry of the problem. This imperfection, namely spatial dispersion,ornonlocality of potential should be found consistently with the potentials the dielectric response function (ω,k) that depends not only outside of the metal slab, where they obey the Laplace on frequency ω but also on wave vector k. In metals, the equation whose solutions to the left (L) and right (R) of the characteristic wave-vector scale of (ω, k)isk ∼ w/VF, where slab are VF is the electron velocity at the Fermi surface. For k g |ω|/ V , there exists the Landau damping that additionally L )RL + L - F æ (kr, z) (kr) exp(krz) â (kr) exp( krz) contributes to the optical losses described by Im(ω, k).10 R )RR - + L - - For such a spatially dispersive dielectric function, we æ (kr, z) (kr) exp[kr(z b)] â (kr) exp[ kr(z b)] should carefully reformulate the boundary conditions for (6) ballistic electrons at the surface of the metal. We will consider density of electrons in the metal as constant From eq 5, performing the inverse Fourier transform over neglecting the narrow (width on order of the Debye screening kz, we express the continuity equation for the left face of radius rD ∼ 0.1 nm) Schottky layer in the metal at the the metal slab as interface. We assume that the semiconductor of the embed- ding medium is undoped and neglect Schottky-layer electric RL + L ) 1 L -V R (kr) â (kr) [uE (kr) E (kr)] (7) fields inside the semiconductor, because they are too weak kr to change its dielectric function. We also neglect the Friedel 10 ∼ ∼ oscillations because their period is too short, 1/kF 0.1 where nm, where kF is the electron wave vector at the Fermi surface. To take into account the effect of boundaries, we assume ∞ kr ∞ exp(2ikznb) specular reflection of electrons from the surface. As was ) u ∑ ∫-∞ dkz 2 shown in ref 11, the ideal specular reflection implies that a πn)-∞ k (ω, k) nonlocal electrostatic problem for a half-infinite metal is ∞ - kr exp[ikz(2n 1)b] equivalent to a problem in bulk metal V) ∞ ∑ ∫-∞ dkz (8) 2 πn)-∞ k (ω, k) ∇ ∇ ) (ˆ æi) 2E⊥(x, y,0)δ(z) (3) Similarly for z ) b (the right face of the slab), we get where E⊥(x, y, 0) is the normal electric field at this surface, R R 1 L R æi is the field potential in the metal, and ˆ is the nonlocal R + ) V - (kr) â (kr) [ E (kr) uE (kr)] (9) dielectric response operator. The Dirac delta function emu- kr lates the boundary condition at the metal surface. For the slab, an electron experiences multiple reflections The other two equations come from the displacement from both its surfaces. To correspondingly generalize eq 3, matching, we reflect each boundary periodically in each other. As a result, the potential æ satisfies an equation L ) RL - L i E (kr) Lkr[ (kr) â (kr)] R ) RR - R ∞ E (kr) Rkr[ (kr) â (kr)] (10) L ∇(ˆ∇æ ) ) 2 ∑ {E⊥(x, y,0)δ(z - 2bn) - i n)-∞ where L and R are the host dielectric permittivities to the 1 R - + left and right of the lens (metal slab). E⊥(x, y, b) δ[z 2b(n )]} (4) 2 Solving eqs 7, 9, and 10 for RR and âR,weget where EL(x, y,0)andER(x, y, b) are the electric fields at the RR RL ⊥ ⊥ ( ) ) Tˆ·( ) (11) left and right faces of the slab. âR âL The solution of eq 4 yields a periodic potential of period 2b in the z direction with discontinuities of the normal electric where Tˆ isa2× 2 transfer matrix with matrix elements L R field 2E⊥(x, y,0)atz ) 2nb and 2E⊥(x, y, b)atz ) (2n + ) V2 - 2 + + - V 1)b.Inthek space T11 [( u )RL u(R L) 1]/(2 R) T ) [(u2 -V2) + u( - ) - 1]/(2V ) 2 ∞ 12 R L R L R ) { L - æ(k) ∑ E (kr) exp(2ikznb) 2 2 2 T ) [(V - u ) + u( - ) + 1]/(2V ) k (ω, k) n)-∞ 21 R L R L R R + } ) 2 -V2 + + + V E (kr) exp[i(2n 1)kzb] (5) T22 [(u )RL u(R L) 1]/(2 R) (12) 340 Nano Lett., Vol.
Load more

Recommended publications
  • Chapter 3 Constitutive Relations
    Chapter 3 Constitutive Relations Maxwell’s equations define the fields that are generated by currents and charges. However, they do not describe how these currents and charges are generated. Thus, to find a self-consistent solution for the electromagnetic field, Maxwell’s equations must be supplemented by relations that describe the behavior of matter under the influence of fields. These material equations are known as constitutive relations. The constitutive relations express the secondary sources P and M in terms of the fields E and H, that is P = f[E] and M = f[H].1 According to Eq. (1.19) this is equivalent to D = f[E] and B = f[H]. If we expand these relations into power series ∂D 1 ∂2D D = D + E + E2 + .. (3.1) 0 ∂E 2 ∂E2 E=0 E=0 we find that the lowest-order term depends linearly on E. In most practical situ- ations the interaction of radiation with matter is weak and it suffices to truncate the power series after the linear term. The nonlinear terms come into play when the fields acting on matter become comparable to the atomic Coulomb potential. This is the territory of strong field physics. Here we will entirely focus on the linear properties of matter. 1In some exotic cases we can have P = f[E, H] and M = f[H, E], which are so-called bi- isotropic or bi-anisotropic materials. These are special cases and won’t be discussed here. 33 34 CHAPTER 3. CONSTITUTIVE RELATIONS 3.1 Linear Materials The most general linear relationship between D and E can be written as2 ∞ ∞ D(r, t) = ε ε˜(r r′, t t′) E(r′, t′) d3r′ dt′ , (3.2) 0 − − −∞Z−∞Z which states that the response D at the location r and at time t not only depends on the excitation E at r and t, but also on the excitation E in all other locations r′ and all other times t′.
    [Show full text]
  • Modeling Optical Metamaterials with Strong Spatial Dispersion
    Fakultät für Physik Institut für theoretische Festkörperphysik Modeling Optical Metamaterials with Strong Spatial Dispersion M. Sc. Karim Mnasri von der KIT-Fakultät für Physik des Karlsruher Instituts für Technologie (KIT) genehmigte Dissertation zur Erlangung des akademischen Grades eines DOKTORS DER NATURWISSENSCHAFTEN (Dr. rer. nat.) Tag der mündlichen Prüfung: 29. November 2019 Referent: Prof. Dr. Carsten Rockstuhl (Institut für theoretische Festkörperphysik) Korreferent: Prof. Dr. Michael Plum (Institut für Analysis) KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft Erklärung zur Selbstständigkeit Ich versichere, dass ich diese Arbeit selbstständig verfasst habe und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe, die wörtlich oder inhaltlich über- nommenen Stellen als solche kenntlich gemacht und die Satzung des KIT zur Sicherung guter wissenschaftlicher Praxis in der gültigen Fassung vom 24. Mai 2018 beachtet habe. Karlsruhe, den 21. Oktober 2019, Karim Mnasri Als Prüfungsexemplar genehmigt von Karlsruhe, den 28. Oktober 2019, Prof. Dr. Carsten Rockstuhl iv To Ouiem and Adam Thesis abstract Optical metamaterials are artificial media made from subwavelength inclusions with un- conventional properties at optical frequencies. While a response to the magnetic field of light in natural material is absent, metamaterials prompt to lift this limitation and to exhibit a response to both electric and magnetic fields at optical frequencies. Due tothe interplay of both the actual shape of the inclusions and the material from which they are made, but also from the specific details of their arrangement, the response canbe driven to one or multiple resonances within a desired frequency band. With such a high number of degrees of freedom, tedious trial-and-error simulations and costly experimen- tal essays are inefficient when considering optical metamaterials in the design of specific applications.
    [Show full text]
  • Transparent Metamaterials with a Negative Refractive Index Determined by Spatial Dispersion
    Transparent metamaterials with a negative refractive index determined by spatial dispersion V.V. Slabko Siberian Federal University, Krasnoyarsk 660041, Russia Institute of Physics of the Russian Academy of Sciences, Krasnoyarsk 660036, Russia Abstract: The paper considers an opportunity for the creation of an artificial two-component metamaterial with a negative refractive index within the radio and optical frequency band, which possesses a spatial dispersion. It is shown that there exists a spectral region where, under certain ratio of volume fraction unit occupied with components, the metamaterial appears transparent without attenuating the electromagnetic wave passing through it and possessing a phase and group velocity of the opposite sign. 1. Introduction J.B. Pendry in co-authorship papers suggested the idea of possible creation of artificial metamaterials with a negative refractive index in the gigahertz frequency band [1,2]. The idea proceeded from the work by V.G. Veselago where the processes of electromagnetic wave propagation in isotropic materials with simultaneously negative permittivity ( ( ) 0) and magnetic permeability ( ( ) 0) was theoretically considered [3]. The latter leads to negative refraction index ( n 0 ), and phase propagation (wave vector k ) and energy-flow (Poynting vector S ) appear counter-directed, with the left-handed triplet of the vectors of magnetic field, electrical field, and the wave vector. Those were called optical negative-index materials (NIM). Interest to such metamaterials is aroused both by possible observation of extremely unusual properties, e.g. a negative refraction at the materials boundary with positive and negative refractive index, Doppler’s and Vavilov-Cherenkov’s effect, nonlinear wave interactions; and by possibilities in the solution of a number of practical tasks, which can overcome the resolution threshold diffracting limit in optical devices and creation of perfect shielding or “cloaking” [4-7].
    [Show full text]
  • Spatial Dispersion Consideration in Dipoles
    Basics of averaging of the Maxwell equations A. Chipouline, C. Simovski, S. Tretyakov Abstract Volume or statistical averaging of the microscopic Maxwell equations (MEs), i.e. transition from microscopic MEs to their macroscopic counterparts, is one of the main steps in electrodynamics of materials. In spite of the fundamental importance of the averaging procedure, it is quite rarely properly discussed in university courses and respective books; up to now there is no established consensus about how the averaging procedure has to be performed. In this paper we show that there are some basic principles for the averaging procedure (irrespective to what type of material is studied) which have to be satisfied. Any homogenization model has to be consistent with the basic principles. In case of absence of this correlation of a particular model with the basic principles the model could not be accepted as a credible one. Another goal of this paper is to establish the averaging procedure for metamaterials, which is rather close to the case of compound materials but should include magnetic response of the inclusions and their clusters. We start from the consideration of bulk materials, which means in the vast majority of cases that we consider propagation of an electromagnetic wave far from the interfaces, where the eigenwave in the medium has been already formed and stabilized. A basic structure for discussion about boundary conditions and layered metamaterials is a subject of separate publication and will be done elsewhere. 1. Material equations
    [Show full text]
  • Operator Approach to Effective Medium Theory to Overcome a Breakdown of Maxwell Garnett Approximation
    Downloaded from orbit.dtu.dk on: Oct 05, 2021 Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation Popov, Vladislav; Lavrinenko, Andrei; Novitsky, Andrey Published in: Physical Review B Link to article, DOI: 10.1103/PhysRevB.94.085428 Publication date: 2016 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Popov, V., Lavrinenko, A., & Novitsky, A. (2016). Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation. Physical Review B, 94(8), [085428]. https://doi.org/10.1103/PhysRevB.94.085428 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. PHYSICAL REVIEW B 94, 085428 (2016) Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation Vladislav Popov* Department of Theoretical Physics and Astrophysics, Belarusian State University, Nezavisimosti avenue 4, 220030, Minsk, Republic of Belarus Andrei V.
    [Show full text]
  • Vector Circuit Theory for Spatially Dispersive Uniaxial Magneto-Dielectric Slabs 3
    Machine Copy for Proofreading, JEWA (Ikonen et al.) VECTOR CIRCUIT THEORY FOR SPATIALLY DISPERSIVE UNIAXIAL MAGNETO-DIELECTRIC SLABS Pekka Ikonen, Mikhail Lapine, Igor Nefedov, and Sergei Tretyakov Radio Laboratory/SMARAD, Helsinki University of Technology P.O. Box 3000, FI-02015 TKK, Finland. Abstract—We present a general dyadic vector circuit formalism, applicable for uniaxial magneto-dielectric slabs, with strong spatial dispersion explicitly taken into account. This formalism extends the vector circuit theory, previously introduced only for isotropic and chiral slabs. Here we assume that the problem geometry imposes strong spatial dispersion only in the plane, parallel to the slab interfaces. The difference arising from taking into account spatial dispersion along the normal to the interface is briefly discussed. We derive general dyadic impedance and admittance matrices, and calculate corresponding transmission and reflection coefficients for arbitrary plane wave incidence. As a practical example, we consider a metamaterial slab built of conducting wires and split-ring resonators, and show that neglecting spatial dispersion and uniaxial nature in this structure leads to dramatic errors in calculation of transmission characteristics. 1 Introduction 2 Transmission matrix 3 Impedance and admittance matrices 4 Reflection and transmission dyadics 5 Practically realizable slabs 6 Specific examples 7 Conclusions Acknowledgment References 1. INTRODUCTION arXiv:physics/0605243v1 [physics.class-ph] 29 May 2006 It is well known that many problems dealing with reflections from multilayered media can be solved using the transmission line analogy when the eigen-polarizations are studied separately (see e.g. [1]). In this case, the amplitudes of tangential electric and magnetic fields are treated as equivalent scalar voltages and currents in the equivalent transmission line section.
    [Show full text]
  • SCIENTIFIC PUBLICATIONS, SERGEI TRETYAKOV Books Book Chapters
    SCIENTIFIC PUBLICATIONS, SERGEI TRETYAKOV Books 6. C. Simovski and S. Tretyakov, An introduction to metamaterials and nanophotonics, Cambridge, UK: Cambridge University Press, 2020. 5. A. Osipov and S. Tretyakov, Modern electromagnetic scattering theory with applications, Chichester, UK: John Wiley & Sons, 2017. 4. S.A. Tretyakov, Analytical modeling in applied electromagnetics, Norwood, MA: Artech House, 2003. 3. D. Lioubtchenko, S. Tretyakov, S. Dudorov, Millimeter-wave waveguides, Boston / Dordrecht / London: Kluwer Academic Publishers, 2003. 2. A.N. Serdyukov, I.V. Semchenko, S.A. Tretyakov, A. Sihvola, Electromagnetics of bi- anisotropic materials: Theory and applications, Amsterdam: Gordon and Breach Science Publishers, 2001. 1. I.V. Lindell, A.H. Sihvola, S.A. Tretyakov, A.J. Viitanen, Electromagnetic waves in chiral and bi-isotropic media, Norwood, MA: Artech House, 1994. Book chapters 19. S. Abadal, X. Timoneda, J. Sole-Pareta, E. Alarcon, A. Cabellos-Aparicio, A. Tasolamprou, O. Tsilipakos, C. Liaskos, M. Kafesaki, E.N. Economou, C. Soukoulis, A. Pitilakis, N.V. Kantartzis, M.S. Mirmoosa, F. Liu, and S. Tretyakov, Nanoscale channel modeling in highly integrated computing packages, in Nanoscale Networking and Communications Handbook, edited by John R. Vacca, CRC Press, Taylor and Francis Group, 2020, pp. 127-150. 18. V. Asadchy, A. Diaz-Rubio, D.-H. Kwon, and S. Tretyakov, Analytical Modeling of Electromagnetic Surfaces, in Surface Electromagnetics, With Applications in Antenna, Microwave, and Optical Engineering, ed. F. Yang and Y. Rahmat-Samii, Cambridge University Press, 2019, pp. 30-65. 17. S. Tretyakov, V. Asadchy, and A. Díaz-Rubio, Metasurfaces for general control of reflection and transmission, in World Scientific Handbook of Metamaterials and Plasmonics, vol.
    [Show full text]
  • Spatial Decomposition of a Broadband Pulse Caused by Strong Frequency Dispersion of Sound in Acoustic Metamaterial Superlattice
    materials Article Spatial Decomposition of a Broadband Pulse Caused by Strong Frequency Dispersion of Sound in Acoustic Metamaterial Superlattice Yuqi Jin 1,2 , Yurii Zubov 1, Teng Yang 1,3, Tae-Youl Choi 2, Arkadii Krokhin 1,4 and Arup Neogi 1,4,* 1 Department of Physics, University of North Texas, P.O. Box 311427, Denton, TX 76203, USA; [email protected] (Y.J.); [email protected] (Y.Z.); [email protected] (T.Y.); [email protected] (A.K.) 2 Department of Mechanical Engineering, University of North Texas, 3940 North Elm Suite, Denton, TX 76207, USA; [email protected] 3 Department of Materials Science and Engineering, University of North Texas, 3940 North Elm Suite, Denton, TX 76207, USA 4 Center for Agile and Adaptive Additive Manufacturing, 3940 North Elm Suite, Denton, TX 76207, USA * Correspondence: [email protected] Abstract: An acoustic metamaterial superlattice is used for the spatial and spectral deconvolution of a broadband acoustic pulse into narrowband signals with different central frequencies. The operating frequency range is located on the second transmission band of the superlattice. The decomposition of the broadband pulse was achieved by the frequency-dependent refraction angle in the superlattice. The refracted angle within the acoustic superlattice was larger at higher operating frequency and verified by numerical calculated and experimental mapped sound fields between the layers. The spatial dispersion and the spectral decomposition of a broadband pulse were studied using lateral position-dependent frequency spectra experimentally with and without the superlattice structure along the direction of the propagating acoustic wave.
    [Show full text]
  • Spatial Dispersion Consideration in Dipoles
    A. Chipouline, C. Simovski, S. Tretyakov, Basics of averaging of the Maxwell equations for bulk materials Basics of averaging of the Maxwell equations for bulk materials A. Chipouline, C. Simovski, S. Tretyakov Abstract Volume or statistical averaging of the microscopic Maxwell equations (MEs), i.e. transition from microscopic MEs to their macroscopic counterparts, is one of the main steps in electrodynamics of materials. In spite of the fundamental importance of the averaging procedure, it is quite rarely properly discussed in university courses and respective books; up to now there is no established consensus about how the averaging procedure has to be performed. In this paper we show that there are some basic principles for the averaging procedure (irrespective to what type of material is studied) which have to be satisfied. Any homogenization model has to be consistent with the basic principles. In case of absence of this correlation of a particular model with the basic principles the model could not be accepted as a credible one. Another goal of this paper is to establish the averaging procedure for bulk MM, which is rather close to the case of compound materials but should include magnetic response of the inclusions and their clusters. In the vast majority of cases the consideration of bulk materials means that we consider propagation of an electromagnetic wave far from the interfaces, where the eigenwave in the medium has been already formed and stabilized. In other words, in this paper we consider the possible eigenmodes, which could exist in the equivalent homogenized media, and the necessary math apparatus for an adequate description of these waves.
    [Show full text]
  • Metamaterials Frequency Dispersion and Spatial Dispersion Split Rings and Related Structures U
    Metamaterials Frequency dispersion and spatial dispersion Split rings and related structures U. Jena, June 2012 Sergei Tretyakov sergei.tretyakov@aalto.fi 1 June 15, 2012 Lecture plan I Introduction: Metamaterials I Frequency dispersion and spatial dispersion I Bi-anisotropy (chirality) and artificial magnetism I Split rings, dual bars, etc. I History and basic properties I Circuit model I Lorentz dispersion Metamaterials, dispersion, SRR. page 2 1 Definition: Metamaterial Meta- denotes position behind, after, or beyond, and also something of a higher or second-order kind. Metamaterial is an arrangement of artificial structural elements, designed to achieve advantageous and unusual electromagnetic properties. More precisely, properties that cannot be achieved at the atomic or molecular level are achieved through the electromagnetic properties of “particles” formed at levels much higher than the atomic level but whose dimensions are small compared to the wavelength of operation. Metamaterials, dispersion, SRR. page 3 1 Nature versus engineering (Picture by N. Zheludev) Metamaterials, dispersion, SRR. page 4 1 Metamaterial concept Metamaterials, dispersion, SRR. page 5 1 Imitating nature. Artificial dielectrics Artificial chiral materials The right figure from J.C. Bose, On the rotation of plane of polarization of electric waves by twisted structure, Proc. Royal Soc., vol. 63, pp. 146-152, 1898. Metamaterials, dispersion, SRR. page 6 1 First ”original metamaterial designs” J. Brown, 1953; W. Rotman, 1961; J. Pendry, 1996. Metamaterials, dispersion,
    [Show full text]
  • Arxiv:1903.09087V3 [Physics.Optics] 3 Apr 2019 C
    Electromagnetic Chirality 1, 2 Christophe Caloz ¤ and Ari Sihvola 1Polytechnique Montréal, Montréal, QC H3T-1J4, Canada 2Aalto University, Espoo, FI-00076, Finland This paper presents a first-principle and global perspective of electromagnetic chirality. It follows for this purpose a bottom-up construction, from the description of chiral particles or metaparticles (microscopic scale), through the electromagnetic theory of chiral media (macroscopic scale), to the establishment ad- vanced properties and design principles of chiral materials and metamaterials. It preliminarily highlights the three fundamental concepts related to chirality – mirror asymmetry, polarization rotation and magne- todielectric coupling – and points out the nontrivial interdependencies existing between them. The first part (chiral particles) presents metamaterial as the most promising technology for chirality, compares two rep- resentative particles involving magnetoelectric coupling, namely the planar Omega particle and the twisted Omega or helix particle, and shows that only the latter is chiral, and finally links the response of microscopic particles to that of the medium formed by arranging them according to a subwavelength lattice structure. The second part (electromagnetic theory) infers from the previous microscopic study the chiral constitutive relations as a subset of the most general bianisotropic relations, derives parity conditions for the chiral pa- rameters, computes the chiral eigenstates as circularly polarized waves, and finally shows that the circular birefringence of these states leads to polarization rotation. The third part (properties and design) introduces an explicit formulation of chirality based on spatial frequency dispersion or nonlocality, analyzes the tempo- ral frequency dispersion or nonlocality of chiral media, and finally provides guidelines to design a practical chiral metamaterial.
    [Show full text]
  • Negative Index Materials: at the Frontier of Macroscopic Electromagnetism Boris Gralak
    Negative index materials: at the frontier of macroscopic electromagnetism Boris Gralak To cite this version: Boris Gralak. Negative index materials: at the frontier of macroscopic electromagnetism. Comptes Rendus Physique, Centre Mersenne, 2020, 21 (4-5), pp.343-366. 10.5802/crphys.29. hal-03087388 HAL Id: hal-03087388 https://hal.archives-ouvertes.fr/hal-03087388 Submitted on 23 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Negative index materials: at the frontier of macroscopic electromagnetism Boris Gralak CNRS, Aix Marseille Univ, Centrale Marseille, Institut Fresnel, Marseille, France Abstract The notions of negative refraction and negative index, introduced by V. Veselago more than 50 years ago, have appeared beyond the frontiers of macroscopic electromagnetism and purely formal during 30 years, until the work of J. Pendry in the late 1990s. Since then, the negative index materials and the metamaterials displayed extraordinary properties and spectacular effects which have tested the domain of validity of macroscopic electromagnetism. In this article, several of these properties and phenomena are reviewed. First, mechanisms underlying the negative index and negative refraction are briefly presented. Then, it is shown that the frame of the time-harmonic Maxwell's equations cannot describe the behavior of electromagnetic waves in the situations of the perfect flat lens and corner reflector due to the presence of essential spectrum at the perfect −1 index frequency.
    [Show full text]