Diamagnetic properties of metamaterials: a magnetostatic analogy

The response of a metamaterial, consisting of a 3D lattice of lossy capacitively loaded metallic loops is studied theoretically when it is inserted into a homogeneous harmonically varying magnetic field. The current distribution is found by taking into account the magnetic coupling between any pair of loops in the approximation of no retardation. It is shown that in a frequency range above its resonant frequency the metamaterial behaves as a diamagnet expelling the applied magnetic field. As the resonant frequency is approached the magnetic field is shown to be expelled not only from the volume of the metamaterial but from a larger zone which in the vicinity of the resonant frequency takes the form of a sphere. In the lossless case the radius of this exclusion sphere tends to infinity. In the presence of losses the maximum radius is limited by the quality factor of the individual elements. The response of a single element is shown to be analogous to that of a sphere of magnetic material, an analogy that leads to an alternative definition of effective permeability.Received: 15 August 2004, Published online: 21 October 2004PACS: 41.20.-q Applied classical electromagnetism - 75.20.-g Diamagnetism, paramagnetism, and superparamagnetism - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.) - 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.)     

Origin of strain-induced resonances in flexible terahertz metamaterials

Two types of flexible terahertz metamaterials were fabricated on polyethylene naphthalate(PEN) substrates. The unit cell of one type consists of two identical split-ring resonators(SRRs) that are arranged face-to-face(i.e., Flex Meta F); the unit cell of the other type has nothing different but is arranged back-to-back(i.e., Flex Meta B). Flex Meta F and Flex Meta B illustrate the similar transmission dips under zero strain because the excitation of fundamental inductive–capacitive(LC)resonance is mainly dependent on the geometric structure of individual SRR. However, if a gradually variant strain is applied to bend Flex Meta F and Flex Meta B, the new resonant peaks appear: in the case of Flex Meta F, the peaks are located at the lower frequencies; in the case of Flex Meta B, the peaks appear at the frequencies adjacent to the LC resonance. The origin and evolution of strain-induced resonances are studied. The origin is ascribed to the detuning effect and the different responses to strain from Flex Meta F and Flex Meta B are associated with the coupling effect. These findings may improve the understanding on flexible terahertz metamaterials and benefit their applications in flexible or curved devices.     

Selective excitation of resonances in gammadion metamaterials for terahertz wave manipulation

A gammadion terahertz(THz) metamaterial embedded with a pair of splits is experimentally investigated. By introducing the pair of splits at different arms, the transmitted amplitude at the resonance frequency can be manipulated from 61% to 24%. Broadband static resonance tunability from 1.11 to 1.51 THz is also demonstrated via varying the relative split positions at certain arms. The amplitude change and static resonance tunability are attributed to the introduced split pairs, which enable selective excitation of different resonance modes in the gammadion metamaterials. This work promises a new approach to design THz functional devices.     

Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry

We report that a resonance response with a very high quality factor can be achieved in a planar metamaterial by introducing symmetry breaking in the shape of its structural elements, which enables excitation of trapped modes, i.e., modes that are weakly coupled to free space.     

Enlarging the negative-index bandwidth of optical metamaterials by hybridized plasmon resonances

By exploiting the concept of internal surface plasmon polariton (I-SPP) resonances, which appear at nonsingle metallic film stacks, we have designed a metamaterial showing a negative effective index within a large frequency bandwidth. The designed structure consists of an arrangement of several fishnet layers. By properly adjusting the lattice and the thickness of the dielectric slab of the fishnet, an I-SPP mode can be excited at a certain frequency, giving rise to a negative permeability. Thus, when combining several fishnet layers, each one configured to excite an I-SPP at a slightly different frequency, the coupling among the fishnet layers will cause a plasmon hybridization effect that enables us to extend the negative-index bandwidth.     

Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles

Silicon carbide particles exhibit both electric and magnetic optical resonances, allowing unexplored dielectric metamaterial designs. Experimental extinction spectra and Mie theory calculations of single microscale rod-shaped particles reveal three observable midinfrared resonant modes. Two of the modes are degenerate, with a frequency that can be tuned according to a resonance condition derived within the Letter. The existence of both electric and magnetic resonances may enable a novel negative refractive index metamaterial design.     

Plasmon-induced transparency in metamaterials

A plasmonic "molecule" consisting of a radiative element coupled with a subradiant (dark) element is theoretically investigated. The plasmonic molecule shows electromagnetic response that closely resembles the electromagnetically induced transparency in an atomic system. Because of its subwavelength dimension, this electromagnetically induced transparency-like molecule can be used as a building block to construct a "slow light" plasmonic metamaterial.     

Nonreciprocity engineering in magnetostatic spin waves

Magnetostatic surface spin waves (MSSW) excited from a coplanar waveguide antenna travel in different directions with different amplitudes. This effect, called nonreciprocity of MSSW, has been investigated by micromagnetic simulations. The ratio of amplitude of two counter propagating spin waves, the nonreciprocity parameter κ, is obtained for different ferromagnetic materials, such as NiFe (Py), CoFeAl, yttrium iron garnet (YIG), and GaMnAs. A device schematic has been proposed in which κ can be tuned to a large value by varying simple geometrical parameters of the device.     

Self-induced supertransparency in small-size injection lasers

The emission spectrum of an injection GaAs laser having a quadrilateral cavity with a 13×13 mm square cross section and with a high pumping level is considered. Anomalously high dispersion revealed for the refractive index for the short-wave mode (ñ>7) and disappearance of dispersion for the long-wave (ñ=3.4) mode indicate in all probability the emergence of a gap in the electron energy spectrum at the wavelength of the fundamental lasing mode. In contrast to [1], the entire long-wave part of the spectrum is emitted coherently at the same frequency and probably without absorption.     

Gap solitons in metamaterials

Electromagnetic localization and the existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band—where the magnetic permeability µ(?) is positive and the dielectric permittivity ε(?) is negative—is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed.     

Indicatrices of magnetostatic surface waves

Indicatrices (isofrequency curves) of magnetostatic surface waves are studied with allowance for wave attenuation. A bias magnetic field is applied tangentially to a ferrite film. Arbitrary angles between the bias magnetic field and the wave vector are examined.     

静磁场中的互作用能

讨论了在激发磁场的电流保持不变时和束缚磁荷作为磁场的不变时，两种情况下磁场的相互作用能。结果与静电场类似，两种情况的互作用能中都含有相互磁化，致使物体磁化状态改变作的功。     

Investigation of magnetostatic waves in photonic crystals

The frequency dependence of the Lyapunov index in the bandgap of a magnetic photonic (spin) crystal has been experimentally determined for the first time.     

Radiation damping of magnetostatic modes in yig

The radiation induced linewidth of magnetostatic modes in spheres of Yttrium Iron Garnet has been measured in microwave experiments. The linewidths of the lowest order modes (n m 0) have a ω²ⁿ⁺¹ frequency dependence which can be explained by multipole radiation.     

Magnetic-roughness-induced magnetostatic interactions in magnetic tunnel junctions

Magnetostatic ferromagnetic coupling in magnetic tunnel junctions was selectively analyzed. We have shown that in samples involving polycrystalline magnetic films, beyond the orange-peel coupling, an important class of interaction is related to the dispersion fields associated to magnetic inhomogeneities. These magnetization fluctuations were described in terms of magnetic roughness arising from the local anisotropy fluctuations. Therefore, using roughness data extracted from atomic/ magnetic force microscopy analysis, the amplitude and the variation with distance of the magnetostatic interactions were selectively quantified. Received 7 December 2001     

Periodic waves in nonlinear metamaterials

Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution.