Electric coupling to the magnetic resonance of split ring resonators

We study both theoretically and experimentally the transmission properties of a lattice of split ring resonators (SRRs) for different electromagnetic (EM) field polarizations and propagation directions. We find unexpectedly that the incident electric field E couples to the magnetic resonance of the SRR when the EM waves propagate perpendicular to the SRR plane and the incident E is parallel to the gap-bearing sides of the SRR. This is manifested by a dip in the transmission spectrum. A simple analytic model is introduced to explain this interesting behavior.Comment: 4 pages, 4 figure

Effective medium theory of left-handed materials

We analyze the transmission and reflection data obtained through transfer matrix calculations on metamaterials of finite lengths, to determine their effective permittivity and permeability. Our study concerns metamaterial structures composed of periodic arrangements of wires, cut-wires, split ring resonators (SRRs), closed-SRRs, and both wires and SRRs. We find that the SRRs have a strong electric response, equivalent to that of cut-wires, which dominates the behavior of left-handed materials (LHM). Analytical expressions for the effective parameters of the different structures are given, which can be used to explain the transmission characteristics of LHMs. Of particular relevance is the criterion introduced by our studies to identify if an experimental transmission peak is left- or right-handed.Comment: to be published in Phys. Rev. Let

Broadband metasurfaces enabling arbitrarily large delay-bandwidth products

Metasurfaces allow for advanced manipulation of optical signals by imposing phase discontinuities across flat interfaces. Unfortunately, these phase shifts remain restricted to values between 0 and 2 pi, limiting the delay-bandwidth product of such sheets. Here, we develop an analytical tool to design metasurfaces that mimic three-dimensional materials of arbitrary thickness. In this way, we demonstrate how large phase discontinuities can be realized by combining several subwavelength Lorentzian resonances in the unit cell of the surface. Our methods open up the temporal response of metasurfaces and may lead to the construction of metasurfaces with a plethora of new optical functions

Levitation of the quantum Hall extended states in the B→B\to 0 limit

We investigate the fate of the quantum Hall extended states within a continuum model with spatially correlated disorder potentials. The model can be projected onto a couple of the lowest Landau bands. Levitation of the $n=0$ critical states is observed if at least the two lowest Landau bands are considered. The dependence on the magnetic length $l_B=(\hbar/(eB))^{1/2}$ and on the correlation length of the disorder potential $\eta$ is combined into a single dimensionless parameter $\hat\eta=\eta/l_B$. This enables us to study the behavior of the critical states for vanishing magnetic field. In the two Landau band limit, we find a disorder dependent saturation of the critical states' levitation which is in contrast to earlier propositions, but in accord with some experiments.Comment: 7 pages, 9 figures. Replaced with published versio

Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder

The fate of the current carrying states of a quantum Hall system is considered in the situation when the disorder strength is increased and the transition from the quantum Hall liquid to the Hall insulator takes place. We investigate a two-dimensional lattice model with spatially correlated disorder potentials and calculate the density of states and the localization length either by using a recursive Green function method or by direct diagonalization in connection with the procedure of level statistics. From the knowledge of the energy and disorder dependence of the localization length and the density of states (DOS) of the corresponding Landau bands, the movement of the current carrying states in the disorder--energy and disorder--filling-factor plane can be traced by tuning the disorder strength. We show results for all sub-bands, particularly the traces of the Chern and anti-Chern states as well as the peak positions of the DOS. For small disorder strength $W$ we recover the well known weak levitation of the critical states, but we also reveal, for larger $W$, the strong levitation of these states across the Landau gaps without merging. We find the behavior to be similar for exponentially, Gaussian, and Lorentzian correlated disorder potentials. Our study resolves the discrepancies of previously published work in demonstrating the conflicting results to be only special cases of a general lattice model with spatially correlated disorder potentials. To test whether the mixing between consecutive Landau bands is the origin of the observed floating, we truncate the Hilbert space of our model Hamiltonian and calculate the behavior of the current carrying states under these restricted conditions.Comment: 10 pages, incl. 13 figures, accepted for publication in PR

Optically Implemented Broadband Blueshift Switch in the Terahertz Regime

Cataloged from PDF version of article.We experimentally demonstrate, for the first time, an optically implemented blueshift tunable metamaterial in the terahertz (THz) regime. The design implies two potential resonance states, and the photoconductive semiconductor (silicon) settled in the critical region plays the role of intermediary for switching the resonator from mode 1 to mode 2. The observed tuning range of the fabricated device is as high as 26% (from 0.76 THz to 0.96 THz) through optical control to silicon. The realization of broadband blueshift tunable metamaterial offers opportunities for achieving switchable metamaterials with simultaneous redshift and blueshift tunability and cascade tunable devices. Our experimental approach is compatible with semiconductor technologies and can be used for other applications in the THz regime

Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials

We present a numerical study of the electromagnetic response of the metamaterial elements that are usedto construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an anti-resonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus anti-resonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the anti-resonant behavior

Left- and right-handed transmission peaks near the magnetic resonance frequency in composite metamaterials

We present free-space microwave measurements on composite metamaterials (CMMs) consisting of split ring resonators (SRRs) and wires either on the same dielectric board or on alternating boards. Our experimental results disprove the widely held belief that the occurrence of a CMM transmission peak within the stop bands of the SRRs alone and wires alone constitutes a clear demonstration of left-handed (LH) behavior. This belief is based on the assumption that the stop bands of SRRs alone and wires alone are not affected by the simultaneous presence of both. We show here that this assumption is wrong: The effective plasma frequency, ω′p, of the CMM is actually substantially lower than the wires-only plasma frequency, ωp; furthermore, the in-plane wires, as opposed to the off-plane case, push the magnetic resonance frequency of the SRRs, ωm, to a higher value, ω′m, for the CMM. We conclude that the criterion for deciding whether a peak in the transmission spectrum through a CMM is really left-handed is for the peak to be located above ω′m and below ω′p. Our results provide a definite way for experimentally identifying ω′p