Th. Koschny

Magnetic Metamaterials at Telecommunication and Visible Frequencies

Arrays of gold split rings with a 50-nm minimum feature size and with an LC resonance at 200 THz frequency (1.5 microm wavelength) are fabricated. For normal-incidence conditions, they exhibit a pronounced fundamental magnetic mode, arising from a coupling via the electric component of the incident light. For oblique incidence, a coupling via the magnetic component is demonstrated as well. Moreover, we identify a novel higher-order magnetic resonance at around 370 THz (800 nm wavelength) that evolves out of the Mie resonance for oblique incidence. Comparison with theory delivers good agreement and also shows that the structures allow for a negative magnetic permeability.

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.

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 epsilon and permeability micro. 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.

Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials

We study the frequency dependence of the effective electromagnetic parameters of left-handed and related metamaterials of the split ring resonator and wire type. We show that the reduced translational symmetry speriodic structured inherent to these metamaterials influences their effective electromagnetic response. To anticipate this periodicity, we formulate a periodic effective medium model which enables us to distinguish the resonant behavior of electromagnetic parameters from effects of the periodicity of the structure. We use this model for the analysis of numerical data for the transmission and reflection of periodic arrays of split ring resonators, thin metallic wires, cut wires, as well as the left-handed structures. The present method enables us to identify the origin of the previously observed resonance-antiresonance coupling as well as the occurrence of negative imaginary parts in the effective permittivities and permeabilities of those materials. Our analysis shows that the periodicity of the structure can be neglected only for the wavelength of the electromagnetic wave larger than 30 space periods of the investigated structure.

Magnetic response of split-ring resonators in the far-infrared frequency regime.

We report on the fabrication, through photolithography techniques, and the detailed characterization, through direct transmission measurements, of a periodic system composed of five layers of photolithographically aligned micrometer-sized Ag split-ring resonators (SRRs). The measured transmission spectra for propagation perpendicular to the SRRs plane show a gap around 6 THz for one of the two possible polarizations of the incident electric field; this indicates the existence of a magnetic resonance, which is verified by detailed theoretical analysis. To our knowledge this is the first time that a system of more than one layer of micrometer-sized SRRs has been fabricated. The measured optical spectra of the Ag microstructure are in very good agreement with the corresponding theoretical calculations.

Conjugated Gammadion Chiral Metamaterial with Uniaxial Optical Activity and Negative Refractive Index

Abstract : We demonstrate numerically and experimentally a conjugated gammadion chiral metamaterial that uniaxially exhibits huge optical activity and circular dichroism, and gives a negative refractive index. This chiral design provides smaller unit cell size and larger chirality compared with other published planar designs. Experiments are performed at GHz frequencies (around 6 GHz) and are in good agreement with the numerical simulations.

Left-handed metamaterials: detailed numerical studies of the transmission properties

Using numerical simulation techniques such as the transfer matrix method and the commercially available code Microwave Studio, we study the transmission properties of left-handed (LH) metamaterials and arrays of split-ring resonators (SRRs). We examine the dependence of the transmission through single- and double-ring SRRs on parameters of the system such as the size and shape of the SRRs, size of the unit cell, dielectric properties of the embedding medium where the SRRs reside, and SRR orientation relative to the incoming electromagnetic field. Moreover, we discuss the role of SRRs and wires on the electric cut-off frequency of the combined system of wires and SRRs, as well as the influence of the various system parameters on the LH transmission peak of a medium composed of SRRs and wires. Finally, demonstrating the disadvantages of the currently used SRR designs due to the lack of symmetry, we discuss more symmetric, multigap SRRs, which constitute very promising components for future two-dimensional and three-dimensional LH structures.

Self-consistent calculation of metamaterials with gain

We present a computational scheme allowing for a self-consistent treatment of a dispersive metallic photonic metamaterial coupled to a gain material incorporated into the nanostructure. The gain is described by a generic four-level system. A critical pumping rate exists for compensating the loss of the metamaterial. Nonlinearities arise due to gain depletion beyond a certain critical strength of a test field. Transmission, reflection, and absorption data as well as the retrieved effective parameters are presented for a lattice of resonant square cylinders embedded in layers of gain material and split ring resonators with gain material embedded into the gaps.

Isotropic three-dimensional left-handed metamaterials

We investigate three-dimensional left-handed and related metamaterials based on a fully symmetric multigap single-ring split-ring resonator sSRRd design and crossing continuous wires. We demonstrate isotropic transmission properties of a SRR-only metamaterial and the corresponding left-handed material that possesses a negative effective index of refraction due to simultaneously negative effective permeability and permittivity. Minor deviations from complete isotropy are due to the finite thickness of the metamaterial. The realization of a perfect lens 1 and other applications of negative refraction require the fabrication of threedimensional, homogeneous, isotropic left-handed materials 2 sLHMd with simultaneously negative permittivity « and magnetic permeability m. So far, no such materials exist, either in nature or in the laboratory. Today’s available LHM structures, based on the periodic arrangement of split-ring resonators 3 sSRRd and continuous metallic wires, 4 are only one dimensional 5‐7 s1Dd, supporting left-handed properties only for propagation with fixed polarization in one direction, or two dimensional 8‐10 s2Dd, where propagation in two directions with fixed polarization or one direction with arbitrary polarization is possible. Earlier attempts to design at least an isotropic SRR sRef. 11d were lacking the symmetry of SRR and unit cell and required individual tuning of the parameters in the different spatial directions. In this paper, we propose a three-dimensional s3Dd isotropic LHM design that allows left-handed behavior for any direction of propagation and any polarization of the electromagnetic wave. Using numerical transfer matrix simulations, we verify the isotropic transmission properties of the proposed structures. Our data show excellent agreement with results expected for a homogeneous slab with the corresponding negative « and m. Our metamaterials are defined as a 3D periodic continuation of a single rectangular unit cell, consisting of SRRs and continuous wires. The sample is a slab of metamaterial with a finite thickness of an integral number of unit cells and infinite extent in the perpendicular direction. The two surfaces of the slab are parallel to any face of the unit cell. An incident electromagnetic plane wave with wave vector k can be characterized by two angles: the incidence angle q P f 0, p /2 d between k and the surface normal n of the sample, and the angle f P s˛p , pg between the projection of k into and some chosen edge of the unit cell inside the surface plane of the sample. The frequency of the incident wave is chosen such that the vacuum wavelength is approximately 10 times larger than the linear size of the unit cell and we expect effective medium behavior.

Repulsive Casimir Force in Chiral Metamaterials

We demonstrate theoretically that one can obtain repulsive Casimir forces and stable nanolevitations by using chiral metamaterials. By extending the Lifshitz theory to treat chiral metamaterials, we find that a repulsive force and a minimum of the interaction energy possibly exist for strong chirality, under realistic frequency dependencies and correct limiting values (for zero and infinite frequencies) of the permittivity, permeability, and chiral coefficients.