Peter Markos

Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients

We analyze the reflection and transmission coefficients calculated from transfer matrix simulations on finite lengths of electromagnetic metamaterials, to determine the effective permittivity ~«! and permeability ~m! .W e perform this analysis on structures composed of periodic arrangements of wires, split ring resonators ~SRRs!, and both wires and SRRs. We find the recovered frequency-dependent« and m are entirely consistent with analytic expressions predicted by effective medium arguments. Of particular relevance are that a wire medium exhibits a frequency region in which the real part of « is negative, and SRRs produce a frequency region in which the real part of m is negative. In the combination structure, at frequencies where both the recovered real parts of « and m are simultaneously negative, the real part of the index of refraction is also found to be unambiguously negative.

Resonant and antiresonant frequency dependence of the effective parameters of metamaterials.

We present a numerical study of the electromagnetic response of the metamaterial elements that are used to 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 antiresonant 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 antiresonant 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 antiresonant behavior.

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.

Transmission properties of composite metamaterials in free space

We propose and demonstrate a type of composite metamaterial which is constructed by combining thin copper wires and split ring resonators (SRRs) on the same board. The transmission measurements performed in free space exhibit a passband within the stop bands of SRRs and thin wire structures. The experimental results are in good agreement with the predictions of the transfer matrix method simulations.

Numerical studies of left-handed materials and arrays of split ring resonators.

We present numerical results on the transmission properties of the left-handed materials (LHMs) and split-ring resonators (SRRs). The simulation results are in qualitative agreement with experiments. The dependence of the transmission through LHMs on the real and imaginary part of the electric permittivity of the metal, the length of the system, and the size of the unit cell are presented. We also study the dependence of the resonance frequency of the array of SRRs on the ring thickness, inner diameter, radial and azimuthal gap, as well as on the electrical permittivity of the board and the embedding medium, where the SRR resides. Qualitatively good agreement with previously published analytical results is obtained.

Transmission properties and effective electromagnetic parameters of double negative metamaterials.

We analyze the transmission properties of double negative metamaterials (DNM). Numerical simulations, based on the transfer matrix algorithm, show that some portion of the electromagnetic wave changes its polarization inside the DNM structure. As the transmission properties depend strongly on the polarization, this complicates the interpretation of experimental and numerical data, both inside and outside of the pass band. From the transmission data, the effective permittivity, permeability and refractive index are calculated. In the pass band, we found that the real part of permeability and both the real and the imaginary part of the permittivity are negative. Transmission data for some new structures are also shown. Of particular interest is the structure with cut wires, which possesses two double negative pass bands.

Transmission studies of left-handed materials

Left-handed materials are studied numerically using an improved version of the transfer-matrix method. The transmission, reflection, phase of reflection, and absorption are calculated and compared with experiments for both single split-ring resonators with negative permeability and left-handed materials, which have both the permittivity \ensuremath{\epsilon} and permeability \ensuremath{\mu} negative. Our results suggest ways of positively identifying materials that have both \ensuremath{\epsilon} and \ensuremath{\mu} negative, from materials that have either \ensuremath{\mu} or \ensuremath{\epsilon} negative.

Transmission losses in left-handed materials.

We numerically analyze the origin of the transmission losses in left-handed structures. Our data confirms that left-handed structures can have very good transmission properties, in spite of the expectable dispersion of their effective permeability and refraction index. The large permittivity of the metallic components improves the transmission. High losses, observed in recent experiments, could be explained by the absorption of the dielectric board.

Absorption losses in periodic arrays of thin metallic wires

We analyze the transmission and reflection of electromagnetic waves calculated from transfer matrix simulations of periodic arrangements of thin metallic wires. The effective permittivity and the absorption of the arrangements of wires are determined. Their dependence on the wire thickness and the conductance of the metallic wires is studied. The cutoff frequency, or effective plasma frequency, is obtained and compared with analytical predictions. It is shown that the periodic arrangement of wires exhibits a frequency region in which the real part of the permittivity is negative while its imaginary part is very small. This behavior is seen for wires with thickness as small as 17 microm with a lattice constant of 3.33 mm.

Left-Handed Materials

Rapidly increasing interest in the left-handed materials (LHM) started after Pendry et al. predicted that certain man-made composite structure could possess, in a given frequency interval, a negative effective magnetic permeability µ eff [1]. Combination of such a structure with negative effective permittivity medium — for instance the regular array of thin metallic wires [2, 3, 4, 5, 6, 7] — enabled the construction of meta-materials with both effective permittivity and permittivity negative. This was confirmed by experiments [8, 9].