Analytic expressions for the constitutive parameters of magnetoelectric metamaterials

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling. © 2010 The American Physical Society.

Resonant transmission near nonrobust periodic slab modes.

We present a precise theoretical explanation and prediction of certain resonant peaks and dips in the electromagnetic transmission coefficient of periodically structured slabs in the presence of nonrobust guided slab modes. We also derive the leading asymptotic behavior of the related phenomenon of resonant enhancement near the guided mode. The theory applies to structures in which losses are negligible and to very general geometries of the unit cell. It is based on boundary-integral representations of the electromagnetic fields. These depend on the frequency and on the Bloch wave vector and provide a complex-analytic connection in these parameters between generalized scattering states and guided slab modes. The perturbation of three coincident zeros-those of the dispersion relation for slab modes, the reflection constant, and the transmission constant-is central to calculating transmission anomalies both for lossless dielectric materials and for perfect metals.

Purification, crystallization and preliminary X-ray diffraction studies of a complex between G protein-coupled receptor kinase 2 and Gbeta1gamma2.

G protein-coupled receptor kinase 2 (GRK2) phosphorylates activated G protein-coupled receptors (GPCRs), which ultimately leads to their desensitization and/or downregulation. The enzyme is recruited to the plasma membrane via the interaction of its carboxyl-terminal pleckstrin-homology (PH) domain with the beta and gamma subunits of heterotrimeric G proteins (Gbetagamma). An improved purification scheme for GRK2 has been developed, conditions under which GRK2 forms a complex with Gbeta(1)gamma(2) have been determined and the complex has been crystallized in CHAPS detergent micelles. Crystals of the GRK2-Gbetagamma complex belong to space group C2 and have unit-cell parameters a = 187.0, b = 72.1, c = 122.0 A, beta = 115.2 degrees. A complete data set has been collected to 3.2 A resolution with Cu Kalpha radiation.