Larry K. Warne

Realizing optical magnetism from dielectric metamaterials.

We demonstrate, for the first time, an all-dielectric metamaterial resonator in the mid-wave infrared based on high-index tellurium cubic inclusions. Dielectric resonators are desirable compared to conventional metallo-dielectric metamaterials at optical frequencies as they are largely angular invariant, free of ohmic loss, and easily integrated into three-dimensional volumes. With these low-loss, isotropic elements, disruptive optical metamaterial designs, such as wide-angle lenses and cloaks, can be more easily realized.

Electrophysics of micromechanical comb actuators

A simple approximate theory is developed for the electrostatic forces operating in a micromechanical comb actuator. The comb drive is considered both without (for simplicity) and with an underlying ground plane. The forces are partitioned into local forces (electric fields confined to the cross-sections of the individual comb fingers) and global force corrections (electric fields resulting from effective equipotential sheets representing the engaged and unengaged comb finger regions). The local forces are obtained by applying the principle of virtual work (both engaged and unengaged regions are involved when a ground plane is present beneath the comb fingers). The global forces are obtained from the force between magnetic current filaments introduced to model the electric-potential discontinuities in the effective equipotential sheets of the engaged and unengaged finger regions. Conformal mapping, in addition to a static mode decay approximation, is used to obtain simple and accurate formulas for the local charge per unit length (local forces) and, when a ground plane is present, for the effective sheet potentials (magnetic currents and global forces). The forces in the separated case (which are also global in nature) are also obtained by the principle of virtual work. The results of the paper show that the attractive local forces are independent of engagement distance and the smaller repulsive global forces are inversely proportional to engagement distance. The attractive separated forces are inversely proportional to the separation distance without the ground plane and inversely proportional to the square of the separation distance with the ground plane. >

Statistical properties of linear antenna impedance in an electrically large cavity

The paper presents models and measurements of linear antenna input impedance in resonant cavities at high frequencies. Results are presented for both the case where the cavity is undermoded (modes with separate and discrete spectra) as well as the overmoded case (modes with overlapping spectra). A modal series is constructed and analyzed to determine the impedance statistical distribution. Both electrically small as well as electrically longer resonant and wall mounted antennas are analyzed. Measurements in a large mode stirred chamber cavity are compared with calculations. Finally, a method based on power arguments is given, yielding simple formulas for the impedance distribution.

Integrated measurement-modeling approaches for evaluating residual stress using micromachined fixed-fixed beams

Two methodologies have been developed to determine the biaxial residual stress value in thin films using electrostatically actuated fixed-fixed beam test structures. In the first, we determine the compliance matrix of the support posts using 3-D finite-element analysis. The residual stress value is then found from the best fit between the measured and modeled deflection curves, with the residual stress as the only free parameter in the model. An accuracy of /spl plusmn/0.5 MPa for the average biaxial residual stress level is evaluated from the reproducibility of independent measurements over a wide range of loadings. The key to the second methodology lies in the recognition that for a given value of residual stress, there exists a unique family of deflection curves associated with two adjacent beams of different lengths. Therefore, compliance information can be extracted directly from the deflection curves. We proceed to show that essentially the same values of residual stress are found by the two methodologies, while the latter allows much more rapid extraction of the residual stress. With the second methodology established, we find that residual stress values vary across a quarter of a six-inch diameter wafer by 2.5 MPa for three structural levels of polycrystalline silicon in our five-level surface micromachining technology.

Equivalent antenna radius for narrow slot apertures having depth

The problem of electromagnetic penetration of a narrow slot aperture in a thick perfectly conducting plane is reduced to the solution of Hallens integral equation with an equivalent antenna radius. The depth and width of the slot are assumed to be small compared to both the length of the slot and the wavelength. The equivalent radius is evaluated in terms of the solution to the transverse static problem. Simple approximations for the equivalent radius is also given. Hallens integral equation is solved by the Galerkin method with piecewise sinusoidal basis functions. Large slot depth-to-width ratios give rise to vanishingly small equivalent radii and thus large antenna resonance quality factors. A simple correction to the static field distribution in the slot is also given. This correction allows the depth to become somewhat larger relative to the wavelength. >

EIGER ™ : An open-source frequency-domain electromagnetics code

EIGERtrade is a general-purpose, 3D frequency-domain electromagnetics code suite consisting of a pre-processor (Jungfrau), the physics code (EIGER), and post processor (Moench). In order to better enable collaborative development, EIGERtrade version 2.0 has been approved for release as open source software under a GNU Public License. EIGERtrade is primarily an integral-equation code for both frequency-domain electromagnetics and electrostatics. This version includes the following Greens functions: 2D and 3D free space, symmetry-planes, periodic and layered media. There is a thin-wire algorithm as well as junction basis functions for attachment of a wire to a conducting surface, and also thin-slot models for coupling into cavities. The code is written in Fortran 90 using object-oriented design and has the capability to run both in parallel and serial.

Slot apertures having depth and losses described by local transmission line theory

The problem of electromagnetic penetration of a narrow slot aperture in a thick conducting plane is considered when the conductivity of the plane (and slot walls) is large but not necessarily infinite and when somewhat lossy gaskets are placed in the slot. The problem is partitioned into a local region, where transmission line theory is used to describe the antenna modes along the slot, and a nonlocal region, where a filament-type integral representation is used. The result is a modified Hallen-type integro-differential equation for the slot voltage (or magnetic current). The local transmission line theory allows the effects of wall loss and gaskets to be included in a simple and intuitive manner. Examples involving a rectangular slot aperture are given. The finite conductivity of the conducting plane, even for good conductors, reduces the penetration when realistic slot dimensions are used. Gaskets, even with relatively small loss tangents, also reduce the penetration when realistic slot dimensions are used. >

Effect of thin silicon dioxide layers on resonant frequency in infrared metamaterials

Infrared metamaterials fabricated on semiconductor substrates exhibit a high degree of sensitivity to very thin (as small as 2 nm) layers of low permittivity materials between the metallic elements and the underlying substrate. We have measured the resonant frequencies of split ring resonators and square loops fabricated on Si wafers with silicon dioxide thicknesses ranging from 0 to 10 nm. Resonance features blue shift with increasing silicon dioxide thickness. These effects are explained by the silicon dioxide layer forming a series capacitance to the fringing field across the elements. Resonance coupling to the Si-O vibrational absorption has been observed. Native oxide layers which are normally ignored in numerical simulations of metamaterials must be accounted for to produce accurate predictions.

Relation between equivalent antenna radius and transverse line dipole moments of a narrow slot aperture having depth

A simple general relationship is shown to exist between the equivalent radius and the transverse line dipole moments of a narrow slot aperture having depth. The cross-sectional dimensions of the aperture are assumed to be small compared to both its length and the wavelength. The general relationship can be put succinctly; the perfect magnetic cylinder, having the equivalent radius of an aperture with depth, has not only the same properties but also the same transverse line dipole moments of the aperture. >

Perturbation Theory in the Design of Degenerate Rectangular Dielectric Resonators

The design of resonators with degenerate magnetic and electric modes usually requires the ability to perturb one or both types of modes in order to induce alignment of magnetic and electric properties. In this paper perturbation theory is used to identify difierent types of inclusions that can be used to realize fundamental- mode degeneracy in a rectangular dielectric resonator and thus, can ultimately be used in the design of negative-index metamaterials. For reasons associated with fabrication in the infrared-frequency regime, rectangular resonator designs are of particular interest.