Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell's Equations

The technique of applying form-invariant, spatial coordinate transformations of Maxwell's equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.Comment: submitted to "Photonics and Nanostructures", Special Issue "PECS VII", Elsevie

Q-based design equations for resonant metamaterials and experimental validation

Practical design parameters of resonant metamaterials, such as loss tangent, are derived in terms of the quality factor $Q$ of the resonant effective medium permeability or permittivity. Through electromagnetic simulations of loop-based resonant particles, it is also shown that the $Q$ of the effective medium response is essentially equal to the $Q$ of an individual resonant particle. Thus, by measuring the $Q$ of a single fabricated metamaterial particle, the effective permeability or permittivity of a metamaterial can be calculated simply and accurately without requiring complex simulations, fabrication, or measurements. Experimental validation shows that the complex permeability analytically estimated from the measured $Q$ of a single fabricated self-resonant loop agrees with the complex permeability extracted from $S$ parameter measurements of a metamaterial slab to better than 20%. This $Q$ equivalence reduces the design of a metamaterial to meet a given loss constraint to the simpler problem of the design of a resonant particle to meet a specific $Q$ constraint. This analysis also yields simple analytical expressions for estimating the loss tangent of a planar loop magnetic metamaterial due to ohmic losses. It is shown that $\tan \delta \approx 0.001$ is a strong lower bound for magnetic loss tangents for frequencies not too far from 1 GHz. The ohmic loss of the metamaterial varies inversely with the electrical size of the metamaterial particle, indicating that there is a loss penalty for reducing the particle size at a fixed frequency

Magnetospheric Radio Tomography: Observables, Algorithms, and Experimental Analysis

This grant supported research towards developing magnetospheric electron density and magnetic field remote sensing techniques via multistatic radio propagation and tomographic image reconstruction. This work was motivated by the need to better develop the basic technique of magnetospheric radio tomography, which holds substantial promise as a technology uniquely capable of imaging magnetic field and electron density in the magnetosphere on large scales with rapid cadence. Such images would provide an unprecedented and needed view into magnetospheric processes. By highlighting the systems-level interconnectedness of different regions, our understanding of space weather processes and ability to predict them would be dramatically enhanced. Three peer-reviewed publications and 5 conference presentations have resulted from this work, which supported 1 PhD student and 1 postdoctoral researcher. One more paper is in progress and will be submitted shortly. Because the main results of this research have been published or are soon to be published in refereed journal articles listed in the reference section of this document, we provide here an overview of the research and accomplishments without describing all of the details that are contained in the articles

A Completely Covariant Approach to Transformation Optics

We show that the Plebanski based approach to transformation optics overlooks some subtleties in the electrodynamics of moving dielectrics that restricts its applicability to a certain class of transformations. An alternative, completely covariant, approach is developed that is more generally applicable and provides a clearer picture of transformation optics.Comment: 10 pages. This version: Additional references added, corrected a small error in Eq. (28) (Eq. (29) in present version), some revision of the text, appendix content moved to the main body of the text, figure removed. Corresponds more closely to published version. Prepared for a special issue on transformation optics published by Journal of Optic