arXiv subjects
Publications and source records attributed to Steven A. Cummer.
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.
We present experimental demonstration of phase conjugation using nonlinear metamaterial elements. Active split-ring resonators loaded with varactor diodes are demonstrated theoretically to act as phase-conjugating or time-reversing discrete elements when parametrically pumped and illuminated with appropriate frequencies. The metamaterial elements were fabricated and shown experimentally to produce a time reversed signal. Measurements confirm that a discrete array of phase-conjugating elements act as a negatively-refracting time reversal RF lens only 0.12$λ$ thick.
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part of free space is distorted in some desired manner. The coordinate transformation is then applied to the permittivity and permeability tensors to yield the specification for a complex medium with desired functionality. The transformation optical structures proposed to date, such as electromagnetic "invisibility" cloaks and concentrators, are inherently reflectionless and leave the transmitted wave undisturbed. Here we expand the class of transformation optical structures by introducing finite, embedded coordinate transformations, which allow the electromagnetic waves to be steered or focused. We apply the method to the design of several devices, including a parallel beam shifter and a beam splitter, both of which exhibit unusual electromagnetic behavior as confirmed by 2D full-wave simulations. The devices are designed to be reflectionless, in accordance with a straightforward topological criterion.
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.
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 $\tan δ\approx 0.001$ 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.
We determine rigorously the effective permeability of magnetic metamaterials composed of passive particles exhibiting magnetic resonances. The effective permeability is expressed in terms of circuit parameters characteristic to these particles (L, C, and R) and particle geometry. The derivation takes into account the magnetic coupling between particles. We show that a bigger concentration of particles leads to an improvement in the metamaterial performances (such as bandwidth or loss tangent), but this effect saturates as the particles are packed more tightly. The theory is validated through numerical simulations of physically realizable metamaterials.
Based on a coordinate transformation approach, Pendry {\it et al.} have reported electromagnetically anisotropic and inhomogeneous shells that, in theory, completely shield an interior structure of arbitrary size from electromagnetic fields without perturbing the external fields. We report full-wave simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters in an effort to understand the challenges of realizing such a structure in practice. The simulations indicate that the performance of the electromagnetic cloaking structure is not especially sensitive to modest permittivity and permeability variations. This is in contrast to other applications of engineered electromagnetic materials, such as subwavelength focusing using negative refractive index materials. The cloaking performance degrades smoothly with increasing loss, and effective low-reflection shielding can be achieved with a cylindrical shell composed of an eight (homogeneous) layer approximation of the ideal continuous medium.