Nathan Ingle Landy

A full-parameter unidirectional metamaterial cloak for microwaves

Invisibility is a notion that has long captivated the popular imagination. However, in 2006, invisibility became a practical matter for the scientific community as well, with the suggestion that artificially structured metamaterials could enable a new electromagnetic design paradigm, now termed transformation optics. Since the advent of transformation optics and subsequent initial demonstration of the microwave cloak, the field has grown rapidly. However, the complexity of the transformation optics material prescription has continually forced researchers to make simplifying approximations to achieve even a subset of the desired functionality. These approximations place profound limitations on the performance of transformation optics devices in general, and cloaks especially. Here, we design and experimentally characterize a two-dimensional, unidirectional cloak that makes no approximations to the underlying transformation optics formulation, yet is capable of reducing the scattering of an object ten wavelengths in size. We demonstrate that this approximation-free design regains the performance characteristics promised by transformation optics.

Designing Three-Dimensional Transformation Optical Media Using Quasiconformal Coordinate Transformations

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasiconformal mapping approach. The generalized quasiconformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional carpet ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices.

Enhancing imaging systems using transformation optics

We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.

Thin low-loss dielectric coatings for free-space cloaking

We report stereolithographic polymer-based fabrication and experimental operation of a microwave X-band cloaking device. The device is a relatively thin (about one wavelength thick) shell of an air-dielectric composite, in which the dielectric component has negligible loss and dispersion. In a finite band (9.7-10.1 GHz), the shell eliminates the shadow and strongly suppresses scattering from a conducting cylinder of six-wavelength diameter for TE-polarized free-space plane waves. The device does not require an immersion liquid or conducting ground planes for its operation. The dielectric constant of the polymer is low enough (ε=2.45) to suggest that this cloaking technique would be suitable for higher frequency radiation, including visible light.

Performance of a three dimensional transformation-optical-flattened Lüneburg lens.

We demonstrate both the beam-forming and imaging capabilities of an X-band (8-12 GHz) operational Lüneburg lens, one side of which has been flattened via a coordinate transformation optimized using quasi-conformal transformation optics (QCTO) procedures. Our experimental investigation includes benchmark performance comparisons between the QCTO Lüneburg lens and a commensurate conventional Lüneburg lens. The QCTO Lüneburg lens is made from a metamaterial comprised of inexpensive plastic and fiberglass, and manufactured using fast and versatile numerically controlled water-jet machining. Looking forward towards the future and advanced TO designs, we discuss inevitable design trade-offs between affordable scalable manufacturing and rigorous adherence to the full TO solution, as well as possible paths to mitigate performance degradation in realizable designs.

Isotropic-medium three-dimensional cloaks for acoustic and electromagnetic waves

We propose a generalization of the two-dimensional eikonal-limit cloak derived from a conformal transformation to three dimensions. The proposed cloak is a spherical shell composed of only isotropic media; it operates in the transmission mode and requires no mirror or ground plane. Unlike the well-known omnidirectional spherical cloaks, it may reduce visibility of an arbitrary object only for a very limited range of observation angles. In the short-wavelength limit, this cloaking structure restores not only the trajectories of incident rays, but also their phase, which is a necessary ingredient to complete invisibility. Both scalar-wave (acoustic) and transverse vector-wave (electromagnetic) versions are presented.

Broadband Wide Angle Lens Implemented with Dielectric Metamaterials

The Luneburg lens is a powerful imaging device, exhibiting aberration free focusing for parallel rays incident from any direction. However, its advantages are offset by a focal surface that is spherical and thus difficult to integrate with standard planar detector and emitter arrays. Using the recently developed technique of transformation optics, it is possible to transform the curved focal surface to a flat plane while maintaining the perfect focusing behavior of the Luneburg over a wide field of view. Here we apply these techniques to a lesser-known refractive Luneburg lens and implement the design with a metamaterial composed of a semi-crystalline distribution of holes drilled in a dielectric. In addition, we investigate the aberrations introduced by various approximations made in the implementation of the lens. The resulting design approach has improved mechanical strength with small aberrations and is ideally suited to implementation at infrared and visible wavelengths.

Two-dimensional metamaterial device design in the discrete dipole approximation

We extend the discrete dipole method to enable the analysis and design of two-dimensional magnetoelectric metamaterial devices based on transformation optics. Key to this method is the evaluation of the dipole moments of the metamaterial elements, which can be accomplished within the framework of a rigorous Bloch wave model based on lattice sums. Corrections to the polarizabilities for spatial dispersion and magnetoelectric coupling are included in the formulation of a generalized Clausius-Mossotti relationship. We demonstrate the utility of the extended approach by designing a cloaking structure that shows considerably improved performance over that designed by assuming the standard Clausius-Mossotti relationship between constitutive parameter and polarizability.

Relaxation approach for the generation of inhomogeneous distributions of uniformly sized particles

For many applications in gradient index devices and photonic crystals, it is necessary to be able to design semicrystalline distributions of particles where the lattice constant of the distribution is an arbitrary function of position. We propose a method to generate such distributions which is physically motivated by a system of interacting particles, and apply it to the design and implementation of a microwave gradient index lens. While the demonstration was preformed at microwave wavelengths, this technique would also be particularly useful for designing devices for operation at IR and visible wavelengths where the fabrication of distributions of uniformly sized holes or columns is very easy.

Quantitative comparison of gradient index and refractive lenses

We analyze the Seidel wavefront aberrations and spot sizes of gradient index (GRIN) singlet lenses with Δn≈1. We consider and compare curved and planar GRIN lenses with F-numbers of 5 and 1 against equivalent refractive lenses. We find that the planar GRIN lenses generally have larger spot sizes compared to their refractive lens equivalents at wide angles. This appears to be due to an inability to correct for coma by adjusting the refractive index gradient alone. We can correct for the coma by bending the GRIN lens. This results in a singlet lens with performance close to but not exceeding that of the equivalent refractive lens. We also examine the impact of anisotropy on the planar GRIN lenses. We find that fabricating the planar GRIN lenses from a uniaxial medium has the potential to improve the performance of the lenses.