Transformation optics design of a planar near field magnifier for sub-diffraction imaging.

It is well established that, under certain conditions, imaging systems with either isotropic negative index, or hyperbolic (indefinite) media can achieve super-resolution. However, achieving sub-diffraction limited imaging along with uniform aberration-free magnification can be challenging. In this article, we design, simulate, and evaluate the performance of planar 2D near-field magnifying lenses, based on the transformation-optic design principle. Specifically, we investigate a grid-relaxed transformation, that results in material properties that are more amenable to implementation. We discuss possible design choices in terms of: material properties, achievable resolution enhancement, adverse effect of loss tangent, magnification factor, and other design constraints affecting the imaging performance. We also present imaging performance results for a planar, near-field, 3× magnifier operating on a standard resolution target, based on a rigorous, 3D, electromagnetic simulation. This computational intensive result was achieved using cylindrical harmonic decomposition and the 2.5D electromagnetic simulation technique. Further, we investigate and propose a path to achieve higher magnification factors using cascaded elements.

Computationally fast EM field propagation through axi-symmetric media using cylindrical harmonic decomposition.

We describe and provide a systematic procedure for computationally fast propagation of arbitrary vector electromagnetic (EM) fields through an axially symmetric medium. A cylindrical harmonic field propagator is chosen for this purpose and in most cases, this is the best and the obvious choice. Firstly, we describe the cylindrical harmonic decomposition technique in terms of both scalar and vector basis for a given input excitation field. Then we formulate a generalized discrete Fourier-Hankel transform to achieve efficient vector basis decomposition. We allow a slower, pre-computation step, that finds a representation of the axi-symmetric medium as a transfer matrix in a discrete, cylindrical-harmonic basis. We find this matrix from a series of axi-symmetric (2D) finite element simulations (also known as the 2.5D technique). This transfer matrix approach significantly reduces the computational load when the transverse size or range exceeds about 30 wavelengths. This matrix is independent of the input excitation field for a given space-bandwidth product and hence makes it reusable for different excitation fields. We numerically validate the above approaches for different axi-symmetric EM scattering media which include a hemispherical gradient-index Maxwell's fish-eye lens, a transformation optics designed spherical invisibility cloak, a thin aspheric lens, and a cylindrical perfect lens.

Experimental realization of a metamaterial detector focal plane array.

We present a metamaterial absorber detector array that enables room-temperature, narrow-band detection of gigahertz (GHz) radiation in the S band (2-4 GHz). The system is implemented in a commercial printed circuit board process and we characterize the detector sensitivity and angular dependence. A modified metamaterial absorber geometry allows for each unit cell to act as an isolated detector pixel and to collectively form a focal plane array . Each pixel can have a dedicated microwave receiver chain and functions together as a hybrid device tuned to maximize the efficiency of detected power. The demonstrated subwavelength pixel shows detected sensitivity of -77 dBm, corresponding to a radiation power density of 27 nW/m(2), with pixel to pixel coupling interference below -14 dB at 2.5 GHz.

Optical design of reflectionless complex media by finite embedded coordinate transformations.

Transformation optics offers an unconventional approach to the control of electromagnetic fields. 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 are reflectionless and exhibit unusual electromagnetic behavior as confirmed by 2D full-wave simulations.

Scattering theory derivation of a 3D acoustic cloaking shell.

Through acoustic scattering theory we derive the mass density and bulk modulus of a spherical shell that can eliminate scattering from an arbitrary object in the interior of the shell--in other words, a 3D acoustic cloaking shell. Calculations confirm that the pressure and velocity fields are smoothly bent and excluded from the central region as for previously reported electromagnetic cloaking shells. The shell requires an anisotropic mass density with principal axes in the spherical coordinate directions and a radially dependent bulk modulus. The existence of this 3D cloaking shell indicates that such reflectionless solutions may also exist for other wave systems that are not isomorphic with electromagnetics.

Full-wave simulations of electromagnetic cloaking structures.

Pendry 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. Neither the coordinate transformation-based analytical formulation nor the supporting ray-tracing simulation indicate how material perturbations and full-wave effects might affect the solution. We report fully electromagnetic simulations of the cylindrical version of this cloaking structure using ideal and nonideal (but physically realizable) electromagnetic parameters that show that the low-reflection and power-flow bending properties of the electromagnetic cloaking structure are not especially sensitive to modest permittivity and permeability variations. 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. An imperfect but simpler version of the cloaking material is derived and is shown to reproduce the ray bending of the ideal material in a manner that may be easier to experimentally realize.

Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials.

We perform an experimental study of the phase and amplitude of microwaves interacting with and scattered by two-dimensional negative index metamaterials. The measurements are performed in a parallel plate waveguide apparatus at X-band frequencies (8-12 GHz), thus constraining the electromagnetic fields to two dimensions. A detection antenna is fixed to one of the plates, while a second plate with a fixed source antenna or waveguide is translated relative to the first plate. The detection antenna is inserted into, but not protruding below, the stationary plate so that fields internal to the metamaterial samples can be mapped. From the measured mappings of the electric field, the interplay between the microstructure of the metamaterial lattice and the macroscopic averaged response is revealed. For example, the mapped phase fronts within a metamaterial having a negative refractive index are consistent with a macroscopic phase-in accordance with the effective medium predictions-which travels in a direction opposite to the direction of propagation. The field maps are in excellent agreement with finite element numerical simulations performed assuming homogeneous metamaterial structures.