For centuries, the conventional approach to lens design has been to grind the surfaces of a uniform material in such a manner as to sculpt the paths that rays of light follow as they transit through the interfaces. Refractive lenses formed by this procedure of bending the surfaces can be of extremely high quality, but are nevertheless limited by geometrical and wave aberrations that are inherent to the manner in which light refracts at the interface between two materials. Conceptually, a more natural--but usually less convenient--approach to lens design would be to vary the refractive index throughout an entire volume of space. In this manner, far greater control can be achieved over the ray trajectories. Here, we demonstrate how powerful emerging techniques in the field of transformation optics can be used to harness the flexibility of gradient index materials for imaging applications. In particular we design and experimentally demonstrate a lens that is broadband (more than a full decade bandwidth), has a field-of-view approaching 180 degrees and zero f-number. Measurements on a metamaterial implementation of the lens illustrate the practicality of transformation optics to achieve a new class of optical devices.

The metasurface concept has emerged as an advantageous reconfigurable antenna architecture for beam forming and wavefront shaping, with applications that include satellite and terrestrial communications, radar, imaging, and wireless power transfer. The metasurface antenna consists of an array of metamaterial elements distributed over an electrically large structure, each subwavelength in dimension and with subwavelength separation between elements. In the antenna configuration we consider here, the metasurface is excited by the fields from an attached waveguide. Each metamaterial element can be modeled as a polarizable dipole that couples the waveguide mode to radiation modes. Distinct from the phased array and electronically scanned antenna (ESA) architectures, a dynamic metasurface antenna does not require active phase shifters and amplifiers, but rather achieves reconfigurability by shifting the resonance frequency of each individual metamaterial element. Here we derive the basic properties of a one-dimensional waveguide-fed metasurface antenna in the approximation that the metamaterial elements do not perturb the waveguide mode and are non-interacting. We derive analytical approximations for the array factors of the 1D antenna, including the effective polarizabilities needed for amplitude-only, phase-only, and binary constraints. Using full-wave numerical simulations, we confirm the analysis, modeling waveguides with slots or complementary metamaterial elements patterned into one of the surfaces.

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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. DOI: 10.1103/PhysRevLett.105.193902 PACS numbers: 42.79.Àe, 42.15.Ài Transformation optics (TO) is a unique tool for the design of complex electromagnetic media [1]. TO makes use of the form invariance of Maxwell's equations to mimic spatial transformations using distributions of inhomogeneous and anisotropic material constitutive parameters. TO has inspired many exotic devices, one of the most compelling of which being the electromagnetic ''invisibility'' cloak. However, the use of TO as a design methodology typically comes at high cost; the media derived from coordinate transformations generally involve spatial gradients in all nine components of the permittivity and permeability tensors. Though it is possible to find a basis that diagonalizes these tensors, the diagonal basis will generally be a function of position for all but the most simplistic and symmetric designs. Moreover, the required response is generally outside of the range of natural materials.Electromagnetic metamaterials (MMs) are used to access the extreme material parameters required by TO media. MMs, for example, were used to demonstrate a negative index of refraction [2,3] and electromagnetic cloaking [4]. However, the performance of these initial MM constructs was limited by a combination of narrow bandwidth and relatively large absorption. The typical limitation for MM designs has been the requirement of constitutive parameters that have a large range of values for both permittivity and permeability. The implementation of artificial paramagnetism, in particular, requires resonant inclusions that are inherently lossy and dispersive, leading to absorption and reduced bandwidth. More recently, the development of coordinate transformation methods in optical design approaches has significantly advanced MM complexity: independent magnetic and electric responses are required in all directions for general TO designs, yet most MM elements provide a controlled response in one or two directions. Were one to attempt to control all of the tensor elements of a MM simultaneously, multiple MM elements would need to be either colocated or closely positioned, introducing very complicated magnetoelectric coupling difficult to control or even quantify using current MM retrieval techniques [5].Fortunately, the enormous degree of flexibility available in coordinate transformations can alleviate many of the c...

Transformation optics is widely associated with the design of unconventional electromagnetic devices, such as electromagnetic cloaks or concentrators. However, a wide range of conventional optical devices with potentially advantageous properties can be designed by the transformation optical approach. For example, a coordinate transformation can be introduced that compresses a region of space, resulting in an overall decrease in the thickness of an optical instrument such as a lens. The optical properties of a transformed lens, such as Fresnel reflection or aberration profile, are equivalent to those of the original lens, while the transformed lens and the bounding transformation optical material are thinner than the original lens. This approach to flattening the profile of a lens represents an advantage over the use of a higher dielectric material because it does not introduce greater Fresnel reflections or require a redesign of the basic optic. Though transformation optical media are generally anisotropic, with both electric and magnetic response, it is possible to arrive at a dielectric-only transformation optical distribution for a lens interacting with transverse-magnetic (TM) polarized light. The dielectric-only distribution can be implemented using broad-band, low-loss metamaterials. Lens designs for both a full transformation and a dielectric-only implementation are discussed and confirmed via finite-element simulations.

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We consider the design and modeling of metasurfaces that couple energy from guided waves to propagating wavefronts. This is a first step towards a comprehensive, multiscale modeling platform for metasurface antennas-large arrays of metamaterial elements embedded in a waveguide structure that radiates intro free-space-in which the detailed electromagnetic responses of metamaterial elements are replaced by polarizable dipoles. We present two methods to extract the effective polarizability of a metamaterial element embedded in a one-or two-dimensional waveguide. The first method invokes surface equivalence principles, averaging over the effective surface currents and charges within an element to obtain the effective dipole moments; the second method is based on computing the coefficients of the scattered waves within the waveguide, from which the effective polarizability can be inferred. We demonstrate these methods on several variants of waveguidefed metasurface elements, finding excellent agreement between the two, as well as with analytical expressions derived for irises with simpler geometries. Extending the polarizability extraction technique to higher order multipoles, we confirm the validity of the dipole approximation for common metamaterial elements. With the effective polarizabilities of the metamaterial elements accurately determined, the radiated fields generated by a metasurface antenna (inside and outside the antenna) can be found self-consistently by including the interactions between polarizable dipoles. The dipole description provides an alternative language and computational framework for engineering metasurface antennas, holograms, lenses, beam-forming arrays, and other electrically large, waveguide-fed metasurface structures.

Accurate and efficient methods for beam-steering of holographic metamaterial antennas is of critical importance for enabling consumer usage of satellite data capacities. We develop an optimization algorithm capable of performing adaptive, realtime control of antenna patterns while operating in dynamic environments. Our method provides a first analysis of the antenna pattern optimization problem in the context of metamaterials and for the purpose of directing the central beam and significantly suppressing sidelobe levels. The efficacy of the algorithm is demonstrated both on a computational model of the antenna and experimentally. Due to their exceptional portability, low-power consumption and lack of moving parts, metamaterial antennas are an attractive and viable technology when combined with proven software engineering strategies to optimize performance.