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.

Optical lens compression via transformation optics

We show in this letter that, by using an inhomogeneous metamaterial shell, it is possible to achieve highly directive emission with a small antenna aperture. The material parameters of the metamaterial substrate are obtained by a nonmonotonic optical transformation. Therefore, a large antenna can be effectively transformed to an equivalent one with much smaller aperture. Full-wave finite-element modeling has been performed to confirm this point. The concept proposed here provides a possible solution to reduce the size of antenna without disturbing the radiation characteristics.

High-directivity antenna with small antenna aperture

In Roman mythology, the god Janus was depicted with two faces, looking in opposite directions. This led to the phrase ‘‘Janus faced’’ which is mostly used for a ‘‘two-faced’’ or deceitful character of a person. Within integrated photonics a concept like Janus can provide a new class of multi-functional optical meta-elements which could be a key ingredient in achieving compact and high speed photonic systems. While therehave been great strides in the miniaturization of optical elements, such photonic integration largely consists of combining discrete components at the chip level. Here, we present a new approach of designing a single optical element that possesses simultaneously multiple distinct functions. We employ transformation optics to design the optical space and manipulate the light propagation using a metamaterial with spatially varying permittivity. Our experiment demonstrates a single optical ‘‘Janus’’ device that acts as a lens as well as a beam-shifter at the same time. The emerging field of transformation optics has provided a new design methodology allowing an unprecedented manipulation of light propagation, with the optical cloak as the most prominent example. [1,2] However, transformation optics can also be used to enhance the functionality of conventional optical elements. Traditionally, these conventional elements only involve stretching or compressing the optical space in one direction whereas the remaining dimensions in space are unaltered. For example, an optical lens can be interpreted as a result of a simple wavefront transformation that molds the flow of light in a particular direction. A lens works well in one direction whereas light propagating perpendicular to this direction is strongly perturbed. Since space can be modified in two or three dimensions simultaneously, the additional degrees of freedom provided by transformation optics can be used to spatially imprint elements into a single optical Janus or metadevice. Here, we present a transformation optics design approach together with an experimental demonstration that takes advantage of this dimensionality by integrating multiple, independent optical

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An optical "Janus" device for integrated photonics.

Transformation Optics has been proven a versatile technique for designing novel electromagnetic devices and it has much wider applicability in many subject areas related to general wave equations. Among them, quasi-conformal transformation optics (QCTO) can be applied to minimize anisotropy of transformed media and has opened up the possibility to the design of broadband antennas with arbitrary geometries. In this work, a wide-angle scanning conformal phased array based on all-dielectric QCTO lens is designed and experimentally demonstrated. Excited by the same current distribution as such in a conventional planar array, the conformal system in presence of QCTO lens can preserve the same radiation characteristics of a planar array with wide-angle beam-scanning and low side lobe level (SLL). Laplace’s equation subject to Dirichlet-Neumann boundary conditions is adopted to construct the mapping between the virtual and physical spaces. The isotropic lens with graded refractive index is realized by all-dielectric holey structure after an effective parameter approximation. The measurements of the fabricated system agree well with the simulated results, which demonstrate its excellent wide-angle beam scanning performance. Such demonstration paves the way to a robust but efficient array synthesis, as well as multi-beam and beam forming realization of conformal arrays via transformation optics.

Experimental demonstration of conformal phased array antenna via transformation optics

Anisotropic metamaterial devices

Transformation optics is a recently appreciated methodology for the design of complex media that control the propagation of electromagnetic and other types of waves. The transformation optical technique involves the use of coordinate transformations applied to some region of space, providing a conceptual means to redirect the flow of waves. Successfully designed devices to date have made use of transformations acting on passive space only; however, the technique can also be applied when source distributions (e.g., current and charge) are included within the space being transformed. In this paper we present examples of source transformations that illustrate the potential of these expanded transformation optical methods. In particular, using finite-element full-wave simulations, we confirm the restoration of dipole radiation patterns from both a distorted ‘pin-wheel’ antenna and a bent dipole partially occluded by a cylindrical scatterer. We propose the technique of source transformations as a powerful approach for antenna design, especially in relation to conformal antennas.

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Optical source transformations.

We apply the theory of transformation electromagnetics to source arrays and show that a complex conformal antenna array can be made to behave like a geometrically different array when surrounded with a properly designed transformation electromagnetics medium Numerical simulations are presented to show how a nonuniform circular array can be made to radiate and receive as a uniformly spaced linear array In this way, transformation electromagnetics provides a method by which all of the advantages of simple arrays in array processing, such as beamforming, can be retained in an array whose elements are constrained to a complex geometry

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Conformal array design with transformation electromagnetics

Transformation optics can be used to design media with unique properties that alter the behavior of electromagnetic waves in passive space and recently in space containing source distributions. We present source transformations where current from a linear radiator is spread over a cylindrical shell with various cross sections. The semianalytic transformations are based on superellipse equations. Finite-element full-wave simulations of transformations from a dipole to a cylinder, diamond-shaped cylinder, and flattened cylinder are presented. The radiation pattern of the dipole seen by an outside observer is replicated in all cases demonstrating the potential applicability of source transformations to conformal antenna design.

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Electromagnetic source transformations using superellipse equations

Transformation optics is a methodology that has proven useful in the design of complex media used to alter and control electromagnetic waves in either passive space or regions that contain source distributions. Recently it has been shown that the application of source transformations can reshape field radiation patterns corresponding to arbitrarily shaped sources. In the accompanying numerical confirmations, the effect of source transformations on fundamental quantities that are critical to the design and evaluation of antenna based systems--such as complex power and impedance, remain unexplored. In this paper, we present results of theoretical analysis as well as full wave finite element simulations, proving that the complex power and impedance associated with an electromagnetic source are not changed by source transformation methods. These results open the door to the application of source transformations for the design of practical antenna based systems, such as conformal and phased array antenna design. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26077

Jeffery Allen

Papers

Optical source transformations.

Conformal array design with transformation electromagnetics

Electromagnetic source transformations using superellipse equations

Impedance and complex power of radiating elements under electromagnetic source transformation