Metasurfaces for general transformations of electromagnetic fields
Professor Sergei Tretyakov, Aalto University, Finland
Electromagnetic fields can be controlled and transformed using engineered materials, often called metamaterials. The conventional paradigm of using metamaterials for transformations of electromagnetic fields implies that we engineer artificial materials in such a way that the polarization and conduction currents induced in the material, acting as secondary sources, create the desired fields outside or inside of the metamaterial sample. Huygens’ principle tells, however, that the same fields outside of the sample volume can be found as those generated by equivalent surface currents flowing only on the volume surface. Thus, it appears that the same field transformations can be achieved by engineering only surface currents of the volume surface, and there appears to be no reason why the volume enclosed by such an “engineered surface” could not be made negligibly small. In this review talk we will discuss electrically (optically) thin composite sheets with engineered and optimized properties: metasurfaces for general transformations of electromagnetic fields. The main motivation is a possibility to realize quite general functionalities (absorption, polarization transformations, control over reflection phase, focusing, etc.) using just single arrays of electrically small engineered particles. In this talk we will explain what physical properties of metasurface unit cells are responsible for various field transformations, provide basic design equations, and illustrate the potentials of this technology by several examples from our experimental work.
Metasurface Transformation Electromagnetics
Professor Stefano Maci, University of Sienna, Italy
Metasurfaces constitute a class of thin metamaterials, able to support surface wave propagation. At microwave frequencies, they are constituted by sub-wavelength size patches printed on thin grounded or ungrounded dielectric substrates. By averaging the tangential fields, the metasurfaces may be characterized by homogenised isotropic or anisotropic boundary conditions, which can be approximated through a homogeneous equivalent impedance. In absence of losses, this impedance supports a surface-wave propagation. The impedance can be spatially modulated by locally changing the sizes/orientation of the local printed element. This allows for a deformation of the wavefront which addresses the local wavector along not-rectilinear paths. In fact, the modulated anisotropic impedance imposes a local modification of the dispersion equation and, at constant operating frequency, of the local wavevector. The effect of the metasurface-modulation can be analized in the framework of Transformation Optics This talk reviews theory and implementation of metasurface transformation optics in microwave devices.
A new look at transformation electromagnetics approach for designing electromagnetic devices such as flat lenses, reflectarrays and blankets for radar cross section reduction of real-world objects
Professor Raj Mittra, Pennsylvania State University, USA
In this paper we present an alternative approach to addressing the problem of designing a number of practical “microwave” devices such as: blankets serving as absorbers for radar targets; flat lenses; and reflectarrays. Recently, these design problems been dealt with by a number of researchers using the transformation optics (TO) algorithm, which is based upon transforming the geometry of an object from real space to virtual space while keeping the Maxwell’s field solutions from real space to virtual space intact. The TO algorithm typically leads to designs that call for anisotropic values in real space in order to preserve the field variations as we navigate from the real space to virtual space and vice versa. In contrast to the TO, the proposed algorithm is based on “Field Transformation (FT),” as opposed to geometry transformation. The FT algorithm has been designed to transform the electromagnetic field distribution in an input aperture, generated by a given source distribution, to a desired distribution in the exit aperture. We show how we can cast the design problem into a Scattering Matrix approach, wherein the case of RCS reduction problem the design is based on controlling only the Magnitude of S11, whereas for the Lens or Reflectarray problems, we specify only the desired Phase of S12 without being concerned about its magnitude. In contrast to this, the TO imposes strict conditions on both the magnitude and phase characteristics of S11 and S12, which in turn calls for anisotropic metamaterials. The Scattering Matrix/Field Transformation approach avoids these problems altogether and is able to work with only materials for the lens and reflectarray problems, and with realizable complex (materials that have wideband characteristics and do not suffer from the shortcomings of the MTMs.
Spatial transformation enabled electromagnetic devices: From radio frequencies to optical wavelengths
Professor Douglas Werner, Pennsylvania State University, USA
Transformation optics provides scientists and engineers with a powerful new design paradigm to tailor the material properties of a medium (i.e., the spatial distribution and/or anisotropy), thereby allowing for comprehensive manipulation of electromagnetic waves with unprecedented flexibility. Based on such a mathematical framework, various interesting electromagnetic wave phenomena have been revealed over the last decade and employed to develop a wide range of novel devices that target applications throughout the electromagnetic spectrum. This presentation will focus on both theoretical and experimental investigations into the design of transformation optics enabled devices for shaping or controlling electromagnetic waves (radiation and scattering), at radio frequencies as well as optical wavelengths. Several types of coordinate mappings, which are variations based on the originally proposed transformation optics design methodology, are exploited for different applications to provide expanded design flexibility, enhanced device performance, and reduced implementation complexity. These include the complex coordinate transformation for simultaneous amplitude and phase control, linear coordinate transformations for broadband operation, conformal mappings with electrically tunable transformed space geometry for microwave antenna systems, and quasi-conformal mappings for optical applications. The illustrated design examples will serve to demonstrate the comprehensive capability of transformation optics in controlling electromagnetic waves, while the associated devices will open up new pathways toward future synthesis and design of integrated electromagnetic components, ranging from the microwave to optical spectral regimes.