Transformation Optics Technique Research Articles

A Transformation-Optics-Based Flat Metamaterial Luneburg Lens Antenna With Zero Focal Length

The transformation optics (TO) technique has been widely applied in the volume reduction of Luneburg lens (LL) in both optical and microwave regimes. However, it is found that the focus is usually not located on the surface of the transformed LL anymore after applying TO. The focus location shift results in a limited volume reduction, severe reflection from the new lens surface, and limited scanning range with increased spillover loss. This article theoretically studies and proposes a TO-based LL antenna with zero focal length by considering the phase mismatch caused by space discontinuity. The study first reveals that the transformation of an LL alone without sustaining the original boundary inherently deteriorates the original focusing property even before exerting any approximation. To validate the idea, a flat metamaterial LL antenna using TO is proposed, approximated, and fabricated using an integrated dielectric and conductive 3-D printing manufacturing process. The feeding patch antenna remains on the surface of the transformed lens. The thickness of the proposed antenna is reduced to 1/3 of a traditional LL in its boresight, while a ±20° beam scanning range is achieved with linearly shifted feedings. The study verifies that it is essential to ensure phase matching at the radiation boundary to maintain the original focusing property of an LL. The information derived from the study evidences the conditions of the enforcement of TO in electromagnetic problems such as dielectric lenses.

Radially Periodic Metasurface Lenses for Magnetic Field Collimation in Resonant Wireless Power Transfer Applications

In this paper, a new procedure and topology of magnetic metasurface lens are proposed for improving the performance of Resonant Wireless Power Transfer systems. Firstly, three subwave-length unit cells are optimized in order to get negative magnetic permeability in the same frequency, each one with a different refractive index, and they are experimentally characterized. Then, the Transformation Optics technique is applied in order to find the unit cell arrangements which lead to the magnetic field focusing in a given direction. For this purpose, two coordinate transformations are proposed, and the effective electric permittivity and permeability that generate these profiles are calculated. It is shown from simulations and measurements that the refractive index gradient produced by the radial disposition of the unit cells can lead to a magnetic field manipulation similar to the optical converging and diverging lenses. Both metamaterials lenses are built, and the calculation of the magnetic flux density as a function of the measured induced voltage in a probe coil verifies their effects on the magnetic field. Finally, their performance in a resonant wireless power transfer system is tested, and improvements in terms of efficiency and range are presented. The proposed design method and the lenses that were developed demonstrate that metasurface lenses can improve efficiency without reducing the range, once these lenses are positioned close to the transmitter coil. Besides that, this method can reduce the losses due to misalignment between coils once the field can be collimated in a specific direction.

Limitations and potentials of generalized Veselago-Pendry lenses

We study the imaging performance of anisotropic generalized Veselago–Pendry (GVP) lenses derived via complex transformation optics technique. The derived material tensors of such generalized lenses can be controlled via a complex coordinate transformation parameter resulting in an anisotropic constitutive tensor with loss/gain characteristics. We discuss their limitations and potentials based on the parametric analysis of material properties. We show that, although GVP lenses are not affected by the loss/gain level, akin to conventional VP lenses, their subwavelength imaging performance is also susceptible to material deviations from their original values. We also discuss that the resolution of GVP lenses can be significantly improved by tuning the real part of the transformation parameter. The proposed GVP lenses could be realized using, for instance, a metal-dielectric structure, with improved subwavelength imaging characteristics.

Plasmon Localization Assisted by Conformal Symmetry

Plasmonic systems have attracted remarkable interest due to their application to the subwavelength confinement of light and the associated enhancement of light-matter interactions. However, this requires light to dwell at a given spatial location over timescales longer than the coupling rate to any relevant loss mechanism. Here we develop a general strategy for the design of stopped-light plasmonic metasurfaces, by taking advantage of the conformal symmetry which underpins near-field optics. By means of the analytical technique of transformation optics, we propose a class of plasmonic gratings which is able to achieve ultra-slow group velocities, effectively freezing surface plasmon polaritons in space over their whole lifetime. Our method can be universally applied to the localization of polaritons in metallic systems, as well as in highly doped semiconductors and even two-dimensional conductive and polar materials, and may find potential applications in nano-focusing, nano-imaging, spectroscopy and light-harvesting.

Surface second-harmonic generation from metallic-nanoparticle configurations: A transformation-optics approach

We study surface second-harmonic generation (SHG) from a singular plasmonic structure consisting of touching metallic wires. We use the technique of transformation optics and relate the structure to a rather simpler geometry, a slab waveguide. This allows us to obtain an analytical solution to the problem, revealing rich physical insights. We identify various conditions that govern the SHG efficiency. Importantly, our analysis demonstrates that apart from the mode-matching condition, phase-matching condition is relevant even for this sub-wavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.

Frequency domain transformation optics for diffusive photon density waves’ cloaking

We make use of transformation optics technique to realize cloaking operation in the light diffusive regime, for spherical objects. The cloak requires spatially heterogeneous anisotropic diffusivity, as well as spatially varying speed of light and absorption. Analytic calculations of Photon's fluence confirm minor role of absorption in reduction of far-field scattering, and a monopole fluence field converging to a constant in the static regime in the invisibility region. The latter is in contrast to acoustic and electromagnetic cloaks, for which the field vanishes inside the core. These results are finally discussed in the context of mass diffusion, where cloaking can be achieved with a heterogeneous anisotropic diffusivity.

A Microwave Invisibility Cloak: The Design, Simulation, and Measurement of a Simple and Effective Frequency-Selective Surface-Based Mantle Cloak

In recent years, there has been a growing interest in developing invisibility cloaks that can conceal an object. These techniques are often based either on coating a dielectric or conducting object with a homogeneous plasmonic layer of negative permittivity [1] or on creating multilayer structure [2] that cancels the scattering of the cloaked object (i.e., scattering cancelation technique). The technique may also be based on an inhomogeneous layer that bends electromagnetic waves around the region occupied by the cloaked object without interacting with it (i.e., transformation optics technique) [3].

Rigorous simulation of nonlinear optomechanical coupling in micro- and nano-structured resonant cavities

A numerical method aimed to predict the optomechanical dynamics in micro- and nano-structured resonant cavities is introduced here. The rigorousness of it is ensured by exploiting the harmonic version of the transformation optics (TO) technique and by considering all the energy-transduction contributions of electrostriction, radiation pressure, photoelasticity and moving boundaries. Since our full-wave approach implements a multi-modal analysis and also considers material losses, from both a mechanical and an optical point of view, a considerable step further has been made in respect to the standard optomechanical perturbative theory. The efficiency and the versatility of the strategy are tested by analysing the optomechanical behaviour of a corrugated Si-based nanobeam and comparing numerical results to experimental ones from the literature.

A reprogrammable multifunctional chalcogenide guided-wave lens.

The transformation optics (TO) technique, which establishes an equivalence between a curved space and a spatial distribution of inhomogeneous constitutive parameters, has enabled an extraordinary paradigm for manipulating wave propagation. However, extreme constitutive parameters, as well as a static nature, inherently limit the simultaneous achievement of broadband performance, ultrafast reconfigurability and versatile reprogrammable functions. Here, we integrate the TO technique with an active phase-change chalcogenide to achieve a reconfigurable multi-mode guided-wave lens. The lens is made of a Rinehart-shaped curved waveguide with an effective refractive index gradient profile through partially crystallizing Ge2Sb2Te5. Upon changing the bias time of the external voltage imparted to the Ge2Sb2Te5 segments, the refractive index gradient profile can be tuned with a transformative platform for various functions for visible light. The electrically reprogrammable multi-mode guided-wave lens is capable of dynamically acquiring various functionalities with an ultrafast response time. Our findings may offer a significant step forward by providing a universal method to obtain ultrafast and highly versatile guided-wave manipulation, such as in Einstein rings, cloaking, Maxwell fish-eye lenses and Luneburg lenses.

Performance enhancement of linear active electronically scanned arrays by means of MbD-synthesized metalenses

The key problem of improving the radiation performances or enabling additive functionalities of linear active electronically scanned arrays (AESAs), without increasing the number of radiating elements nor requiring a re-design of the radiators and/or the feeding network, is addressed by means of a suitably formulated Material-by-Design (MbD) approach. The quasi-conformal transformation optics (QCTO) technique and a customized source inversion (SI) strategy are jointly exploited to synthesize enhanced architectures, composed by a metamaterial lens and a tapered version of the original feeding network, able to match the radiation characteristics of significantly larger and/or different (from the original one) apertures. A set of representative benchmark results is reported to assess the effectiveness of the proposed MbD-designed architecture as well as to highlight the existing trade-off between achievable improvements and the complexity of the arising architectural solution.

Perfectly matched layers for flexural waves in Kirchhof–Love plates

We propose Perfectly Matched Layers (PMLs) for flexural waves in plate structures. The analytical model is based on transformation optics techniques applied to the biharmonic fourth-order partial differential equation describing flexural vibrations in Kirchhoff–Love plates. We show that perfect boundary conditions are not an optimal solution, since they depend on the incident waves. The full analytical form of PMLs and zero reflection conditions at the boundary between homogeneous and PML domains are given. The implementation in a Finite Element (FEM) code is described and an eigenfrequency analysis is given as a possible methodology to check the implementation itself. A measure of the performances of the PMLs is introduced and the effects of element discretization, boundary conditions, frequency, dimension of the PML, amount of transformation and dissipation are detailed. It is shown that the model gives excellent results also when the applied load approaches the PML domain.

Bespoke Lenses Based on Quasi-Conformal Transformation Optics Technique

In this paper, a systematic method to design a quasi-optimum lens profile based on quasi-conformal transformation optics technique for a given excitation is presented. This method is applied to a number of conventional antennas, such as an aperture and a log-spiral slot. In all these configurations, an increase of the directivity is observed. Furthermore, using this method, a quasi-optimum graded index lens for a broadband enhanced leaky slot excitation is designed and the results are compared with a hyperhemispherical lens with and without matching layers. Our proposed methodology demonstrates to be able to increase the directivity, to reduce the sidelobes and the cross polarization in a broad bandwidth from 20 to 70 GHz. Due to the continuously changed dielectric constant of the lens profile, reflections are also reduced considerably inside the lens.

Transformation-optics simulation method for stimulated Brillouin scattering

We develop a novel approach to enable the full-wave simulation of stimulated Brillouin scattering and related phenomena in a frequency-domain, finite-element environment. The method uses transformation optics techniques to implement a time-harmonic coordinate transform that reconciles the different frames of reference used by electromagnetic and mechanical finite-element solvers. We show how this strategy can be successfully applied to bulk and guided systems, comparing the results with the predictions of established theory.

Perfectly matched layers for flexural waves: An exact analytical model

In this paper we present an analytical model of Perfectly Matched Layers for flexural waves within elongated beam structures. The model is based on transformation optics techniques and it is shown to work both in time harmonic and transient regimes. A comparison between flexural and longitudinal waves is detailed and it is shown that the bending problem requires special interface conditions. A connection with transformation of eigenfrequencies and eigenmodes is given and the effect of the additional boundary conditions introduced at the border of the Perfectly Matched Layer domain is discussed in detailed. Such a model is particularly useful for Finite Element analyses pertaining propagating flexural waves in infinite domain.

Full-wave algorithm to model effects of bedding slopes on the response of subsurface electromagnetic geophysical sensors near unconformities

We propose a full-wave pseudo-analytical numerical electromagnetic (EM) algorithm to model subsurface induction sensors, traversing planar-layered geological formations of arbitrary EM material anisotropy and loss, which are used, for example, in the exploration of hydrocarbon reserves. Unlike past pseudo-analytical planar-layered modeling algorithms that impose parallelism between the formation's bed junctions however, our method involves judicious employment of Transformation Optics techniques to address challenges related to modeling relative slope (i.e., tilting) between said junctions (including arbitrary azimuth orientation of each junction). The algorithm exhibits this flexibility, both with respect to loss and anisotropy in the formation layers as well as junction tilting, via employing special planar slabs that coat each "flattened" (i.e., originally tilted) planar interface, locally redirecting the incident wave within the coating slabs to cause wave fronts to interact with the flattened interfaces as if they were still tilted with a specific, user-defined orientation. Moreover, since the coating layers are homogeneous rather than exhibiting continuous material variation, a minimal number of these layers must be inserted and hence reduces added simulation time and computational expense. As said coating layers are not reflectionless however, they do induce artificial field scattering that corrupts legitimate field signatures due to the (effective) interface tilting. Numerical results, for two half-spaces separated by a tilted interface, quantify error trends versus material and sensor characteristics. We finally exhibit responses of sensors traversing three-layered media, where we vary the anisotropy, loss, and relative tilting of the formations and explore the sensitivity of the sensor's complex-valued measurements.

Steering electromagnetic beams with conical curvature singularities.

We describe how the transformation-optics technique can be used to design an effective medium mimicking the conical curvature singularity. Anholonomic coordinate transformation gives rise to linear topological defects that break the rotational symmetry. The bending and splitting of the optical beams are found analytically and numerically, depending on the incident direction and the topological charge. Beyond their practical applications to omnidirectional beam steering for photonics, our findings set forth an attractive realm to simulate the relevant physical phenomena in the optical laboratory.

Array Miniaturization Through <italic>QCTO-SI</italic> Metamaterial Radomes

The array miniaturization problem is addressed by means of a material-by-design approach. More specifically, an innovative strategy that integrates a quasi-conformal transformation optics ( QCTO ) technique and a source inversion method is proposed to design radome-coated arrays exhibiting the same radiation properties of wider virtual arrangements comprising more antenna elements. Toward this end, the state-of-the-art QCTO theory is generalized to account for source constraints within the synthesis process. Representative numerical examples are provided to assess the reliability, the flexibility, and the effectiveness of the proposed synthesis approach as well as the possibility to realize suboptimal radomes with simplified, but cheaper/easier, structures (e.g., structures based on tiles of isotropic dielectrics).

Anisotropy minimization via least squares method for transformation optics.

In this work the least squares method is used to reduce anisotropy in transformation optics technique. To apply the least squares method a power series is added on the coordinate transformation functions. The series coefficients were calculated to reduce the deviations in Cauchy-Riemann equations, which, when satisfied, result in both conformal transformations and isotropic media. We also present a mathematical treatment for the special case of transformation optics to design waveguides. To demonstrate the proposed technique a waveguide with a 30° of bend and with a 50% of increase in its output width was designed. The results show that our technique is simultaneously straightforward to be implement and effective in reducing the anisotropy of the transformation for an extremely low value close to zero.

Interface-Flattening Transform for EM Field Modeling in Tilted, Cylindrically Stratified Geophysical Media

We propose and investigate an “interface-flattening” transformation, hinging upon transformation optics (TO) techniques, to facilitate the rigorous analysis of electromagnetic (EM) fields radiated by sources embedded in tilted, cylindrically layered geophysical media. Our method addresses the major challenge in such problems of appropriately approximating the domain boundaries in the computational model while, in a full-wave manner, predicting the effects of tilting in the layers. When incorporated into standard pseudo-analytical algorithms, moreover, the proposed method is quite robust, as it is not limited by absorption, anisotropy, and/or eccentering profile of the cylindrical geophysical formations, nor is it limited by the radiation frequency. These attributes of the proposed method are in contrast to past analysis methods for tilted-layer media that often place limitations on the source and medium characteristics. Through analytical derivations as well as a preliminary numerical investigation, we analyze and discuss the method's strengths and limitations.

Near-perfect nonmagnetic invisibility cloaking

We suggest a way to obtain a near-perfect nonmagnetic invisibility cloak structure. Within the particular example of cylindrical geometry and transverse magnetic polarization of light, we show that such a cloak can operate for a cylindrical object of very large diameter, keeping the total scattering cross section limited by $2\ensuremath{\lambda}/\ensuremath{\pi}$. We also demonstrate that proposed cloak does not require extremely high values of dielectric permittivity, in contrast to the cloaks designed according to a transformation optics technique.