Transformation Optics Research Articles

Conformal optical devices based on geodesic lenses.

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on geodesic lenses with special closed surfaces. The requirement is a continuous refractive index profile of dielectrics, which shows the almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal transparency (invisibility without cloaking region) and reflection. We can further achieve conformal invisible cloaks by two methods with perfect conductors. The conformal transformation optics method based on geodesic lenses may also find applications in other waves that obey the Helmholtz wave equation in two dimensions.

Smoothed Particle Method for Full-Wave Simulation of Microwave Applicators With Translational-Rotary Elements

Elements in both translation and rotation such as the screw propeller are widely applied to improve microwave heating uniformity. However, it is challenging to numerically model this heating process due to the difficulties in dynamic meshing for the moving elements. Our previous transformation optics method will be also burdensome to use in this case because it is very difficult to get the permittivity and permeability tensors. In this letter, a mesh-free numerical calculation based on a smoothed particle method is proposed to solve this complicated case. The proposed method uses smoothed particles to replace the meshes. Thus, the motion of the elements can be replaced by the motion of the particles and the dynamic meshing process can be avoided. A 2-D model is computed and the results are compared with those calculated by the finite element method. Good agreements are achieved.

Generalized Veselago-Pendry lenses via complex transformation optics.

Field solutions for a conventional Veselago-Pendry (VP) flat lens with ϵ=-ϵ 0 and μ=-μ 0 can be derived based on transformation optics (TO) principles. The TO viewpoint makes it clear that perfect imaging by a VP lens is a consequence of multivalued nature of the particular coordinate transformation involved. This transformation is equivalent to a "space folding" whereby one point in the transformed domain (source point) is mapped to three different points in the physical domain (the original source point plus two focal points). In theory, a VP lens would enable the recovery of the entire range of spectral components, i.e. both propagating and evanescent fields, thus characterizing a "perfect lens". Such lens, if lossess, is indeed "perfect" for monochromatic waves; however, for any realistic wave packet the space folding interpretation provided by TO makes it clear that a VP lens violates primitive causality constraints, which precludes any practical realization. Here, we utilize complex transformation optics (CTO) to derive generalized Veselago-Pendry (GVP) lenses without requiring a multivalued transformation. Unlike the conventional VP lens, the proposed lenses can fully recover the evanescent spectra under more general conditions that include the presence of (anisotropic) material loss/gain.

Space wave channeling enabled by conformal transformation optics

Transformation optics (TO) methodology provides an unconventional approach to mold the path of electromagnetic (EM) waves. Most of the previous works reported today are limited to control EM waves in either reflection or transmission mode. However, by merging TO and geometrical optics, we present a concept of space wave channeling metamaterial (SWCM) to manipulate backward and forward scattered waves simultaneously. As proof-of-principle, backward anomalous scattering, forward anomalous scattering, and multibeam arbitrary scattering patterns are realized through only one inhomogeneous isotropic dielectric medium with proper arrangement of embedded perfect electric conductor (PEC) pieces. Numerical full-wave simulations are performed to verify the potential realization of SWCM with all-dielectric gradient refractive index metamaterials. The proposed designing approach paves the way to the development of EM wave manipulations with feasible constitutive materials.

Cloaking of irregularly shaped bodies using coordinate transformation

The inception of transformation optics has opened avenues for designing of a plethora of applications related to the propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate transformation for the purpose of designing a cloak for a body having an arbitrary convex geometry. For the purpose of verification of the algorithm, a ray tracing process is carried out for an ellipsoid as well as an irregularly shaped body, both having axial symmetry. The ray tracing is carried out in a two dimensional plane since the transmitted ray vector would lie in the plane of incidence containing the incident ray vector and the normal vector to the cloak at the point of incidence. The approach not only reduces the numerical and analytical complexity compared to the conventional approach, but also reduces the order of singularity of the equation of Hamiltonian, improving the ability of the algorithm to cloak bodies with complex geometries which cannot be done using the conventional method.

Hydrodynamic Metamaterial Cloak for Drag-Free Flow.

Metamaterials engineered based on transformation optics have facilitated inaccessible manipulation of various physical phenomena. However, such metamaterials have not been introduced for flowing viscous matter. Here we propose a hydrodynamic metamaterial cloak that can conceal an object in two-dimensional creeping flow by guiding viscous forces. Coordinate transformation of fluidic space is implemented to calculate a tensoric viscosity based on a form invariance of Navier-Stokes equations. The hydrodynamic cloak with the viscosity tensor is numerically simulated to verify a fictitious fluidic empty space created in it. The corresponding metamaterial microstructure is systemically designed and fabricated in a microfluidic device. The experimental results reveal that a solid object amid the flow can be hydrodynamically hidden without entailing a disturbance in flow fields and experiencing a drag.

Non-paraxial design and fabrication of a compact OAM sorter in the telecom infrared

A novel optical device is designed and fabricated in order to overcome the limits of the traditional sorter based on log-pol optical transformation for the demultiplexing of optical beams carrying orbital angular momentum (OAM). The proposed configuration simplifies the alignment procedure and significantly improves the compactness and miniaturization level of the optical architecture. Since the device requires to operate beyond the paraxial approximation, a rigorous formulation of transformation optics in the non-paraxial regime has been developed and applied. The sample has been fabricated as 256-level phase-only diffractive optics with high-resolution electron-beam lithography, and tested for the demultiplexing of OAM beams at the telecom wavelength of 1310 nm. The designed sorter can find promising applications in next-generation optical platforms for mode-division multiplexing based on OAM modes both for free-space and multi-mode fiber transmission.

On-chip wavefront shaping with dielectric metasurface

Metasurfaces can be programmed for a spatial transformation of the wavefront, thus allowing parallel optical signal processing on-chip within an ultracompact dimension. On-chip metasurfaces have been implemented with two-dimensional periodic structures, however, their inherent scattering loss limits their large-scale implementation. The scattering can be minimized in single layer high-contrast transmitarray (HCTA) metasurface. Here we demonstrate a one-dimensional HCTA based lens defined on a standard silicon-on-insulator substrate, with its high transmission (<1 dB loss) maintained over a 200 nm bandwidth. Three layers of the HCTAs are cascaded for demonstrating meta-system functionalities of Fourier transformation and differentiation. The meta-system design holds potential for realizing on-chip transformation optics, mathematical operations and spectrometers, with applications in areas of imaging, sensing and quantum information processing.

An Axial Compression Planar Lens Antenna Based on Discrete Transformation Electromagnetics Using High-Impedance Surface Cells

A two-dimensional (2-D) convex lens is reshaped and compressed into a 2-D flat lens with a compression ratio of 52.6% by discrete transformation electromagnetics. The single-layer high-impedance surface cells are used to fill with the compressed zone to form a planar flat lens. A parallel-plate waveguide and a 1/4 λ reflector are used to ensure that the electromagnetic energy generated by the monopole flows to the lens. The planar lens antenna, 4.35 λ × 4 λ on the lens plane and 0.375 λ tall, is fabricated and measured in TM mode at 7.5 GHz. The measured data indicate that the proposed planar lens antenna achieves an 11.3 dBi gain, 16.7° half-power beamwidth on H -plane, and almost 260 MHz impedance bandwidth for S 11. The joint design of discrete transform electromagnetics and high-impedance surface cells is a new method, which has strong reference value for the miniaturization of other lens antennas.

Optofluidic light routing via analytically configuring streamlines of microflow

Transformation optics (TO) has emerged as an effective method to design metamaterials that can manipulate electromagnetic fields. Different from the traditional TO techniques which are mostly based on the solid metamaterials with a limited range of tunability, a novel streamline tracing-based transformation optofluidic (STTOF) method is proposed to manipulate the light path by analytically designating the light-carrying streamlines of the flow in a two-dimensional circular bounded domain. A dipole flow model is built to analytically calculate the streamlines of the flow field inside the domain permitting optical/fluidic source and sink pairs at arbitrary positions. Liquid core/liquid cladding (L2) configuration is used in the experiment to carry the light via following a specific streamline. Experimental results verify that the light paths agree well with the theoretical predictions, and show that a good range of tunability can be achieved by adjusting either the flow rates or the positions of optical/fluidic source and sink pairs.

Experimentally approaching to reciprocal cloaks via annulus-dielectric-metamaterials

Transformation optics has brought a wave of fanaticism among researchers to realize the first-ever invisible cloak over the past decade. Several relevant devices, including internal cloaks, external cloaks, and mantle cloaks, have already been proposed, with a few being experimentally demonstrated. Still, the proposed cloaks possess their insufficiencies to realize a reciprocal cloak. To better illustrate the cloak, here we report a new approach to a transformation-optics-based reciprocal cloak with designed dielectric-annulus-based metamaterials. Our results indicate we can easily control the anisotropic constitutive parameters at will. In addition, the as-fabricated cloak enables concurrent vision and movements of a hidden object, evidenced by both simulated and measured field distributions. More importantly, the cloak demands no bespoke design and is applicable to arbitrary electric-large objects. We affirm that we provide a method to developing the first-ever reciprocal cloak in experiments, and believe that the cloak could be further operated at visible ranges through the methodology we introduced, paving a route toward future applications in the fields of optics, physics, materials science, etc.

Cloaking of structures with convex or concave geometry using higher order parameterised function verified using ray tracing

The accomplishment of design for devices and applications such as cloaking has been feasible using transformation optics. This feasibility has been extended to the design of cloaks for concave bodies. Even though the process of cloaking in concave shaped bodies has been addressed in literature, the problem of poor accuracy and poor quality of cloaking remains. In accordance with the aim to outmanoeuvre the problem, the surface of interest which could be of convex or concave nature is modelled using a piecewise higher order parametric function. This function is expressed using Lagrange's interpolation. The calculation of piecewise model involves the inversion of the Lagrangian polynomial. But the inverse is numerically unstable because it is a Vandermonde matrix. Here, a method which is more stable than one that involves the direct inversion of the Vandermonde matrix, has been suggested using a recurrence relation. As the order of the function increases, it is observed that the efficiency of the cloaking improves further. It can be inferred that usage of the piecewise higher order parametric function along with a recurrence relation leads to an improvement in the quality and accuracy of cloaking.

Experimental demonstration of irregular thermal carpet cloaks with natural bulk material

Invisibility carpet cloak has been typically captivated as a popular notion that can render the objects beneath invisible from detection. Previous attempts either forcefully remove the small anisotropy caused by quasi-conformal mapping or resort to stacked multilayers according to the linear transformation optics. However, these classical prescriptions face complex implications of material parameter approximations and large carpet-to-object ratio in volume. Here, we build an easy-to-implement high-performance bilayer carpet cloak based on the analytical design for three different cloaking scenarios corresponding to bell-shaped, flat and semicircular carpet cloaks. The proposed methodology, which makes no approximation in any parameters, could fit irregular shapes of objects with existing natural bulk materials. We experimentally validate the proposed design for the above three cloaking scenarios. Our approach may inspire new alternatives to the functionalities for Laplacian fields.

Approximate cloaking for electromagnetic waves via transformation optics: Cloaking versus infinite energy

We study the approximate cloaking via transformation optics for electromagnetic waves in the time harmonic regime in which the cloaking device only consists of a layer constructed by the mapping technique. Due to the fact that no-lossy layer is required, resonance might appear and the analysis is delicate. We analyze both non-resonant and resonant cases. In particular, we show that the energy can blow up inside the cloaked region in the resonant case and/whereas cloaking is achieved in both cases. Moreover, the degree of visibility depends on the compatibility of the source inside the cloaked region and the system. These facts are new and distinct from known mathematical results in the literature.

A New Strategy for Transformation Optics With Index-Only Media

A new method to implement transformation optics is proposed. The method is simple but very effective. As long as the transformed regions in the virtual and physical spaces are finite, the material parameters obtained are free of zero or infinite values and can be realized by index-only media. It is the first time that the absence of zero values is guaranteed by the transformation scheme itself. The range for the refractive index is easy to control since the proposed scheme only requires the operation of stretching transformation. The designs of multibeam antennas, which convert the cylindrical waves to plane waves, are illustrated in this paper. The proposed method can be used to achieve many other electromagnetic and optical devices.

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.

Hybridization of singular plasmons via transformation optics

Surface plasmon resonances of metallic nanostructures offer great opportunities to guide and manipulate light on the nanoscale. In the design of novel plasmonic devices, a central topic is to clarify the intricate relationship between the resonance spectrum and the geometry of the nanostructure. Despite many advances, the design becomes quite challenging when the desired spectrum is highly complex. Here we develop a theoretical model for surface plasmons of interacting nanoparticles to reduce the complexity of the design process significantly. Our model is developed by combining plasmon hybridization theory with transformation optics, which yields an efficient way of simultaneously controlling both global and local features of the resonance spectrum. As an application, we propose a design of metasurface whose absorption spectrum can be controlled over a large class of complex patterns through only a few geometric parameters in an intuitive way. Our approach provides fundamental tools for the effective design of plasmonic metamaterials with on-demand functionality.

Application of transformation optics in radar cross section reduction of targets with arbitrary two-dimensional geometries

Transformation optics (TO) provides an unconventional approach to control electromagnetic (EM) waves in an arbitrary manner. In this study, a new strategy of radar cross section reduction (RCSR) was proposed for two-dimensional (2D) targets of arbitrary shape. Applying a complex coordinate transformation allowed us to control both the amplitude and the phase of EM fields. Inspired by the black hole concept, a swampy coating layer (SCL) was designed to make EM fields spin around the target and dissipate gradually. To achieve this goal, a complex Archimedean coordinate transformation function was exploited. This forced the incoming EM waves to propagate on a lossy path that was longer than the conventional radar absorbing materials (RAMs). Hence, it provided sufficient time for the SCL to dissipate the trapped EM wave. Depending on the target size, the SCL materials were analytically derived based on the coordinate transformation theory. However, these materials are feasibly independent of the target geometry and its constitutive materials. Several examples were provided to highlight the capability of the proposed TO-based strategy. This method reduced the radar cross section of 2D targets with irregular geometries and different materials. Numerical simulations were carried out to verify the feasibility of design by using a composite of the split ring resonator-meander line array. A significant RCSR level was noticed whose operating bandwidth was dictated by the employed metamaterial unit cell. So, the simplicity of the design sacrificed the RCSR bandwidth. Therefore, this paper revealed a new class of TO-based RAMs for 2D arbitrary-geometry targets of different materials.

Photonic crystal waveguide crossing based on transformation optics

The absolute instruments like the Maxwell’s fisheye (MFE) lens with aberration-free imaging properties have found interesting applications such as waveguide crossing. The flat wavefront of an optical wave in the waveguide does not match with the circular wavefront of the circular MFE lens at its edge, hence, we design and study the performance of a square MFE lens as photonic crystal waveguide crossing medium. We also have truncated the square MFE lens to a cross-shaped lens to squeeze it inside the crossing waveguides, therefore, practically no extra footprint is consumed by the truncated MFE lens. The numerical simulations show that graded photonic crystal-based implementation of the truncated MFE lens provides a bandwidth of 186 nm covering the entire S- and C-bands and partially covering the E- and L-bands of optical communication. The crosstalk levels are lower than −18 dB while the average insertion loss is 0.32 dB in the C-band.

Optimization of conformal whispering gallery modes in lima\xe7on-shaped transformation cavities

Directional light emission from high-Q resonant modes without significant Q-spoiling has been a long standing issue in deformed dielectric cavities. In limaçon-shaped gradient index dielectric cavities recently proposed by exploiting conformal transformation optics, the variation of Q-factors and emission directionality of resonant modes was traced in their system parameter space. For these cavities, their boundary shapes and refractive index profiles are determined in each case by a chosen conformal mapping which is taken as a coordinate transformation. Through the numerical exploration, we found that bidirectionality factors of generic high-Q resonant modes are not directly proportional to their Q-factors. The optimal system parameters for the coexistence of strong bidirectionality and a high Q-factor was obtained for anisotropic whispering gallery modes supported by total internal reflection.