Transformation-optical design of adaptive beam bends and beam expanders

Polariton Microfluidics for Nonreciprocal Dragging and Reconfigurable Shaping of Polaritons

Dielectric environment engineering is an efficient and general approach to manipulating polaritons. Liquids serving as the surrounding media of polaritons have been used to shift polariton dispersions and tailor polariton wavefronts. However, those liquid-based methods have so far been limited to their static states, not fully unleashing the promise offered by the mobility of liquids. Here, we propose a microfluidic strategy for polariton manipulation by merging polaritonics with microfluidics. The diffusion of fluids causes gradient refractive indices over microchannels, which breaks the symmetry of polariton dispersions and realizes the microfluidic analogue to nonreciprocal polariton dragging. Based on polariton microfluidics, we also designed a set of on-chip polaritonic elements to actively shape polaritons, including planar lenses, off-axis lenses, Janus lenses, bends, and splitters. Our strategy expands the toolkit for the manipulation of polaritons at the subwavelength scale and possesses potential in the fields of polariton biochemistry and molecular sensing.

Design of a Low-Reflection Flat Lens Antenna Based on Conformal Transformation Optics

In this paper, a wideband flat lens antenna with low reflection and good performance is presented based on conformal transformation optics (CTO). Physical space optimization is applied to eliminate singular refractive index values. Furthermore, we employ the optical path rescaling method to enhance the sub-unity refractive indices and to reduce reflection. Therefore, an implementable all-dielectric isotropic medium is obtained. The final flat lens profile comprises six layers with a constant permittivity value in each layer. Simulation results of the three-dimensional structure indicate that the designed flat lens operates in a wide frequency bandwidth. The flat lens antenna has an S₁₁ value of less than -15 dB in the frequency range of 13 to 30 GHz. The proposed lens was designed and simulated using COMSOL Multiphysics, and radiation performance results were validated using the CST Studio Suite. The simulated radiation pattern shows that the side lobe level is less than -16.5 dB in two simulation software programs, and the half-power beam width varies from 5.6° to 2.7° with increasing frequency. Moreover, the simulated antenna gain is about 28.3-35.5 dBi in the 13-30 GHz frequency range.

Transformation-optics modeling of 3D-printed freeform waveguides

Multi-photon lithography allows us to complement planar photonic integrated circuits (PIC) by in-situ 3D-printed freeform waveguide structures. However, design and optimization of such freeform waveguides using time-domain Maxwell's equations solvers often requires comparatively large computational volumes, within which the structure of interest only occupies a small fraction, thus leading to poor computational efficiency. In this paper, we present a solver-independent transformation-optics-(TO-) based technique that allows to greatly reduce the computational effort related to modeling of 3D freeform waveguides. The concept relies on transforming freeform waveguides with curved trajectories into equivalent waveguide structures with modified material properties but geometrically straight trajectories, that can be efficiently fit into rather small cuboid-shaped computational volumes. We demonstrate the viability of the technique and benchmark its performance using a series of different freeform waveguides, achieving a reduction of the simulation time by a factor of 3-6 with a significant potential for further improvement. We also fabricate and experimentally test the simulated waveguides by 3D-printing on a silicon photonic chip, and we find good agreement between the simulated and the measured transmission at λ = 1550 nm.

Strictly conformal transformation optics for directivity enhancement and unidirectional cloaking of a cylindrical wire antenna

Using conformal transformation optics, a cylindrical shell made of an isotropic refractive index material is designed to improve the directivity of a wire antenna while making it unidirectionally invisible. If the incident wave comes from a specific direction, it is guided around the wire. Furthermore, when an electrical current is used to excite the wire, the dielectric shell transforms the radiated wave into two lateral beams, improving directivity. The refractive index of the dielectric shell is calculated using the transformation optics recipe after establishing a closed-form conformal mapping between an annulus and a circle with a slit. The refractive index is then modified and discretized using a hexagonal lattice. Ray-tracing and full-wave simulations with COMSOL Multiphysics are used to validate the functionality of the proposed shell.

Transformation Metamaterials

Based on the form-invariance of Maxwell's equations under coordinate transformations, mathematically smooth deformation of space can be physically equivalent to inhomogeneous and anisotropic electromagnetic (EM) medium (called a transformation medium). It provides a geometric recipe to control EM waves at will. A series of examples of achieving transformation media by artificially structured units from conventional materials is summarized here. Such concepts are firstly implemented for EM waves, and then extended to other wave dynamics, such as elastic waves, acoustic waves, surface water waves, and even stationary fields. These shall be cataloged as transformation metamaterials. In addition, it might be conceptually attractive and practically useful to control diverse waves for multi-physics designs.

Optical meta-waveguides for integrated photonics and beyond

The growing maturity of nanofabrication has ushered massive sophisticated optical structures available on a photonic chip. The integration of subwavelength-structured metasurfaces and metamaterials on the canonical building block of optical waveguides is gradually reshaping the landscape of photonic integrated circuits, giving rise to numerous meta-waveguides with unprecedented strength in controlling guided electromagnetic waves. Here, we review recent advances in meta-structured waveguides that synergize various functional subwavelength photonic architectures with diverse waveguide platforms, such as dielectric or plasmonic waveguides and optical fibers. Foundational results and representative applications are comprehensively summarized. Brief physical models with explicit design tutorials, either physical intuition-based design methods or computer algorithms-based inverse designs, are cataloged as well. We highlight how meta-optics can infuse new degrees of freedom to waveguide-based devices and systems, by enhancing light-matter interaction strength to drastically boost device performance, or offering a versatile designer media for manipulating light in nanoscale to enable novel functionalities. We further discuss current challenges and outline emerging opportunities of this vibrant field for various applications in photonic integrated circuits, biomedical sensing, artificial intelligence and beyond.

Field Decorrelation and Isolation Improvement in an MIMO Antenna Using an All-Dielectric Device Based on Transformation Electromagnetics

This work presents a new technique for enhancing the performance of a multiple-input multiple-output (MIMO) antenna by improving its correlation coefficient ρ. A broadband dielectric structure is designed using the transformation electromagnetics (TE) concept to decorrelate the fields of closely placed radiating elements of an MIMO antenna, thereby decreasing ρ and mutual coupling. The desired properties of the broadband dielectric wave tilting structure (DWTS) are determined by using quasi-conformal transformation electromagnetics (QCTE). Next, the permittivity profile of the DWTS is realized by employing air-hole technology, which is based on the effective medium theory, and the DWTS is fabricated using the additive manufacturing (3D printing) technique. The effectiveness of the proposed technique is verified by designing two-element patch-based MIMO antenna prototypes operating at 3 GHz, 5 GHz, and 7 GHz, respectively. The proposed technique helped to reduce the correlation coefficient ρ in the range of 37% to 99% in the respective operating bandwidth of each MIMO antenna, thereby, in each case, improving the isolation between antenna elements by better than 3 dB, which is an excellent performance.

Flat lens design to rotate a cylindrical beam of a line source to an arbitrary angle

The theory of transformation optics is used to adjust the direction of emitted beams from a flat lens. In this paper, a planar lens is presented based on the transformation optics approach, which converts cylindrical beams emitted from a line source into a planar beam at the desired angle. The index profile of a planar inhomogeneous lens is considered as the refractive index of the original coordinate system. So, this yields a lens that produces a flat wave at an arbitrary angle. The performance of the structure is confirmed by COMSOL software.

Directivity enhancement of a cylindrical wire antenna by a graded index dielectric shell designed using strictly conformal transformation optics

A transformation-optical method is presented to enhance the directivity of a cylindrical wire antenna by using an all-dielectric graded index medium. The strictly conformal mapping between two doubly connected virtual and physical domains is established numerically. Multiple directive beams are produced, providing directive emission. The state-of-the-art optical path rescaling method is employed to mitigate the superluminal regions. The resulting transformation medium is all-dielectric and nondispersive, which can provide broadband functionality and facilitate the realization of the device using available fabrication technologies. The realization of the device is demonstrated by dielectric perforation based on the effective medium theory. The device’s functionality is verified by carrying out both ray-tracing and full-wave simulations using finite-element-based software COMSOL Multiphysics.

Light-trapping structures for planar solar cells inspired by transformation optics

Optimal light absorption is decisive in obtaining high-efficiency solar cells. An established, if not to say the established, approach is to texture the interface of the light-absorbing layer with a suitable microstructure. However, structuring the light-absorbing layer is detrimental concerning its electrical properties due to an increased surface recombination rate (owing to enlarged surface area and surface defects) caused by the direct patterning process itself. This effect lowers the efficiency of the final solar cells. To circumvent this drawback, this work theoretically explores a transformation optics (TrO) inspired approach to map the nanopatterned texture onto a planar equivalent. This offers a pattern with the same optical functionality but with much improved electrical properties. Schwarz-Christoffel mappings are used for ensuring conformality of the maps. It leads to planar, inhomogeneous, dielectric-only materials for the light trapping structure to be placed on top of the planar light-absorbing layer. Such a design strategy paves a way towards a novel approach for implementing light-trapping structures into planar solar cells.

The required acoustic parameters simplification of invisibility cloaks and concentrators using the impedance-tunable coordinate transformation

Transformation acoustics, as an unconventional theory, provides a powerful tool to design various kinds of acoustic devices with excellent functionalities. However, the required ideal parameters, which are prescribed by the method, are both complex and hard to implement-even using acoustic metamaterials. Furthermore, simplified parameter materials are generally favored in transformation-acoustic design due to its easier realization with artificial structures. In this letter, we propose a coordinate transformation methodology for achieving simplified parameters by tuning the impedance distribution in the geometric limit, where the transformation media parameters can be derived by setting tunable impedance functions in the original space and a combination of suitable linear or nonlinear coordinate transformation. Based on this approach, both two-dimensional acoustic cloak and concentrators are designed with different sets of simplified parameters. Numerical simulations indicate good performance of these devices with minimized scattering at higher frequencies. The proposed method provides more opportunities to realize the designed acoustic devices experimentally, and can also be used for other transformation-acoustic designs including 3D cases.

Designing a wideband dielectric polygonal directional beam antenna using the ray inserting method

This paper presents the design of a wideband polygonal directional beam antenna based on the ray inserting method. The wideband characteristic of the directional beam antenna is achieved thanks to the use of inhomogeneous dielectric material. Also, unlike most previous works, the present design can be implemented with the isotropic and above unity refractive index materials, consequently simplifying its fabrication process. The finite difference time domain scheme is used to evaluate the directional beam antenna.

Controlling refractive index of transformation-optics devices via optical path rescaling

We present a general method of designing optical devices based on optical conformal mapping and rescaling the optical path along a given bunch of rays. It provides devices with the same functionality as those based purely on conformal mapping, but enables to manipulate the refractive index to a great extent—for instance, eliminate superluminal regions of space as well as reduce the refractive index in other regions significantly. The method is illustrated in two examples, a waveguide coupler and a plasmonic bump cloak, and numerical simulations confirm its functionality.

Polymer multimode waveguide bend based on a multilayered Eaton lens

Reducing the bending radius of low-index-contrast waveguides is essential in reducing the size of the integrated optical components. A polymeric multimode waveguide bend is presented based on the Eaton lens. Ray-tracing calculations are utilized to truncate the Eaton lens in order to improve the performance of the bend. The truncation of the lens decreases the footprint of the bend as well. A designed waveguide bend with a radius of 18.4 μm is implemented by a concentric cylindrical multilayer structure. Average bend losses of 0.69 and 0.87 dB are achieved for the TM₀ and TM₁ modes, respectively, in the C-band of optical communication. The bend loss is lower than 1 dB in a bandwidth of 1520-1675 nm for both modes.

Design of an acoustic illusion device based on a shifting medium and multi-folded transformation

An acoustic illusion device that can act as an invisible cloak or a shifting medium depending on the value of shift distance, which is about twice the circum-radius of the outer polygon, is proposed and designed based on linear coordinate transformation. A multi-folded transformation approach is used to design an illusion device with a circular opening window that allows for information interaction with the outside world. The results show that the proposed device can hide objects with arbitrary shapes or positions. Furthermore, in order to remove the material anisotropy of the proposed illusion device, a layered structure composed of homogenous and isotropic material is used based on the effective medium theory. The combination of the layered structure and the circular opening provide a flexible and feasible approach to achieve the partial implementation of the illusion device. It is hoped that these results may open an avenue for designing and implementing invisibility cloaks or illusion devices, and speed up potential applications for noise shielding, target camouflage, or target protection from active sonar signals.

All-dielectric transformation medium mimicking a broadband converging lens

Radio waves carrying orbital angular momentum (OAM) may potentially increase spectrum efficiency and channel capacity based on their extra rotational degree of freedom. However, due to their divergence characteristics, vortex waves are not suitable to transmit over a long distance in the radio frequency (RF) and microwave domains. In this paper, a transformation optics (TO) based all-dielectric converging lens is proposed. The beam divergence angle of the vortex wave passing through the lens can be decreased from 25° to 9°. The transformed material parameters of the converging lens are determined by solving Laplace's equation subject to specific boundary conditions. Far-field antenna radiation patterns as well as near-field helical phase and electric field amplitude distributions obtained from numerical simulations are reported, demonstrating the broadband characteristics of the proposed microwave lens. Moreover, the all-dielectric compact lens design comprised by a graded permittivity profile can be fabricated by additive manufacturing technology, which greatly facilitates the potential development and application of vortex wave based wireless communications.

Orbital angular momentum generation method based on transformation electromagnetics

Orbital angular momentum (OAM) vortex waves generated by conventional spiral phase plates and metasurfaces have been widely discussed. In this work, we propose an innovative OAM generation method based on transformation optics (TO). By solving Laplace's equation with specific boundary conditions, an oblate cylindrical shaped physical domain is designed to imitate a gradient shaped virtual domain which is able to generate a vortex beam upon reflection. As a proof-of-concept demonstration, a broadband all-dielectric microwave lens for vortex beam generation is presented with a topological charge of + 1. The corresponding far-field patterns as well as near-field helical phase and doughnut-shaped amplitude distributions of the lens, obtained from numerical simulations, are reported along with a wide operational bandwidth spanning from 8 to 16 GHz. As a transformation method, the proposed TO technique provides an effective way to realize a conversion from plane waves to vortex waves, which can greatly facilitate the potential implementation of OAM waves in microwave wireless communication systems.

Realizable design of field taper via coordinate transformation

Complex electromagnetic structures can be designed by exploiting the concept of spatial coordinate transformations. In this paper, we define a coordinate transformation scheme that enables one to taper the electric field between two waveguides of different cross-sections. The electromagnetic field launched from the wide input waveguide is compressed in the proposed field tapering device and guided into the narrow output waveguide. In closed rectangular waveguide configurations, the taper can further play the role of a mode selector due to the output waveguide's cut-off frequency. Realizable permittivity and permeability values that can be achieved with common existing metamaterials are determined from the transformation equations and simplified by a proposed parameter reduction method. Both a 2D continuous design model and a potential 3D discretized realization model are presented at microwave frequencies and the performances of the tapering devices are verified by full-wave finite element numerical simulations. Finally, near-field distributions are shown to demonstrate the field tapering functionality.

Ultra-short beam expander with segmented curvature control: the emergence of a semi-lens

We introduce direct curvature control in designing a segmented beam expander, and explore novel design possibilities for ultra-compact beam expanders. Assisted by the particle swarm optimization algorithm, we search for an optimal curvature-controlled multi-segment taper that maintains width continuity. Counterintuitively, the optimization yields a structure with abrupt width discontinuity and width compression features. Through spatial phase and parameterized analysis, a semi-lens feature is revealed that helps to flatten the wavefront at the output end for higher coupling efficiency. Such functionality cannot be achieved by normal tapers in a short distance. The structure is fabricated and characterized experimentally. By a figure of merit that accounts for expansion ratio, length, and efficiency, this structure outperforms an adiabatic taper by 9 times.

Non-contact method to freely control the radiation patterns of antenna with multi-folded transformation optics

In this paper, we propose to use multi-folded transformation optics method to design a non-contact illusion device that can distantly and freely manipulate the radiation behavior of antenna located at a certain distance and such manipulation is enabled by the use of mapped electromagnetic medium coated with the transformed medium. The proposed design aims to achieve the radiation pattern of our choice from the antenna that does not possess any electromagnetic medium. Based on this, the functionality of parabolic antenna is distantly achieved from the point source. We further extended our idea to array of antennas in which the proposed device distantly makes the linear array of antennas behave like a geometrically different array of antennas. Our work extends the concept of illusion optics for active scatterer that will be very helpful for future antenna design.

Ultrathin metasurface-based carpet cloak for terahertz wave

Ultrathin metasurfaces with local phase compensation deliver new schemes to cloaking devices. Here, a large-scale carpet cloak consisting of an ultrathin metasurface is demonstrated numerically and experimentally in the terahertz regime. The proposed carpet cloak is designed based on discontinuous-phase metallic resonators fabricated on a polyimide substrate, offering a wide range of reflection phase variations and an excellent wavefront manipulation along the edges of the bump. The invisibility is verified when the cloak is placed on a reflecting triangular surface (bump). The multi-step discrete phase design method would greatly simplify the design process and is probable to achieve large-dimension cloaks, for applications in radar and antenna systems as a thin, lightweight, and easy-to-fabricate solution for radio and terahertz frequencies.

Reflectionless compact nonmagnetic optical waveguide coupler design based on transformation optics

The design of an optical waveguide coupler has several challenges, such as reflection losses at the interfaces of the coupler, material complexity for optical applications, and the coupling between arbitrary materials at the input and the output of the coupler. In this paper, for the first time to the best of our knowledge, we propose a solution to overcome the above difficulties. For this purpose, we introduce an auxiliary transformation function and an impedance scaling function. The auxiliary function specifies the matched dielectric materials at the input and output interfaces of the coupler, and the scaling function suppresses the reflections and makes the material nonmagnetic for transverse magnetic (TM) polarization. As a result, an optical waveguide coupler is designed that can ideally couple two waveguides with arbitrary dielectric materials and arbitrary cross sections using a nonmagnetic material. Validation of the design method is done by using COMSOL Multiphysics.

3D field-shaping lens using all-dielectric gradient refractive index materials

A novel three-dimensional (3D) optical lens structure for electromagnetic field shaping based on spatial light transformation method is proposed at microwave frequencies. The lens is capable of transforming cylindrical wavefronts into planar ones, and generating a directive emission. Such manipulation is simulated and analysed by solving Laplace's equation, and the deformation of the medium during the transformation is theoretically described in detail. The two-dimensional (2D) design method producing quasi-isotropic parameters is further extended to a potential 3D realization with all-dielectric gradient refractive index metamaterials. Numerical full-wave simulations are performed on both 2D and 3D models to verify the functionality and broadband characteristics of the calculated lens. Far-field radiation patterns and near-field distributions demonstrate a highly radiated directive beam when the lens is applied to a conical horn antenna.

Spherical aberration in electrically thin flat lenses

We analyze the spherical aberration of a new generation of lenses made of flat electrically thin inhomogeneous media. For such lenses, spherical aberration is analyzed quantitatively and qualitatively, and comparison is made to the classical gradient index rod. Both flat thin and thick lenses are made of gradient index materials, but the physical mechanisms and design equations are different. Using full-wave three-dimensional numerical simulation, we evaluate the spherical aberrations using the Maréchal criterion and show that the thin lens gives significantly better performance than the thick lens (rod). Additionally, based on ray tracing formulation, third-order analysis for longitudinal aberration and optical path difference are presented, showing strong overall performance of thin lenses in comparison to classical rod lenses.

Electromagnetic field tapering using all-dielectric gradient index materials

The concept of transformation optics (TO) is applied to control the flow of electromagnetic fields between two sections of different dimensions through a tapering device. The broadband performance of the field taper is numerically and experimentally validated. The taper device presents a graded permittivity profile and is fabricated through three-dimensional (3D) polyjet printing technology using low-cost all-dielectric materials. Calculated and measured near-field mappings are presented in order to validate the proposed taper. A good qualitative agreement is obtained between full-wave simulations and experimental tests. Such all-dielectric taper paves the way to novel types of microwave devices that can be easily fabricated through low-cost additive manufacturing processes.

Three-dimensional multiway power dividers based on transformation optics

The two-dimensional (2D) or three-dimensional (3D) multiway power dividers based on transformation optical theory are proposed in this paper. It comprises of several nonisotropic mediums and one isotropic medium without any lumped and distributed elements. By using finite embedded coordinate transformations, the incident beam can be split and bent arbitrarily in order to achieve effective power division and transmission. In addition, the location of the split point can be employed to obtain unequal power dividers. Finally, several typical examples of the generalized power divider without limitation in 3D space are performed, which shows that the proposed power divider can implement required functions with arbitrary power division and arbitrary transmission paths. The excellent simulated results verify the novel design method for power dividers.

Refraction in electrically thin inhomogeneous media

This work presents a new formulation for refraction from flat electrically thin lenses and reflectors comprised of inhomogeneous material. Inhomogeneous electrically thin flat lenses and reflectors cannot make use of the Snell law since this classical formulation works solely at interfaces of planar homogeneous media. The refraction of a perpendicularly incident plane wave at a planar interface is physically explained through the phase advance of the rays within the medium. The Huygens principle is then used to construct the refracted wavefront. The formulation is validated using numerical full wave simulation for several examples where the refractive angle is predicted with good accuracy. Furthermore, the formulation gives a physical insight of the phenomenon of refraction from electrically thin inhomogeneous media.

Omnidirectional optical attractor in structured gap-surface plasmon waveguide

An optical attractor based on a simple and easy to fabricate structured metal-dielectric-metal (SMDM) waveguide is proposed. The structured waveguide has a variable thickness in the vicinity of an embedded microsphere and allow for adiabatic nano-focusing of gap-surface plasmon polaritons (GSPPs). We show that the proposed system acts as an omnidirectional absorber across a broad spectral range. The geometrical optics approximation is used to provide a description of the ray trajectories in the system and identify the singularity of the deflection angle at the photon sphere. The analytical theory is validated by full-wave numerical simulations demonstrating adiabatic, deep sub-wavelength focusing of GSPPs and high local field enhancement. The proposed structured waveguide is an ideal candidate for the demonstration of reflection free omnidirectional absorption of GSPP in the optical and infrared frequency ranges.

Coherent beam control with an all-dielectric transformation optics based lens

Transformation optics (TO) concept well known for its huge possibility in patterning the path of electromagnetic waves is exploited to design a beam steering lens. The broadband directive in-phase emission in a desired off-normal direction from an array of equally fed radiators is numerically and experimentally reported. Such manipulation is achieved without the use of complex and bulky phase shifters as it is the case in classical phased array antennas. The all-dielectric compact low-cost lens prototype presenting a graded permittivity profile is fabricated through three-dimensional (3D) polyjet printing technology. The array of radiators is composed of four planar microstrip antennas realized using standard lithography techniques and is used as excitation source for the lens. To validate the proposed lens, we experimentally demonstrate the broadband focusing properties and in-phase directive emissions deflected from the normal direction. Both the far-field radiation patterns and the near-field distributions are measured and reported. Measurements agree quantitatively and qualitatively with numerical full-wave simulations and confirm the corresponding steering properties. Such experimental validation paves the way to inexpensive easy-made all-dielectric microwave lenses for beam forming and collimation.

Applications of gradient index metamaterials in waveguides

In this letter, we find that gradient index metamaterials (GIMs) could be utilized to manipulate wave propagation in waveguides. Through manipulating the conversion between propagating wave and surface wave, we can design some interesting applications in waveguides, such as controlling transmission effect, realizing bending waveguide and achieving waveguide splitting effect. These devices not only work for both transverse electric and magnetic polarized waves, but also function for a broadband of spectra. Numerical simulations are performed to verify our findings.

Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will

A new theory on designing electromagnetic/optical devices is proposed, namely, an optical surface transformation (OST). One arbitrary surface can establish the corresponding relationship with another surface entirely optically with an optic-null medium (ONM), (i.e. the electromagnetic wave propagates from one surface to its equivalent surface without any phase delay). Many novel optical devices can be designed by an OST with the help of an ONM. Compared with traditional devices designed by Transformation Optics, our optical surface-reshaping devices have two main advantages. Firstly, the design process is very simple (i.e. we do not need to consider any mathematics on how to make a coordinate transformation, and what we need to do is simply to design the shapes of the input and the output surfaces of the devices). Secondly, we only need one homogeneous anisotropic medium to realize all devices designed by this method. Our method will explore a new way to design novel optical devices without considering any coordinate transformations.

Omnidirectional diffraction control with rotational topological defects

We present a new scheme for the directional diffraction management of light with incompatible transformation optics. By introducing the concept of disclinations into transformation optics, we demonstrate that the rotational incompatible mapping violates the integrability condition of the coordinate transformation and gives rise to the non-vanishing Frank vector. It is revealed that such special coordinate transformations can produce rotational topological defects in physical space, which magnifies or compresses the diffraction of light beams propagating in arbitrary directions. We verify our theoretical analysis by numerical simulations of the light scattering from a cylinder of a generic disclination medium.

Electrically thin flat lenses and reflectors

We introduce electrically thin dielectric lenses and reflectors that focus a plane wave based on the principles of phase compensation and constructive wave interference. Phase compensation is achieved by arranging thin rectangular slabs having different dielectric permittivity according to a permittivity profile obtained through analytic design equations. All incident rays parallel to the optical axis converge to a focal point with equalized optical paths resulting in constructive interference. Plane wave simulations indicate strong focusing, even in the presence of impedance mismatch between free space and the dielectric layers composing the lens. We demonstrate focusing at 9.45 GHz using a lens fabricated with commercially available dielectric materials. In addition to focusing, the flat lens proposed here demonstrates relatively high power gain at the focal point. We also present a flat reflector based on the same concept. We believe that the proposed dielectric lens and reflector are strong candidates to replace heavy metallic dishes and reflectors used in a variety of applications, especially satellites.

Experimental Realization of Extreme Heat Flux Concentration with Easy-to-Make Thermal Metamaterials

The ability to harvest thermal energy and manipulate heat fluxes has recently attracted a great deal of research interest because this is critical to achieve efficient solar-to-thermal energy conversion in the technology of concentrated solar thermal collectors. Thermal metamaterials with engineered thermal conduction are often utilized to control the diffusive heat flow in ways otherwise not possible with naturally occurring materials. In this work, we adopt the transformation thermodynamics approach to design an annular fan-shaped thermal metamaterial which is capable of guiding heat fluxes and concentrating thermal energy to the central region of the metamaterial device without disturbing the temperature profile outside the structure – a fascinating and unique feature impossibly achieved with homogeneous materials. In experiment, this rationally-designed metamaterial structure demonstrates extreme heat flux compression from both line-shaped and point thermal sources with measured concentration efficiency up to 83.1%, providing the first experimental realization of our recent theoretical prediction (T. Han et al., Energy Environ. Sci., 2013, 6, 3537-3541). These unprecedented results may open up new possibilities for engineering thermal materials with desired properties that can be used for dramatically enhancing the efficiency of the existing solar thermal collectors.

Conceptual design of a beam steering lens through transformation electromagnetics

In this paper, based on transformation electromagnetics, the design procedure of a lens antenna, which steers the radiated beam of a patch array, is presented. Laplace's equation is adopted to construct the mapping between the virtual space and the physical space. The two dimensional (2D) design method can be extended to a potential three-dimensional (3D) realization, and with a proper parameter simplification, the lens can be further realized by common metamaterials or isotropic graded refractive index (GRIN) materials. Full wave simulations are performed to validate the proposed concept. It is observed that by placing the lens on a feeding source, we are able to steer the radiation emitted by the latter source.

Analytical models for electrically thin flat lenses and reflectors

This work presents analytical models for two-dimensional (2D) and three-dimensional (3D) electrically thin lenses and reflectors. The 2D formulation is based on infinite current line sources, whereas the 3D formulation is based on electrically small dipoles. These models emulate the energy convergence of an electrically thin flat lens and reflector when illuminated by a plane wave with specific polarization. The advantages of these models are twofold: first, prediction of the performance of electrically thin flat lenses and reflectors can be made significantly faster than full-wave simulators, and second, providing insight on the performance of these electrically thin devices. The analytic models were validated by comparison with full-wave simulation for several interesting examples. The validation results show that the focal point of the electrically thin flat lenses and reflectors can be accurately predicted through a design that assumes low coupling between different layers of an inhomogeneous media.

Design of an ultra-short coupler in an asymmetric twin-waveguide structure using transformation optics

An integrated vertical coupler that transfers light from the lower passive waveguide to the upper active waveguide in an asymmetric twin-waveguide integration structure (in InGaAsP/InP material system) is designed using transformation optics (TO). The length of the coupler is as short as 3 μm, which is two orders of magnitude shorter than that of traditional tapered couplers. According to three-dimensional full-wave simulations, the designed optimized coupler has a high coupling efficiency of 94.9%, and a low reflection at the wavelength of 1.55 μm. Subsequently, quasi-conformal mapping is employed to reduce the material complexity and to make it possible to realize the coupler by purely using an isotropic dielectric material. Applying TO to integrated photonic devices may motivate new applications, and improve integration density on the InP platform.

Anisotropic zero-index waveguide with arbitrary shapes

We design a series of waveguides composed of uniform anisotropic epsilon-near-zero media. Unlike normal waveguides in which the transmission rate strongly depends on the width and the boundary shape, such waveguides can achieve high transmission with almost arbitrary width and boundary shapes, leading to applications such as unusual waveguides, wave expanders and compressors, splitters, bends, and devices with combined purposes. The physical origin of such high transmission can be explained by using transformation optics and the condition for total transmission is derived. Numerical simulations with multilayers consisting of dielectric and negative-permittivity materials proved our theory. Our work provides a unified physical picture for waveguide structures based on anisotropic epsilon-near-zero media.

An efficient plate heater with uniform surface temperature engineered with effective thermal materials

Extended from its electromagnetic counterpart, transformation thermodynamics applied to thermal conduction equations can map a virtual geometry into a physical thermal medium, realizing the manipulation of heat flux with almost arbitrarily desired diffusion paths, which provides unprecedented opportunities to create thermal devices unconceivable or deemed impossible before. In this work we employ this technique to design an efficient plate heater that can transiently achieve a large surface of uniform temperature powered by a small thermal source. As opposed to the traditional approach of relying on the deployment of a resistor network, our approach fully takes advantage of an advanced functional material system to guide the heat flux to achieve the desired temperature heating profile. A different set of material parameters for the transformed device has been developed, offering the parametric freedom for practical applications. As a proof of concept, the proposed devices are implemented with engineered thermal materials and show desired heating behaviors consistent with numerical simulations. Unique applications for these devices can be envisioned where stringent temperature uniformity and a compact heat source are both demanded.

Bayesian Nonparametric Modeling for Rapid Design of Metamaterial Microstructures

We consider the problem of rapid design of massive metamaterial (MTM) microstructures from a statistical point of view. A Bayesian nonparametric model, namely, Gaussian Process (GP) mixture, is developed to generate the mapping relationship from the microstructure’s geometric dimension to the electromagnetic response, which is approximately expressed in a closed form of Drude-Lorentz type model. This GP mixture model is neatly able to tackle nonstationarity, discontinuities in the mapping function. The inference is performed using a Markov chain relying on Gibbs sampling. Experimental results demonstrate that the proposed approach is highly efficient in facilitating rapid design of MTM with accuracy.

Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials

It has long been conjectured that isotropic radiation by a simple coherent source is impossible due to changes in polarization. Though hypothetical, the isotropic source is usually taken as the reference for determining a radiator's gain and directivity. Here, we demonstrate both theoretically and experimentally that an isotropic radiator can be made of a simple and finite source surrounded by electric-field-driven LC resonator metamaterials designed by space manipulation. As a proof-of-concept demonstration, we show the first isotropic source with omnidirectional radiation from a dipole source (applicable to all distributed sources), which can open up several possibilities in axion electrodynamics, optical illusion, novel transformation-optic devices, wireless communication, and antenna engineering. Owing to the electric- field-driven LC resonator realization scheme, this principle can be readily applied to higher frequency regimes where magnetism is usually not present.

Pulsed dipole radiation in a transformation-optics wedge waveguide designed by azimuthal space compression

A transformation-optics wedge waveguide designed for the simultaneous collection and directional collimation of pulsed dipole radiation is described and tested with numerical simulation. Azimuthal compression of free space toward a narrow fan-shaped waveguide sector allows dipole pulse radiation in free space to be transformed into a directional non-dispersive pulse propagating within that sector. The collection and collimation ability of the proposed structure is compared with classical approaches using metallic wedge mirrors and parabolic mirrors, which inherently allow multiple internal reflections and thus generate significant pulse distortion and low light-collection efficiency. It is shown that the optical pulse generated by the dipole and propagated through the proposed transformation-optics waveguide maintains its original shape within the structure, and demonstrates enhanced optical power.

One-way invisible cloak using parity-time symmetric transformation optics

We propose a one-way invisible cloak using transformation optics of parity-time (PT) symmetric optical materials. At the spontaneous PT-symmetry breaking point, light is scattered only for incidence along one direction since the phase-matching condition is unidirectionally satisfied, making the cloak one-way invisible. Moreover, optical scattering from the one-way cloak can be further engineered to realize more interesting effects, for example, creating a unidirectional optical illusion of the concealed object.

Transformation inverse design

We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap because transformation optics circumvents the need to solve Maxwell's equations at each step. We apply this technique to the design of multimode waveguide bends (realized experimentally in a previous paper) and mode squeezers, in which all modes are transported equally without scattering. In addition to the optimization, a key point is the identification of the correct boundary conditions to ensure reflectionless coupling to untransformed regions while allowing maximum flexibility in the optimization. Many previous authors in transformation optics used a certain kind of quasiconformal map which overconstrained the problem by requiring that the entire boundary shape be specified a priori while at the same time underconstraining the problem by employing "slipping" boundary conditions that permit unwanted interface reflections.

Reducing physical appearance of electromagnetic sources

We propose to use the concept of transformation optics for the design of novel radiating devices. By applying transformations that compress space, and then that match it to the surrounding environment, we show how the electromagnetic appearance of radiating elements can be tailored at will. Our efficient approach allows one to realize a large aperture emission from a small aperture one. We describe transformation of the metric space and the calculation of the material parameters. Full wave simulations are performed to validate the proposed approach on different space compression shapes, factors and impedance matching. The idea paves the way to interesting applications in various domains in microwave and optical regimes, but also in acoustics.

Wide-angle scannable reflector design using conformal transformation optics

A flat reflector capable of scanning over wide angles is designed using a transformation optics approach. This reflector is derived from its virtual parabolic counterpart using a conformal coordinate transformation that determines the permittivity profile of the flat reflector. By changing the permittivity profile, the flat reflector is then capable of scanning up to 47° away from broadside while maintaining good beam characteristics across a wide frequency range. Moreover, its directivity is comparable to that of the virtual parabolic reflector, even at high scan angles. We use the Schwarz-Christoffel transformation as a versatile tool to produce perfect conformal mapping of coordinates between the virtual and flat reflectors, thereby avoiding the need to monitor the anisotropy of the material that results when employing quasi-conformal methods.

Transformation bending device emulated by graded-index waveguide

We demonstrate that a transformation device can be emulated using a gradient-index waveguide. The effective index of the waveguide is spatially varied by tailoring a gradient thickness dielectric waveguide. Based on this technology, we demonstrate a transformation device guiding visible light around a sharp corner, with low scattering loss and reflection loss. The experimental results are in good agreement with the numerical results.

Controlling electromagnetic scattering of a cavity by transformation media

Based on the transformation media theory, we proposed a way to control the scattering of a cavity, or trench, located on a metallic plane. Specifically, we show how is possible to design transformation medium to fill up a cavity with arbitrary cross section, which is capable of enhancing the specularly reflection wave. As the inverse problem, we also address the design of transformation medium coating, which is laid on the metallic plane, to mimic the scattering of the cavity. Based on the effective medium theory, the transformation medium for the case of a polygonal cavity can be realized by oblique layered structures, and each layered structure is consisting of two kinds of isotropic dielectrics, thus leading an ease of practical fabrication.

Experimental demonstration of light bending at optical frequencies using a non-homogenizable graded photonic crystal

Experimental results on light bending in a non-homogenizable graded photonic crystal operating at optical wavelengths are presented in this paper. A square lattice silicon on insulator photonic crystal made of a two-dimensional chirp of the air-hole filling factor is exploited to produce the bending effect in a near bandgap frequency range. The sensitivity of light paths to wavelength tuning is also exploited to show demultiplexing capability with low insertion loss (<2dB) and low crosstalk (~-20dB). This experimental demonstration opens opportunities for light manipulation using a generalized two-dimensional chirp of photonic crystal lattice parameters. It also constitutes an alternative solution to the use of photonic metamaterials combining dielectric and metallic materials with sub-wavelength unit cells.

Metal-dielectric metamaterials for guided wave silicon photonics

The aim of the present paper is to investigate the potential of metallic metamaterials for building optical functions in guided wave optics at 1.5 µm. A significant part of this work is focused on the optimization of the refractive index variation associated with localized plasmon resonances. The minimization of metal related losses is specifically addressed as well as the engineering of the resonance frequency of the localized plasmons. Our numerical modeling results show that a periodic chain of gold cut wires placed on the top of a 100 nm silicon waveguide makes it possible to achieve a significant index variation in the vicinity of the metamaterial resonance and serve as building blocks for implementing optical functions. The considered solutions are compatible with current nano-fabrication technologies.