Showing papers on "Transformation optics published in 2019"

Electromagnetic metasurfaces: physics and applications

Abstract: Metasurfaces are ultrathin metamaterials consisting of planar electromagnetic (EM) microstructures (e.g., meta-atoms) with pre-determined EM responses arranged in specific sequences. Based on careful structural designs on both meta-atoms and global sequences, one can realize homogenous and inhomogeneous metasurfaces that can possess exceptional capabilities to manipulate EM waves, serving as ideal candidates to realize ultracompact and highly efficient EM devices for next-generation integration-optics applications. In this paper, we present an overview on the development of metasurfaces, including both homogeneous and inhomogeneous ones, focusing particularly on their working principles, the fascinating wave-manipulation effects achieved both statically and dynamically, and the representative applications so far realized. Finally, we also present our own perspectives on possible future directions of this fast-developing research field in the conclusion.

On-chip wavefront shaping with dielectric metasurface.

Abstract: 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. Metasurfaces can be programmed for a spatial transformation of the wavefront, allowing on-chip optical signal processing. Here, the authors demonstrate a one-dimensional high-contrast transmitarray metasurface-based lens on SOI substrate and demonstrate functionalities of Fourier transformation and differentiation.

Encrypted Thermal Printing with Regionalization Transformation.

Abstract: Artificially structured thermal metamaterials provide an unprecedented possibility of molding heat flow that is drastically distinct from the conventional heat diffusion in naturally conductive materials. The Laplacian nature of heat conduction makes the transformation thermotics, as a design principle for thermal metadevices, compatible with transformation optics. Various functional thermal devices, such as thermal cloaks, concentrators, and rotators, have been successfully demonstrated. How far can it possible go beyond just realizing a heat-distribution function in a thermal metadevice? Herein, the concept of encrypted thermal printing is proposed and experimentally validated, which could conceal encrypted information under natural light and present static or dynamic messages in an infrared image. Regionalization transformation is developed for structuring thermal metamaterial-strokes as infrared signatures, enabling letters of the alphabet to be written, paintings to be drawn, movies to be made, and information to be displayed. This strategy successfully demonstrates an extreme level of manipulation of heat flow for encryption, illusions, and messaging.

Hydrodynamic Metamaterial Cloak for Drag-Free Flow.

Abstract: 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.

Optical Fourier surfaces

Abstract: Gratings and holograms are patterned surfaces that tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be discovered. Further advances could exploit Fourier optics, which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. To shape the optical wavefront, the ideal surface profile should contain a precise sum of sinusoidal waves, each with a well-defined amplitude, spatial frequency, and phase. However, because fabrication techniques typically yield profiles with at most a few depth levels, complex 'wavy' surfaces cannot be obtained, limiting the straightforward mathematical design and implementation of sophisticated diffractive optics. Here we present a simple yet powerful approach to eliminate this design-fabrication mismatch by demonstrating optical surfaces that contain an arbitrary number of specified sinusoids. We combine thermal scanning-probe lithography and templating to create periodic and aperiodic surface patterns with continuous depth control and sub-wavelength spatial resolution. Multicomponent linear gratings allow precise manipulation of electromagnetic signals through Fourier-spectrum engineering. Consequently, we immediately resolve an important problem in photonics by creating a single-layer grating that simultaneously couples red, green, and blue light at the same angle of incidence. More broadly, we analytically design and accurately replicate intricate two-dimensional moir\'e patterns, quasicrystals, and holograms, demonstrating a variety of previously impossible diffractive surfaces. Therefore, this approach provides instant benefit for optical devices (biosensors, lasers, metasurfaces, and modulators) and emerging topics in photonics (topological structures, transformation optics, and valleytronics).

Multiplication and division of the orbital angular momentum of light with diffractive transformation optics

Abstract: We present a method to efficiently multiply or divide the orbital angular momentum (OAM) of light beams using a sequence of two optical elements. The key element is represented by an optical transformation mapping the azimuthal phase gradient of the input OAM beam onto a circular sector. By combining multiple circular-sector transformations into a single optical element, it is possible to multiply the value of the input OAM state by splitting and mapping the phase onto complementary circular sectors. Conversely, by combining multiple inverse transformations, the division of the initial OAM value is achievable by mapping distinct complementary circular sectors of the input beam into an equal number of circular phase gradients. Optical elements have been fabricated in the form of phase-only diffractive optics with high-resolution electron-beam lithography. Optical tests confirm the capability of the multiplier optics to perform integer multiplication of the input OAM, whereas the designed dividers are demonstrated to correctly split up the input beam into a complementary set of OAM beams. These elements can find applications for the multiplicative generation of higher-order OAM modes, optical information processing based on OAM beam transmission, and optical routing/switching in telecom.

Total angular momentum sorting in the telecom infrared with silicon Pancharatnam-Berry transformation optics.

Abstract: Parallel sorting of orbital angular momentum (OAM) and polarization has recently acquired paramount importance and interest in a wide range of fields ranging from telecommunications to high-dimensional quantum cryptography. Due to their inherently polarization-sensitive optical response, optical elements acting on the geometric phase prove to be useful for processing structured light beams with orthogonal polarization states by means of a single optical platform. In this work, we present the design, fabrication and test of a Pancharatnam-Berry optical element in silicon implementing a log-pol optical transformation at 1310 nm for the realization of an OAM sorter based on the conformal mapping between angular and linear momentum states. The metasurface is realized in the form of continuously variant subwavelength gratings, providing high-resolution in the definition of the phase pattern. A hybrid device is fabricated assembling the metasurface for the geometric-phase control with multi-level diffractive optics for the polarization-independent manipulation of the dynamic phase. The optical characterization confirms the capability to sort orbital angular momentum and circular polarization at the same time.

Ultrasensitive polarization-dependent terahertz modulation in hybrid perovskites plasmon-induced transparency devices

Abstract: Active control of metamaterial properties with high tunability of both resonant intensity and frequency is essential for advanced terahertz (THz) applications, ranging from spectroscopy and sensing to communications. Among varied metamaterials, plasmon-induced transparency (PIT) has enabled active control with giant sensitivity by embedding semiconducting materials. However, there is still a stringent challenge to achieve dynamic responses in both intensity and frequency modulation. Here, an anisotropic THz active metamaterial device with an ultrasensitive modulation feature is proposed and experimentally studied. A radiative-radiative-coupled PIT system is established, with a frequency shift of 0.26 THz in its sharp transparent windows by polarization rotation. Enabled by high charge-carrier mobility and longer diffusion lengths, we utilize a straightforwardly spin-coated MAPbI3 film acting as a photoactive medium to endow the device with high sensitivity and ultrafast speed. When the device is pumped by an ultralow laser fluence, the PIT transmission windows at 0.86 and 1.12 THz demonstrate a significant reduction for two polarizations, respectively, with a full recovery time of 561 ps. In addition, we numerically prove the validity that the investigated resonator structure is sensitive to the optically induced conductivity. The hybrid system not only achieves resonant intensity and frequency modulations simultaneously, but also preserves the all-optical-induced switching merits with high sensitivity and speed, which enriches multifunctional subwavelength metamaterial devices at THz frequencies.

Transformation optics from macroscopic to nanoscale regimes: a review

Abstract: Transformation optics is a mathematical method that is based on the geometric interpretation of Maxwell’s equations. This technique enables a direct link between a desired electromagnetic (EM) phenomenon and the material response required for its occurrence, providing a powerful and intuitive design tool for the control of EM fields on all length scales. With the unprecedented design flexibility offered by transformation optics (TO), researchers have demonstrated a host of interesting devices, such as invisibility cloaks, field concentrators, and optical illusion devices. Recently, the applications of TO have been extended to the subwavelength scale to study surface plasmon-assisted phenomena, where a general strategy has been suggested to design and study analytically various plasmonic devices and investigate the associated phenomena, such as nonlocal effects, Casimir interactions, and compact dimensions. We review the basic concept of TO and its advances from macroscopic to the nanoscale regimes.

Merging transformation optics with electron-driven photon sources.

Abstract: Relativistic electron beams create optical radiation when interacting with tailored nanostructures. This phenomenon has been so far used to design grating-based and holographic electron-driven photon sources. It has been proposed recently that such sources can be used for hybrid electron- and light-based spectroscopy techniques. However, this demands the design of a thin-film source suitable for electron-microscopy applications. Here, we present a mesoscopic structure composed of an array of nanoscale holes in a gold film which is designed using transformation optics and delivers ultrashort chirped electromagnetic wave packets upon 30–200 keV electron irradiation. The femtosecond photon bunches result from coherent scattering of surface plasmon polaritons with hyperbolic dispersion. They decay by radiation in a broad spectral band which is focused into a 1.5 micrometer beam waist. The focusing ability and broadband nature of this photon source will initiate applications in ultrafast spectral interferometry techniques. There is growing interest in designing platforms for coherent electron-driven photon sources for hybrid light and electron spectroscopy. Here the authors demonstrate generation of coherent broadband ultrashort light pulses upon electron irradiation to nanostructured gold plated film.

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

Abstract: 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.

Geometrically flat hyperlens designed by transformation optics

Abstract: Here, we present a geometrically flat hyperlens that can still magnify and transfer sub-wavelength objects to the far-field. The flat hyperlens is designed using the transformation optics approach, which transforms the virtual space of the cylindrical coordinate into the physical space of the trapezoidal coordinate. We also suggest the possible design of two alternating multilayers by using an effective medium approximation. The sub-wavelength magnification using the designed flat hyperlens is numerically demonstrated. Such a flat hyperlens has great potential for practical application by solving many problems of conventional curvilinear hyperlenses arisen from their geometries.

Electromagnetically induced transparency in terahertz complementary spiral-shape metamaterials

Abstract: We propose and demonstrate two designs of complementary spiral-shape metamaterials (CSSM) with square and hexagonal meta-atom arrangements in the terahertz (THz) frequency range. For convenience, they are denoted as CSSM-S and CSSM-H for CSSM with square and hexagonal meta-atom arrangements, respectively. The electromagnetic responses are investigated for CSSM with different spiral angle (θ). CSSM-S exhibits dual-, triple-, and quad-resonance for θ = 360°, θ = 540° and θ = 720°, respectively in transverse electric (TE) mode and exhibits single-, dual-, and triple-resonance for θ = 360°, θ = 540° and θ = 720°, respectively in transverse magnetic (TM) mode. By applying a direct-current (dc) bias voltage on CSSM-S, it shows the actively tunable resonance with a tuning range of 0.12 THz and switching polarization characteristics. Furthermore, to facilitate the flexibility and applicability of CSSM, the unit cell of CSSM with different θ is superimposed to form CSSM-H. CSSM-H possesses the combination of electromagnetic behaviors generated by each unit cell of CSSM with different θ. This study provides a design of complementary THz metamaterials to have electromagnetically induced transparency (EIT) analog characteristics, which shows single-digital and multi-digital signals for the programmable metamaterial application. It paves a way to the possibility of THz metamaterials with great tunability and good polarization-dependence.

Transformation optics for perfect two-dimensional non-magnetic all-mode waveguide couplers

Abstract: Here, we demonstrate that transformation optics can be used to produce 2-D non-magnetic waveguide couplers with no reflections. Our approach consists of using a scaling function for reflection suppression and introducing an auxiliary function in the transformation optics formulation to achieve a non-magnetic medium for coupling the TM polarization. To demonstrate the potential of this method, two non-magnetic waveguide couplers are designed. The first one satisfies the Brewster angle condition for any arbitrary incidence angle (TMn modes), extending the performance of couplers previously reported in the literature that only operate for TEM (TM0 mode), i.e. waves with normal incidence. Our method can be applied to match any given dielectric constant. Our results demonstrate that for a given mode (angle), we achieve a perfect match to a defined dielectric constant. The second design removes the dependence of the reflectionless condition to the incident angle at the boundary. Hence, this coupler works for all incident angles (TMn modes). It is used to compress all the modes into a region with a higher predefined refractive index.

Conformal optical devices based on geodesic lenses.

Abstract: 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.

Design and Validation of an All-Dielectric Metamaterial Medium for Collimating Orbital-Angular-Momentum Vortex Waves at Microwave Frequencies

Abstract: Vortex waves have potential applications in wireless communication, because of their advantages in improving channel-transmission efficiency. However, the peculiar divergence of vortex waves seriously limits their propagation distance for communication. Thus the authors propose an innovative method for collimating vortex waves at microwave frequencies, based on transformation optics. Their all-dielectric device can reduce the divergence angle of vortex waves over a wide bandwidth, and collimate vortex beams with multiple modes.

Optimization of the electromagnetic scattering problem based on the topological derivative method

Abstract: A new optimization method based on the topological derivative concept is developed for the electromagnetic design problem. Essentially, the purpose of the topological derivative method is to measure the sensitivity of a given shape functional with respect to a singular domain perturbation, so that it has applications in many relevant fields such as shape and topology optimization for imaging processing, inverse problems, and design of metamaterials. The topological derivative is rigorously derived for the electromagnetic scattering problem and used as gradient descent direction to find local optima for the design of electromagnetic devices. We demonstrate that the resulting topology design algorithm is remarkably simple and efficient and naturally leads to binary designs, while depending only on the solution of the conventional finite element formulation for electrodynamics. Finally, several numerical experiments in two and three spatial dimensions are presented to illustrate the performance of the proposed formulation.

Hybridization of singular plasmons via transformation optics

Abstract: 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.

A reflecting-type highly efficient terahertz cross-polarization converter based on metamaterials

Abstract: We propose and experimentally demonstrate a wideband linear polarization converter in a reflection mode operating from 2.4 to 4.2 THz with conversion efficiency of more than 80%. Our device can expand the applications to a higher frequency band. A numerical simulation is performed for this metamaterial converter, which shows a good agreement with experimental results. Importantly, a concise and intuitive calculating model is proposed for the Fabry–Perot cavity. The theoretical results indicate that the underlying reason for the enhanced polarization conversion is the additional phase difference induced by the resonance of the meta-structure and multiple reflections within the Fabry–Perot cavity.

Optimization of conformal whispering gallery modes in lima\c{c}on-shaped transformation cavities

Abstract: In limacon-shaped gradient index dielectric cavities designed by 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.

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

Abstract: 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, the phase-matching condition is relevant even for this subwavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.

Exploiting transformation optics for arbitrary manipulation of antenna radiation pattern

Abstract: Using transformation optics, a general method for tailoring the radiation pattern of a monopole antenna encompassed by a coating layer is proposed. Unlike previous studies, the propounded approach is not restricted to special patterns and can produce arbitrary radiation pattern with customisable beam parameters such as number, direction, and directivity in both azimuthal and elevation planes. A linear coordinate transformation is established to simplify the coating layer realisation via offering homogeneous materials. As proof-of-principle, two different antennas capable of generating multiple beams and a single-directive beam, are elaborately acquired by a meta-structure consisting of a split-ring resonator-wire array composite. It was observed that the experimental results corroborate numerical simulations. The proposed approach is believed to have potential applications in antenna technologies, satellite communication, and multiple-input multiple-output systems.

Subwavelength negative-index waveguiding enabled by coupled spoof magnetic localized surface plasmons

Abstract: Magnetic localized surface plasmon modes are supported on metallic spiral structures. Coupling mechanisms for these metamaterial resonators, which are the joint action of magnetic and electric coupling, are studied. Based on the strong coupling, spoof magnetic plasmon modes propagating in the backward direction are proposed along a chain of subwavelength resonators. The theoretical analysis, numerical simulations, and experiments are in good agreement. The proposed novel route for achieving negative-index waveguiding has potential applications in integrated devices and circuits.

Designing Anisotropic, Inhomogeneous Metamaterial Devices Through Optimization

Abstract: A method for designing multi-input, multi-output metamaterial devices is presented. The devices are 2-D anisotropic, inhomogeneous media. The design technique consists of a custom finite-element method solver coupled to a constrained, nonlinear minimization algorithm. The design method has advantages over existing metamaterial design methods such as transformation optics, in that material constraints can be imposed and multi-input, multi-output functionality allowed. Transformation optics devices only achieve multi-input, multi-output functionality through geometrical symmetry. The gradient-based optimization method employed in the metamaterial design process is fast given that an analytic expression for the gradient of the cost function can be written. The proposed technique is demonstrated through the design of two beamforming devices. A commercial full-wave solver is used to validate the design approach. The constitutive parameters of these 2-D designs can be implemented using printed-circuit board metamaterials, such as tensor transmission-line metamaterials.

Optimization of conformal whispering gallery modes in limaçon-shaped transformation cavities.

Abstract: Directional light emission from high-Q resonant modes without significant Q-spoiling has been a long standing issue in deformed dielectric cavities. In limacon-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.

Common elements for uncommon light: vector beams with GRIN lenses.

Abstract: A well-known defect introduced during the fabrication of GRIN lenses can be exploited for the creation, detection and wave-guiding of exotic forms of vectorial structured light, bringing the toolkit into the realm of common laboratory optics.

Conformal Singularities and Topological Defects from Inverse Transformation Optics

Abstract: The conventional approach to transformation optics starts with a virtual space and determines a complicated material profile in physical space, to achieve unconventional phenomena. The authors take a reverse approach, and find that the conformal singularities in the refractive-index profile are equivalent to topological defects. Optical splitting and illusion effects are confirmed. They furthermore fabricate a device with a positive topological defect, and demonstrate its light-bending functionality. Their methods could be used to connect conventional geometric optics with on-chip applications.