A rigorous semi-analytical Floquet analysis is proposed for a zero-thickness space-time modulated Huygens' metasurface to model and determine the strengths of the new harmonic components of the scattered fields. The proposed method is based on Generalized Sheet Transition Conditions (GSTCs) treating a metasurface as a spatial discontinuity. The metasurface is described in terms of Lorentzian electric and magnetic surface susceptibilities, $χ_\text{e}$ and $χ_\text{m}$, respectively, with parameters (e.g. resonant frequency) that are periodically modulated in both space and time. The unknown scattered fields are expressed in terms of Floquet harmonics, for which the amplitudes can be found by numerically solving a set of linear equations, leading to the total scattered fields. Using existing computational techniques, the method is validated using several examples of pure-space and pure-time modulation with different modulation strengths and pumping frequencies. Finally, two cases of spacetime modulation (standing wave perturbation and a traveling wave perturbation) are presented to demonstrate the breaking of Lorentz reciprocity. The proposed method is simple and versatile and able to determine the steady-state response of a space-time modulated Huygen's metasurface that is excited with an oblique plane wave, or a general incident field such as a Gaussian beam.
We introduce the concept and a generic approach to realize Extreme Huygens' Metasurfaces by bridging the concepts of Huygens' conditions and optical bound states in the continuum. This novel paradigm allows creating Huygens' metasurfaces whose quality factors can be tuned over orders of magnitudes, generating extremely dispersive phase modulation. We validate this concept with a proof-of-concept experiment at the near-infrared wavelengths, demonstrating all-dielectric Huygens' metasurfaces with different quality factors. Our study points out a practical route for controlling the radiative deca…
An explicit time-domain finite-difference technique for modelling zero-thickness Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and demonstrated using full-wave simulations. The Huygens' metasurface is modelled using electric and magnetic surface susceptibilities, which are found to follow a double-Lorentz dispersion profile. To solve zero-thickness Huygens' metasurface problems for general broadband excitations, the double-Lorentz dispersion profile is combined with GSTCs, leading to a set of first-order differential fields equations in time-domain…
Subwavelength-thin metasurfaces have shown great promises for the control of optical wavefronts, thus opening new pathways for the development of efficient flat optics. In particular, Huygens' metasurfaces based on all-dielectric resonant meta-atoms have already shown a huge potential for practical applications with their polarization insensitivity and high transmittance efficiency. Here, we experimentally demonstrate a polarization insensitive holographic Huygens' metasurface based on dielectric resonant meta-atoms capable of complex wavefront control at telecom wavelengths. Our metasurface p…
Optical metasurfaces have developed as a breakthrough concept for advanced wave-front engineering enabled by subwavelength resonant nanostructures. However, reflection and/or absorption losses as well as low polarisation-conversion efficiencies pose a fundamental obstacle for achieving high transmission efficiencies that are required for practical applications. Here we demonstrate, for the first time to our knowledge, highly efficient all-dielectric metasurfaces for near-infrared frequencies using arrays of silicon nanodisks as meta-atoms. We employ the main features of Huygens' sources, namel…
Parity-Time (PT) symmetric optical structures exhibit several unique and interesting characteristics with the most popular being exceptional points. While the emerging concept of PT-symmetry has been extensively investigated in bulky photonic designs, its exotic functionalities in nanophotonic non-Hermitian plasmonic systems still remain relatively unexplored. Towards this goal, in this work we analyze the unusual properties of a plasmonic Huygens metasurface composed of an array of active metal-dielectric core-shell nanoparticles. By calculating the reflection and transmission coefficients of…
An all-dielectric Huygens metasurface supporting electric and magnetic resonances is a promising platform for a variety of optical applications that require a combination of extremely high transmission and broad-range control of the phase of the transmitted light. A highly efficient wave plate is one example of such an application. In combination with high spectral selectivity and strong optical energy concentration, such phase plates are desirable for precision sensing and high efficiency nonlinear optics. We propose a novel approach to realizing such ultra-thin optical plates: an anisotropic…
Optical dielectric metasurfaces composed of arrayed nanostructures are expected to enable arbitrary spatial control of incident wavefronts with subwavelength spatial resolution. For phase modulation, one often resorts to two physical effects to implement a 2π-phase excursion. The first effect relies on guidance by tall nanoscale pillars and the second one exploits resonant confinement by nanoresonators with two degenerate Mie-resonances. The first approach requires high aspect ratios, while the second one, known as Huygens metasurfaces, is much flatter, and thus easier to manufacture. We compa…
A rigorous Floquet mode analysis is proposed for a zero thickness space-time modulated Huygens' metasurface to model and determine the strengths of the new harmonic components of the scattered fields. The proposed method is based on Generalized Sheet Transition Conditions (GSTCs) treating a metasurface as a spatial discontinuity. The metasurface is described in terms of Lorentzian electric and magnetic surface susceptibilities, $χ_\text{ee}$ and $χ_\text{mm}$, respectively, and its resonant frequencies are periodically modulated in both space and time. The unknown scattered fields are then exp…
We report the design, fabrication, and characterization of bianisotropic Huygens' metasurfaces (BHMSs) for refraction of normally incident beams towards 71.8 degrees. As previously shown, all three BHMS degrees of freedom, namely, electric polarizability, magnetic polarizability and omega-type magnetoelectric coupling, are required to ensure no reflections occur for such wide-angle impedance mismatch. The unit cells are composed of three metallic layers, yielding a printed-circuit-board (PCB) structure. The fabricated BHMS is characterized in a quasi-optical setup, used to accurately assess sp…
Scattering of refracting Huygens' metasurfaces is revisited. A new analytical closed-form solution is obtained for the two-dimensional problem under transverse electric (TE) plane-wave incidence -- a solution which gives the scattering for any (in-plane) angle of incidence and frequency. In the process of obtaining the solution, interesting mathematical concepts are considered -- such as solving and enforcing uniqueness upon an infinite system of equations. The obtained solution uncovers two previously unknown functionalities of refracting Huygens' metasurfaces -- namely reflectionless refract…
We report on a chiral nanostructure, which we term a "butterfly nanoantenna," that, when used in a metasurface, allows the direct conversion of a linearly polarized beam into a nonlinear optical far-field of arbitrary complexity. The butterfly nanoantenna exhibits field enhancement in its gap for every incident linear polarization, which can be exploited to drive nonlinear optical emitters within the gap, for the structuring of light within a frequency range not accessible by linear plasmonics. As the polarization, phase and amplitude of the field in the gap are highly controlled, nonlinear em…
We present a semi-analytical formulation of the interaction between a given source field and a scalar Huygens metasurface (HMS), a recently introduced promising concept for wavefront manipulation based on a sheet of orthogonal electric and magnetic dipoles. Utilizing the equivalent surface impedance representation of these metasurfaces, we establish that an arbitrary source field can be converted into directive radiation via a passive lossless HMS if two physical conditions are met: local power conservation and local impedance equalization. Expressing the fields via their plane-wave spectrum a…
Metasurfaces are an enabling technology for complex wave manipulation functions, including in the terahertz frequency range, where they are expected to advance security, imaging, sensing, and communications technology. For operation in transmission, Huygens' metasurfaces are commonly used, since their good impedance match to the surrounding media minimizes reflections and maximizes transmission. Recent theoretical work has shown that Huygens' metasurfaces are non-optimal, particularly for large angles of refraction, and that to eliminate reflections and spurious diffracted beams it is necessar…
One of the long-standing problems in antenna engineering is the realization of highly-directive beams using low-profile devices. In this paper we provide a solution to this problem by means of Huygens' metasurfaces (HMSs), based on the equivalence principle. This principle states that a given excitation can be transformed to a desirable aperture field by inducing suitable electric and magnetic surface currents. Building on this concept, we propose and demonstrate cavity-excited HMS antennas, where the single-source cavity excitation is designed to optimize aperture illumination, while the HMS …
In-line Dispersion Control of Femtosecond Laser Pulses by Multilayer Huygens' Metasurfaces
Friedrich-Schiller-University Jena（耶拿弗里德里希·席勒大学）；Australian National University（澳大利亚国立大学）；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所）
Novel display technologies aim at providing the users with increasingly immersive experiences. In this regard, it is a long-sought dream to generate three-dimensional (3D) scenes with high resolution and continuous depth, which can be overlaid with the real world. Current attempts to do so, however, fail in providing either truly 3D information, or a large viewing area and angle, strongly limiting the user immersion. Here, we report a proof-of-concept solution for this problem, and realize a compact holographic 3D near-eye display with a large exit pupil of 10mm x 8.66mm. The 3D image is gener…
Metasurfaces enable a new paradigm of controlling electromagnetic waves by manipulating subwavelength artificial structures within just a fraction of wavelength. Despite the rapid growth, simultaneously achieving low-dimensionality, high transmission efficiency, real-time continuous reconfigurability, and a wide variety of re-programmable functions are still very challenging, forcing researchers to realize just one or few of the aforementioned features in one design. In this study, we report a subwavelength reconfigurable Huygens' metasurface realized by loading it with controllable active ele…
High refractive index dielectric nanoparticles have provided a new platform for exotic light manipulation through the interference of multipole modes. The Kerker effect is one example of a Huygens source design. Rather than exploiting interference between the electric dipole and magnetic dipole, as in many conventional Huygens source designs, we explore Kerker-type suppressed backward scattering mediated by the dominant electric dipole, toroidal dipole and magnetic quadrupole. These modes are provided by a designed and fabricated CMOS compatible ultra-thin Silicon nanodisk metasurface with a s…
Metasurfaces composed of subwavelength unit cells usually require a large number of unit cells which leads to complicated design and optimization. Aggressive discretization in a metasurface can significantly reduce the number of unit cells within a period, resulting in lower requirement for phase and/or surface impedance coverage. Additionally, the enlarged unit cells will encounter negligible mutual couplings when combined together, hence making straightforward the process of metasurface design. These advantages combine to allow the design of a novel class of metasurfaces which support the hi…
Over the past decades, many radome designs to extend the angular scan range of phased-array antennas have been devised by utilizing dielectric materials and metamaterials. More recently, metasurface technology such as planar lenses and beam deflectors have been applied to phased arrays, enabling scan-angle enhancers to have a low profile. In this work, a physical Huygens' metasurface (HMS) two-lens system for scanangle doubling of a phased array is presented. For the HMS unit cells, the wire-loop topology is deployed to achieve high transmission for the required phase-angle shift. The proposed…
Zhejiang Key Laboratory of 3D Micro/Nano Fabrication and Characterization, Department of Electronic Science and Engineering, School of Engineering, Westlake University（西湖大学工程学院电子科学与工程系三维微纳加工与表征浙江省重点实验室）；Westlake Center for Micro/Nano Fabrication, Westlake University（西湖大学微纳加工中心）；Eastern Institute of Technology（宁波东方理工大学）
For transmissive applications of electromagnetic metasurfaces, an array of subwavelength Huygens' metaatoms are typically used to eliminate reflection and achieve a high transmission power efficiency together with a wide transmission phase coverage. We show that the underlying principle of low reflection and full control over transmission is asymmetric scattering into the specular reflection and transmission directions that results from a superposition of symmetric and anti-symmetric scattering components, with Huygens' meta-atoms being one example configuration. Available for oblique illumina…
Realization of the anomalous refraction effects predicted by Huygens' metasurfaces (HMS) have required tedious and time-consuming trial-and-error numerical full-wave computations. It is shown herein that these requirements can be alleviated for transverse magnetic (TM) propagation by a periodic dielectric-based HMS consisting of an electrically thick array of cascaded Fabry-Pérot etalons. This "Fabry-Pérot HMS" (FP-HMS) is easily designed to mimic the local scattering coefficients of a standard zero-thickness HMS (ZT-HMS) which, according to homogenization theory, should result in the desired …
Interference is the cornerstone of Huygens source design for reshaping and controlling scattering patterns. The conventional underpinning principle, such as for the Kerker effect, is the interference of electric and magnetic dipole and quadrupole modes. Here a route to realize transverse Kerker scattering through employing only the interference between the electric dipole and magnetic quadrupole is demonstrated. The proposed approach is numerically validated in an ultra-thin Silicon square nanoplate metasurface, and is further verified by multipole decomposition. The metasurface is shown to be…
A finite-difference time-domain (FDTD) modelling of finite-size zero thickness space-time modulated Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and numerically demonstrated. A typical all-dielectric Huygens' unit cell is taken as an example and its material permittivity is modulated in both space and time, to emulate a travelling-type spatio-temporal perturbation on the metasurface. By mapping the permittivity variation onto the parameters of the equivalent Lorentzian electric and magnetic susceptibility densities, $\tildeχ_\text{ee}$ and $\tilde…
Harnessing Selective State Space Models to Enhance Semianalytical Design of Fabrication-Ready Multilayered Huygens' Metasurfaces: Part I - Field-based Semianalytical Synthesis
In this paper we describe a methodology for tailoring the design of metamaterial dielectric resonators, which represent a promising path toward low-loss metamaterials at optical frequencies. We first describe a procedure to decompose the far field scattered by subwavelength resonators in terms of multipolar field components, providing explicit expressions for the multipolar far fields. We apply this formulation to confirm that an isolated high-permittivity cube resonator possesses frequency separated electric and magnetic dipole resonances, as well as a magnetic quadrupole resonance in close p…
Controlling directionality of emission, scattering and waveguiding is an important requirement in quantum optical technology, integrated photonics and new metasurface designs, as well as radio and microwave engineering. Recently, several approaches have been developed to achieve unidirectional scattering in the far-field relying on Huygens' dipolar sources, and in waveguided optics based on spin-Hall effects involving circularly polarised electric or magnetic dipoles, all of which can be realised with plasmonic or dielectric nanoparticles. Here we show that there exists a dipolar source compli…
Huygens' metasurfaces have demonstrated almost arbitrary control over the shape of a scattered beam, however, its spatial profile is typically fixed at fabrication time. Dynamic reconfiguration of this beam profile with tunable elements remains challenging, due to the need to maintain the Huygens' condition across the tuning range. In this work, we experimentally demonstrate that a time-varying metadevice which performs frequency conversion can steer transmitted or reflected beams in an almost arbitrary manner, with fully dynamic control. Our time-varying Huygens' metadevice is made of both el…
A single-order transmission diffraction grating based on dispersion engineered all-dielectric metasurfaces is proposed and its wavelength discriminating properties have been theoretically described and confirmed using numerical simulations. The metasurface is designed using a 2D array of all-dielectric resonators, which emulates a Huygens source configuration to achieve a perfect match to free-space in broad bandwidth. Using a holey dielectric nanodisk structure as the unit cell, the resonant wavelength is tapered across the metasurface to engineer the wavelength dependent spatial phase gradie…
Harnessing Selective State Space Models to Enhance Semianalytical Design of Fabrication-Ready Multilayered Huygens' Metasurfaces: Part II - Generative Inverse Design (MetaMamba)
All-dielectric nanophotonics has become one of the most active fields of research in modern optics, largely due to the opportunities offered by the simultaneous resonant control of electric and magnetic components of light at the nanoscale. In this rapidly evolving scenario, the possibility to design artificial Huygens sources by overlapping electric and magnetic resonances has established a new paradigm in flat optics, bringing devices closer to efficient wavefront shaping with a direct phase engineering at the level of the individual meta-atoms. However, their efficiency is fundamentally lim…
In the wake of intense research on metamaterials the two-dimensional analogue, known as metasurfaces, has attracted progressively increasing attention in recent years due to the ease of fabrication and smaller insertion losses, while enabling an unprecedented control over spatial distributions of transmitted and reflected optical fields. Metasurfaces represent optically thin planar arrays of resonant subwavelength elements that can be arranged in a strictly or quasi periodic fashion, or even in an aperiodic manner, depending on targeted optical wavefronts to be molded with their help. This pap…
The ongoing effort to implement compact and cheap optical systems is the main driving force for the recent flourishing research in the field of optical metalenses. Metalenses are a type of metasurface, used for focusing and imaging applications, and are implemented based on the nanopatterning of an optical surface. The challenge faced by metalens research is to reach high levels of performance, using simple fabrication methods suitable for mass-production. In this paper we present a Huygens nanoantenna based metalens, designed for outdoor photographic/surveillance applications in the near-infr…
Space-time modulation induced non-reciprocity in EM metasurfaces is proposed and numerically demonstrated using rigorous Generalized Sheet Transitions Conditions (GSTCs) under oblique plane-wave incidence. It is phenomenologically shown that the space-time modulation of surface susceptibilities create an inherent asymmetry with respect to the directional perturbation on the metasurface and the transverse wave momentum of the input wave, between forward and backward propagations, resulting in non-reciprocal wave transmission. Exploiting the periodicity of the surface susceptibilities in both ti…
We present a general theory for designing realistic omega-type bianisotropic metasurfaces (O-BMSs), unlocking their full potential for molding electromagnetic fields. These metasurfaces, characterized by electric surface impedance, magnetic surface admittance, and magnetoelectric coupling coefficient, were previously considered for wavefront manipulation. However, previous reports mainly considered plane-wave excitations, and implementations included cumbersome metallic features. In this work, we prove that any field transformation which locally conserves real power can be implemented via pass…
Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical…
All-dielectric resonant nanophotonics lies at the heart of modern optics and nanotechnology due to the unique possibilities to control scattering of light from high-index dielectric nanoparticles and metasurfaces. One of the important concepts of dielectric Mie-resonant nanophotonics is associated with the Kerker effect that drives the unidirectional scattering of light from nanoantennas and Huygens' metasurfaces. Here we suggest and demonstrate experimentally a novel effect manifested in the nearly complete simultaneous suppression of both forward and backward scattered fields. This effect is…
In this study, we demonstrate first, to the best of our knowledge, robust and dynamically polarization-controlled tunable-high-Q PIT in designed nanostructures metasurface, whose sharp resonance is guaranteed by design and protected against large geometrical imperfections. By employing the explicit analysis of near-field characteristic in the reciprocal-space based on the momentum matching, and the far-field radiation features with point-scattering approach in real-space sparked from Huygens's principles, the physics of interference resonance in the spectra for plane-wave optical transmission …
This work theoretically and experimentally studies metasurfaces with spatially-discrete, traveling-wave modulation (SD-TWM). A representative metasurface is considered consisting of columns of time-modulated subwavelength unit cells, referred to as stixels. SD-TWM is achieved by enforcing a time delay between temporal waveforms applied to adjacent columns. In contrast to the continuous traveling-wave modulation commonly assumed in studies of space-time metasurfaces, here the modulation is spatially discretized. In order to account for the discretized spatial modulation, a modified Floquet anal…
One of the most promising metasurface architectures for the microwave and terahertz frequency ranges consists of three patterned metallic layers separated by dielectrics. Such metasurfaces are well suited to planar fabrication techniques and their synthesis is facilitated by modelling them as impedance sheets separated by transmission lines. We show that this model can be significantly inaccurate in some cases, due to near-field coupling between metallic layers. This problem is particularly severe for higher frequency designs, where fabrication tolerances prevent the patterns from being highly…
Compact, lightweight and high-performance spatial light modulators (SLMs) are crucial for modern optical technologies. The drive for pixel miniaturization, necessary to improve their performance, has led to a promising alternative, active optical metasurfaces, which enable tunable subwavelength wavefront manipulation. Here, we demonstrate an all-solid-state programmable transmissive SLM device based on Huygens dielectric metasurfaces. The metasurface features electrical tunability, provided by mature liquid crystals (LCs) technology. In contrast to conventional LC SLMs, our device enables high…
Exceptional Points, Lasing, and Coherent Perfect Absorption in Floquet Scattering Systems
Vienna University of Technology (TU Wien)（维也纳工业大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of Graz（格拉茨大学）；NAWI Graz（NAWI格拉茨）；Riga Technical University（里加技术大学）
