This paper presents space-time varying (STV) metasurfaces for simultaneously controlling the spatial and temporal spectra of electromagnetic waves. These metasurfaces transform incident electromagnetic waves into specified reflected and transmitted waves, with arbitrary temporal and spatial frequencies. They are synthesized in terms of time-domain generalized sheet transition conditions (GSTCs). Moreover, they are characterized using an analytical method and the unstaggered finite-difference time-domain (FDTD) technique adapted to space-time metasurfaces. STV metasurfaces performing pulse shaping, time reversal and differentiation are demonstrated as examples.
With their self-tuned time-varying responses, waveform-selective metasurfaces embedded with nonlinear electronics have shown fascinating applications, including distinguishing different electromagnetic waves depending on the pulse width. However, thus far they have only been realized with a spatially homogeneous scattering profile. Here, by modeling a metasurface as time-varying admittance sheets, we provide an analytical calculation method to predict the metasurface time-domain responses. This allows derivation of design specifications in the form of equivalent sheet admittance, which is usef…
In this letter, we propose a magnet-less non-reciprocal isolating system based on time-varying metasurfaces. Two parallel time-varying metasurfaces, one for frequency up-conversion and one for down-conversion by the same amount, are used for realizing a region of space where incident waves from opposite directions experience an opposite Doppler frequency shift. As a result, any device within this region becomes sensitive to the illumination direction, exhibiting a different scattering response from opposite directions and thus breaking reciprocity. Very importantly, thanks to the opposite freq…
The recently proposed extreme-ultraviolet (EUV) beams with time-varying orbital angular momentum (OAM) realized by high-harmonic generation (HHG) provides extraordinary tools for quantum excitation control and particle manipulation. However, such an approach is not easily scalable to other frequency regimes. Here, we design a space-time-coding digital metasurface operating in microwave frequencies to experimentally generate different modes of time-varying OAM. We also introduce a concept of superhelicity of time-varying OAM with a higher-order twist of the wavefront structure, which can be fur…
Known coherent metasurfaces control interference of waves of a given frequency with other coherent waves at the same frequency, either illuminating from a different direction or created as intermodulation products. In this paper, we introduce a class of metasurfaces that are modulated in time coherently with the illuminating radiation. Importantly, such modulation opens a possibility to control reflection, absorption, and transmission at multiple frequencies, including illuminations by two or more incoherent waves. In particular, we study dynamic resistive layers and show how to use them to de…
Amplified up-conversion of electromagnetic waves using time-varying metasurfaces
ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Research School of Physics, The Australian National University（澳大利亚国立大学变革性超光学系统卓越研究中心物理研究学院）；Instituto de Telecomunicações and Department of Electronics, Telecommunications and Informatics, University of Aveiro（阿威罗大学电信研究所电子、电信与信息系）
Metasurfaces have shown unprecedented possibilities for wavefront manipulation of waves. The research efforts have been focused on the development of metasurfaces that perform a specific functionality for waves of one physical nature, for example, for electromagnetic waves. In this work, we propose the use of power-flow conformal metamirrors for creation of multiphysics devices which can simultaneously control waves of different nature. In particular, we introduce metasurface devices which perform specified operations on both electromagnetic and acoustic waves at the same time. Using a purely …
We introduce chiral gradient metasurfaces that allow perfect transmission of all the incident wave into a desired direction and simultaneous perfect rotation of the polarization of the refracted wave with respect to the incident one. Besides using gradient polarization densities which provide bending of the refracted wave with respect to the incident one, using metasurface inclusions that are chiral allows the polarization of the refracted wave to be rotated. We suggest a possible realization of the proposed device by discretizing the required equivalent surface polarization densities realized…
Metasurfaces possess the outstanding ability to tailor phase, amplitude and even spectral responses of light with an unprecedented ultrahigh resolution, thus have attracted significant interests. Here, we propose and experimentally demonstrate a novel meta-device that integrates color printing and computer-generated holograms within a single-layer dielectric metasurface by modulating spectral and spatial responses at subwavelength scale, simultaneously. In our design, such metasurface appears as a microscopic color image under white light illumination, while encrypting two different holographi…
Metasurfaces are engineered thin surfaces comprising two dimensional (2D) arrays of sub-wavelength spaced and sub-wavelength sized resonators. Metasurfaces can locally manipulate the amplitude, phase and polarization of light with high spatial resolution. In this study, we report numerical and experimental results of a vortex-beam-generating metasurface fabricated specifically for infrared (IR) and terahertz (THz) wavelengths. The designed metasurface consisted of a 2D array of dielectric cross-shaped resonators with spatially varying length, thereby providing desired spatially varying phase s…
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…
This work presents the design and fabrication of simple, polymeric, structure-based optical filters that simultaneously focus light. These filters represent a novel design at the boundary between diffractive optics and metasurfaces that may provide significant advantages for both digital and hyperspectral imaging. The fabrication process for the proposed filters resembles 3D printing, and is based on direct laser writing of a polymeric material using two-photon lithography. In addition, printed structures could be used to create molds for nanoimprint replication and mass production. Filters fo…
The possibility of integration of two important categories of optical components, i.e., circular polarizer and lens, into a thin plasmonic metasurface is examined. After exploring general theoretical formulation, optimal designs to realize polarizing lenses at mid-infrared frequencies are presented, for the cases when metal losses cannot be neglected. A two-dimensional array of Y-shaped nanoantennas with polarization dependent and spatially varying phase response is the basis for such a unique compact polarizing lens, whose properties can have a high impact in integrated optics.
Optical wave-based computing has enabled the realization of real-time information processing in both space and time domains. In the past few years, analog computing has experienced rapid development but mostly for a single function. Motivated by parallel space-time computing and miniaturization, we show that reconfigurable graphene-based metasurfaces offer a promising path towards spatiotemporal computing with integrated functionalities by properly engineering both spatial- and temporal-frequency responses. This paper employs a tunable graphene-based metasurface to enable analog signal and ima…
Dynamically switchable half-/quarter-wave plates have recently been the focus in the terahertz regime. Conventional design philosophy leads to multilayer metamaterials or narrowband metasurfaces. Here we propose a novel design philosophy and a VO2-metal hybrid metasurface for achieving broadband dynamically switchable half-/quarter-wave plate (HWP/QWP) based on the transition from the overdamped to the underdamped resonance. Results show that, by varying the VO2 conductivity by three orders of magnitude, the proposed metasurface's function can be switched between an HWP with polarization conve…
Parametric oscillation is a fundamental concept that underlies nonlinear wave-matter interactions, leading to generation or amplification of new frequency components. Using a temporal modulation generated by the heterodyne interference of a control direct current (dc) electric field and an optical field, we resonantly drive large-amplitude oscillations of amorphous silicon meta-atoms - nanoscale building blocks of an optical metasurface. We observed gigantically enhanced second harmonic generation (SHG) with an electric-field-controlled on off ratio over 10000 and an ultra-high modulation dept…
A cornerstone equation of optics, Snell's law, relates the angles of incidence and refraction for light passing through an interface between two media. It is built on two fundamental constrains: the conservation of tangential momentum and the conservation of energy. By relaxing the classical Snell law photon momentum conservation constrain when using space-gradient phase discontinuity, optical metasurfaces enabled an entirely new class of ultrathin optical devices. Here, we show that by eradicating the photon energy conservation constrain when introducing time-gradient phase discontinuity, we …
The conventional approach to nanophotonic metasurface design and optimization for a targeted electromagnetic response involves exploring large geometry and material spaces, which is computationally costly, time consuming and a highly iterative process based on trial and error. Moreover, the non-uniqueness of structural designs and high non-linearity between electromagnetic response and design makes this problem challenging. To model this non-intuitive relationship between electromagnetic response and metasurface structural design as a probability distribution in the design space, we introduce …
The paper presents the general concept of spacetime processing metasurfaces, synthesized by generalized sheet transition conditions (GSTCs). It is shown that such metasurfaces can perform multiple simultaneous spatio-temporal processing transformations on incident electromagnetic waves. A time-reversal space-generalized-refraction metasurface and a multi-time-space-differentiating metasurfaces are presented as applications of the general spacetime processing metasurface concept.
Metasurfaces consisting of electrically thin and densely packed planar arrays of subwavelength elements enable an unprecedented control of the impinging electromagnetic fields. Spatially modulated metasurfaces can efficiently tailor the spatial distribution of these fields with great flexibility. Similarly, time modulated metasurfaces can be successfully used to manipulate the frequency content and time variations of the impinging field. In this paper, we present time-modulated reflective metasurfaces that cause a frequency shift to the impinging radiation, thus realizing an artificial Doppler…
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…
Inhomogeneous metasurfaces have shown possibilities for unprecedented control of wave propagation and scattering. While it is conventional to shine a single incident plane wave from one side of these metastructures, illuminating by several waves simultaneously from both sides may enhance possibilities to control scattered waves, which results in additional functionalities and novel applications. Here, we unveil how using coherent plane-wave illumination of a properly designed inhomogeneous metasurface sheet it is possible to realize controllable retroreflection. We call these metasurfaces as "…
Bound states in the continuum in multilayered time-varying metasurfaces
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论固体物理研究所）；Institute for Analysis, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院分析学研究所）；Institute of Nanotechnology, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院纳米技术研究所）；Center for Integrated Quantum Science and Technology (IQST), Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院综合量子科学与技术中心）
Measuring light's state of polarization is an inherently difficult problem, since the phase information between orthogonal polarization states is typically lost in the detection process. In this work, we bring to the fore the equivalence between normalized Stokes parameters and diffraction contrasts in appropriately designed phase-gradient birefringent metasurfaces and introduce a concept of all-polarization birefringent metagratings. The metagrating, which consists of three interweaved metasurfaces, allows one to easily analyze an arbitrary state of light polarization by conducting simultaneo…
Two key metrics for imaging systems are their magnification and optical bandwidth. While high-quality imaging systems today achieve bandwidths spanning the whole visible spectrum and large changes in magnification via optical zoom, these often entail lens assemblies with bulky elements unfit for size-constrained applications. Metalenses present a methodology for miniaturization but their strong chromatic aberrations and the lack of a varifocal achromatic element limit their utility. While exemplary broadband achromatic metalenses are realizable via dispersion engineering, in practice, these de…
In analogy with electromagnetic networks which connect multiple input-output ports, metasurfaces can be considered as multi-port devices capable of providing different functionalities for waves of different polarizations illuminating the surface from different directions. The main challenge in the design of such multichannel metasurfaces is to ensure independent and full control of the electromagnetic response for each channel ensuring the fulilment of the boundary condition at the metasurface. In this work, we demonstrate that by properly engineering the evanescent fields excited at each port…
Phase, polarization, amplitude and frequency represent the basic dimensions of light, playing crucial roles for both fundamental light-mater interactions and all major optical applications. Metasurface emerges as a compact platform to manipulate these knobs, but previous metasurfaces have limited flexibility to simultaneous control them. Here, we introduce a multi-freedom metasurface that can simultaneously and independently modulate phase, polarization and amplitude in an analytical form, and further realize frequency multiplexing by a k-space engineering technique. The multi-freedom metasurf…
Metasurfaces are arrays of subwavelength meta-atoms that shape waves in a compact and planar form factor. Analysis and design of metasurfaces require methods for modeling their interactions with waves. Conventional modeling techniques assume that metasurfaces are locally periodic structures excited by plane waves, restricting their applicability to gradually varying metasurfaces that are illuminated with plane waves. Here we introduce the discrete-space impulse response concept that enables the development of accurate and general models for metasurfaces. According to the proposed model, discre…
Plasmonic metasurfaces enable simultaneous control of the phase, momentum, amplitude and polarisation of light and hence promise great utility in realisation of compact photonic devices. In this paper, we demonstrate a novel chip-scale device suitable for simultaneous polarisation and spectral measurements through use of six integrated plasmonic metasurfaces (IPMs), which diffract light with a given polarisation state and spectral component into well-defined spatial domains. Full calibration and characterisation of our device is presented, whereby good spectral resolution and polarisation accu…
Space-time modulated metasurfaces have attracted significant attention due to the additional degree of freedom in manipulating the electromagnetic (EM) waves in both space and time domains. However, the existing techniques have limited wave control capabilities, leading to just a few feasible schemes like regulation of only one specific harmonic. Here, we propose to realize independent manipulations of arbitrarily dual harmonics and their wave behaviors using a space-time-coding (STC) digital metasurface. By employing different STC sequences to the reflection phase of the metasurface, independ…
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…
The ability to control waves at the nanoscale has attracted considerable attention to ultrathin metasurface lenses (metalenses) in optical imaging and encryption systems. We propose an approach to active tuning metasurfaces by integrating an ultrathin layer of indium-tin-oxide (ITO) into a unit cell as an electro-optically tunable material. A proposed design features two orthogonal wings that can independently manipulate waves with corresponding orthogonal polarizations. The charge carrier concentration in the ITO accumulation layer is altered by modulating the applied bias voltage. This bias …
The effect of terahertz (THz) pulse generation has revolutionized broadband coherent spectroscopy and imaging at THz frequencies. However, THz pulses typically lack spatial structure, whereas structured beams are becoming essential for advanced spectroscopy applications. Non-linear optical metasurfaces with nanoscale THz emitters can provide a solution by defining the beam structure at the generation stage. We develop a non-linear InAs metasurface consisting of nanoscale optical resonators for simultaneous generation and structuring of THz beams. We find that THz pulse generation in the resona…
Optical metasurfaces (subwavelength-patterned surfaces typically described by variable effective surface impedances) are typically modeled by an approximation akin to ray optics: the reflection or transmission of an incident wave at each point of the surface is computed as if the surface were "locally uniform", and then the total field is obtained by summing all of these local scattered fields via a Huygens principle. (Similar approximations are found in scalar diffraction theory and in ray optics for curved surfaces.) In this paper, we develop a precise theory of such approximations for varia…
Metasurfaces represent one of the most vibrant fields of modern science and technology. A metasurface is a complex electromagnetic structure, that is typically deeply subwavelength in thickness, electrically large in transverse size and composed of subwavelength scattering particles with extremely small features; it may generally be bianisotropic, spacevarying and time-varying, nonlinear, curved and multiphysics. With such complexity, the design of a metasurface requires a holistic approach, involving synergistic synthesis and analysis operations, based on a solid model. The Generalized Sheet …
Control of the phase and polarization states of light is an important goal for nearly all optical research. The development of an efficient optical component that allows the simultaneous manipulation of the polarization and phase distribution is needed. Traditional methods require the combination of multiple optical devices, and a single optical device cannot easily realize full control of light. We theoretically predict and experimentally verify that our proposed dual-metasurfaces provide an excellent means to simultaneously manipulate the phase and polarization of transmission light at the n…
Recently, metasurfaces have gained popularity due to their ability to offer a spatially varying phase response, low intrinsic losses and high transmittance. Here, we demonstrate numerically and experimentally a silicon metasurface at THz frequencies that converts a Gaussian beam into a Vortex beam independent of the polarization of the incident beam. The metasurface consists of an array of sub-wavelength silicon cross resonators made of a high refractive index material on substrates such as sapphire and CaF$_2$ that are transparent at IR-THz spectral range. With these substrates, it is possibl…
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…
During the past few years, metasurfaces have been used to demonstrate optical elements and systems with capabilities that surpass those of conventional diffractive optics. Here we review some of these recent developments with a focus on dielectric structures for shaping optical wavefronts. We discuss the mechanisms for achieving steep phase gradients with high efficiency, simultaneous polarization and phase control, controlling the chromatic dispersion, and controlling the angular response. Then we review applications in imaging, conformal optics, tunable devices, and optical systems. We concl…
We present nonlinear optical four-wave mixing in a silicon nanodisk dimer metasurface. Under the oblique incident plane waves, the designed metasurface exhibits a multi-resonant feature with simultaneous excitations of three quasi-bound states in the continuum (BIC). Through employing these quasi-BICs with maximizing electric field energy at the input bump wavelengths, significant enhancement of third-order nonlinear processes including third-harmonic generation, degenerate and non-degenerate four-wave mixing are demonstrated, giving rise to ten new frequencies in the visible wavelengths. This…
In passive linear systems, complete combining of powers carried by waves from several input channels into a single output channel is forbidden by the energy conservation law. Here, we demonstrate that complete combination of both coherent and incoherent plane waves can be achieved using metasurfaces with properties varying in space and time. The proposed structure reflects waves of the same frequency but incident at different angles towards a single direction. The frequencies of the output waves are shifted by the metasurface, ensuring perfect incoherent power combining. The proposed concept o…
