We propose novel quantum antennas and metamaterials with strong magnetic response at optical frequencies. Our design is based on the arrangement of natural atoms with only electric dipole transition moments at distances smaller than a wavelength of light but much larger than their physical size. In particular, we show that an atomic dimer can serve as a magnetic antenna at its antisymmetric mode to enhance the decay rate of a magnetic transition in its vicinity by several orders of magnitude. Furthermore, we study metasurfaces composed of atomic bilayers with and without cavities and show that they can fully reflect the electric and magnetic fields of light, thus, forming nearly perfect electric/magnetic mirrors. The proposed quantum metamaterials can be fabricated with available state-of-the-art technologies and promise several applications both in classical optics and quantum engineering.
Frequency Band of 0.5 THz to 1.1 THz (WR1.5 and WR1) is one of the promising bands when it comes to 6G. In this paper, we propose a novel metamaterial absorber suitable to be used at lower WR1 frequencies in TE mode. Alternatively, the design can be used as a strong absorber at lower Terahertz frequencies. In addition, when used in TM mode the absorber works as a perfect absorber at higher WR1 band.
We have fabricated a quarter-wave plate from a single layer birefringent metamaterial. For comparison, an appropriately scaled double layer meanderline structure was fabricated. At the design frequency of 639 GHz, the metamaterial structure achieves 99.9% circular polarization while the meanderline achieves 99.6%. The meanderline displays a larger bandwidth of operation, attaining over 99% circular polarization from 615 - 743 GHz, while the metamaterial achieves 99% from 626 - 660 GHz. However, both are broad enough for use with CW sources making metamaterials a more attractive choice due to t…
The recent advance in the assembly of metallic nanoparticles (NPs) has enabled sophisticated engineering of unprecedented light-matter interaction at the optical domain. In this work, I expand the design flexibility of NP optical metamaterial to push the upper limit of accessible refractive index to the unnaturally high regime. The precise control over the geometrical parameters of NP superlattice monolayer conferred the dramatic increase in electric resonance and related effective permittivity far beyond the naturally accessible regime. Simultaneously, effective permeability, another key fact…
Metamaterial effective parameters may exhibit freedom from typical dispersion constraints. For instance, the emergence of a magnetic response in arrays of split-ring resonators for long wavelengths cannot be attained in a passive continuous system obeying the Kramers-Kronig relations. We characterize such freedom by identifying the three possible asymptotes which effective parameters can approach when analytically continued. Apart from their dispersion freedom, we also demonstrate that the effective parameters may be redefined in such a way that they have a certain physical meaning for all fre…
Cactus-like Metamaterial Structures for Electromagnetically Induced Transparency at THz frequencies
Foundation for Research and Technology-Hellas（希腊研究与技术基金会）；National and Kapodistrian University of Athens（雅典国立卡波季斯特里大学）；National Hellenic Research Foundation（国家希腊研究基金会）；University of Regensburg（雷根斯堡大学）
In this paper, we present the design of cylindrical and spherical electromagnetic cloaks working at visible frequencies. The cloak design is based on the employment of layered structures consisting of alternating plasmonic and non-plasmonic materials and exhibiting the collective behavior of an effective epsilon-near-zero material at optical frequencies. The design of a cylindrical cloak to hide cylindrical objects is firstly presented. Two alternative layouts are proposed and both magnetic and non-magnetic objects are considered. Then, the design of spherical cloaks is also presented. The ful…
Light propagation in all-dielectric rod-type metamaterials is studied theoretically. The electric and magnetic dipole moments of the rods are derived analytically in the long-wavelength limit. The effective permittivity and permeability of a square lattice of rods are calculated by homogenizing the corresponding array of dipoles. The role of dipole resonances in the optical properties of the rod array is interpreted. This structure is found to exhibit a true left-handed behavior, confirming previous experiments [L. Peng \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 157403 (2007)]. A scaling a…
Losses in metamaterials render the applications of such exotic materials less practical unless an efficient way of reducing them is found. We present two different techniques to reduce ohmic losses at both lower and higher frequencies, based on geometric tailoring of the individual magnetic constituents. We show that an increased radius of curvature, in general, leads to the least losses in metamaterials. Particularly at higher THz frequencies, bulky structures outperform the planar structures.
Metamaterials have paved the way to unprecedented control of the electromagnetic field1,2. The conjunction with space coordinate transformation has led to a novel "relativity inspired" approach for the control of light propagation. "Invisibility cloak" is the most fascinating proposed devices3,4. However, the realized structures up to now used a graded "metamagnetic" so as to achieve the cloaking function11. Artificial magnetism is however still very challenging to obtain in optics despite the currently promising building blocks13-17, not suited for optical cloaking. We report here the first e…
In this paper, mu-near-zero (MNZ) metamaterials are utilized to achieve an ultrathin absorber with a thickness of only about one percent of the operating wavelength. The metamaterial absorber (MA) is made of double-layered metallic spiral arrays designed to have a large purely imaginary permeability at low microwave frequencies (~ 1.7 GHz). An absorption efficiency above 90% is demonstrated at illumination angles up to 60 degrees. A polarization-insensitive MA implemented by 2D isotropic metamaterials is also studied. Our designs have great application potential as compared with the traditiona…
Metamaterials--artificially structured materials with tailored electromagnetic response--can be designed to have properties difficult to achieve with existing materials. Here we present a structured metamaterial, based on conducting split ring resonators (SRRs), which has an effective index-of-refraction with a constant spatial gradient. We experimentally confirm the gradient by measuring the deflection of a microwave beam by a planar slab of the composite metamaterial over a broad range of frequencies. The gradient index metamaterial represents an alternative approach to the development of gr…
The design of artificial nonlinear materials requires control over the internal resonant charge densities and local electric field distributions. We present a MM design with a structurally controllable oscillator strength and local electric field enhancement at terahertz frequencies. The MM consists of a split ring resonator (SRR) array stacked above an array of nonresonant closed conducting rings. An in-plane, lateral shift of a half unit cell between the SRR and closed ring arrays results in a decrease of the MM oscillator strength by a factor of 4 and a 40% change in the amplitude of the re…
We present and analyze a dielectric cluster based on subwavelength LiTaO3 polaritonic cylinders for demonstrating toroidal response in THz regime due to mutual coupling of Mie- resonance modes of the cylinders. Based on this cluster, we demonstrate a low-loss metamaterial with the dominant toroidal response, which plays a key role in achieving resonant total transmission.
We demonstrate a thermally tunable optical metamaterial with negative permeability working in the visible range. By covering coupled metallic nanostrips with aligned nematic liquid crystals (NLCs), the magnetic response wavelength of the metamaterial is effectively tuned through control of the ambient temperature, changing the refractive index of LC via phase transitions. By increasing the ambient temperature from 20 degree to 50 degree, the magnetic response wavelength shifts from 650nm to 632nm. Numerical simulations confirm our tests and match the experimental observations well.
We study numerically and experimentally magnetic metamaterials based on cut-wire pairs instead of split-ring resonators. The cut-wire pair planar structure is extended in order to create a truly two-dimensional metamaterial suitable for scaling to optical frequencies. We fabricate the cut-wire metamaterial operating at microwave frequencies with lattice spacing around 10% of the free-space wavelength, and find good agreement with direct numerical simulations. Unlike the structures based on split-ring resonators, the nearest-neighbor coupling in cut-wire pairs can result in a magnetic stop-band…
Metamaterials based on effective media have achieved a lot of unusual physics (e.g. negative refraction and invisibility cloaking) owing to their abilities to tailor the effective medium parameters that do not exist in nature. Recently, coding metamaterials have been suggested to control electromagnetic waves by designing the coding sequences of digital elements '0' and '1', which possess opposite phase responses. Here, we propose the concept of anisotropic coding metamaterial at terahertz frequencies, in which coding behaviors in different directions are dependent on the polarization status o…
We investigate a dynamically controllable electromagnetically induced transparency-like metamaterial. The unit structure of the metamaterial consists of a low-quality-factor resonator and a high-quality-factor resonator. The field gradient of the incident electromagnetic wave in the transverse direction induces coupling between these two types of resonators and causes a transparency phenomenon. We present the simulation and experimental results for the dynamic control of the electromagnetic response.
We demonstrate resonant Faraday polarization rotation in plasmonic arrays of bimetallic nano-ring resonators consisting of Au and Ni sections. This metamaterial design allows to optimize the trade-off between the enhancement of magneto-optical effects and plasmonic dissipation. Although Ni sections correspond to as little as ~6% of the total surface of the metamaterial, the resulting magneto-optically induced polarization rotation is equal to that of a continuous film. Such bimetallic metamaterials can be used in compact magnetic sensors, active plasmonic components and integrated photonic cir…
We theoretically study fishnet metamaterials at optical frequencies. In contrast to earlier works, we provide a microscopic description by tracking the transversal and longitudinal flows of energy through the fishnet mesh composed of intersecting subwavelength plasmonic waveguides. The analysis is supported by a semi-analytical model based on surface-plasmon coupled-mode equations, which provides accurate formulas for the fishnet refractive index, including the real-negative and imaginary parts. The model simply explains how the surface plasmons couple at the waveguide intersections and it shi…
Toroidal multipoles are the terms missing in the standard multipole expansion; they are usually overlooked due to their relatively weak coupling to the electromagnetic fields. Here we propose and theoretically study all-dielectric metamaterials of a special class that represent a simple electromagnetic system supporting toroidal dipolar excitations in the THz part of the spectrum. We show that resonant transmission and reflection of such metamaterials is dominated by toroidal dipole scattering, the neglect of which would result in a misunderstanding interpretation of the metamaterials macrosco…
Artificial magnetism, negative permeability and negative refractive index are demonstrated in 3D-chiral metamaterial that shows giant polarization rotation and circular dichroism.
Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index, ultra-high index and chiral optical properties. Recently, metamaterials with near-zero refractive index have drawn much attention. Light inside such materials experiences no spatial phase change and extremely large phase velocity, properties that can be applied for realizing directional emission, tunneling waveguides, large area single mode devices, and electromagnetic cloaks. However, at optical frequencies previously demonstrated zero- or negative-r…
Optical materials with vanishing dielectric permittivity, known as epsilon-near-zero (ENZ) materials, have been shown to possess enhanced nonlinear optical responses in their ENZ region. These strong nonlinear optical properties have been firmly established in homogeneous materials; however, it is as of yet unclear whether metamaterials with effective optical parameters can exhibit a similar enhancement. Here, we probe an optical ENZ metamaterial composed of a subwavelength periodic stack of alternating Ag and SiO$_2$ layers and measure a nonlinear refractive index $n_2 = (1.2 \pm 0.1) \times …
Since the introduction of the artificially designed negative-index metamaterial (NIM) introduced in 2001, its extraordinary electromagnetic properties, which cannot be attained from naturally occurring materials, have continuously attracted many researchers to study them. Various types of NIMs with the resonant frequencies shifted from gigahertz all the way to higher frequencies have been actualized over the past decade. For the actual applications, the most fascinating and significant goal of research on NIMs is to achieve negative refraction at visible wavelengths. According to the effective…
Metamaterials with artificial optical properties have attracted significant research interest. In particular, artificial magnetic resonances in non-unity permeability tensor at optical frequencies in metamaterials have been reported. However, only non-unity diagonal elements of the permeability tensor have been demonstrated to date. A gyromagnetic permeability tensor with non-zero off-diagonal elements has not been observed at the optical frequencies. Here we report the observation of gyromagnetic properties in the near-infrared wavelength range in a magneto-plasmonic metamaterial. The non-zer…
We present a general approach for the numerical calculation of the effective dielectric tensor of metamaterials and show that our formalism can be used to study metamaterials beyond the long wavelength limit. We consider a system composed of high refractive index cylindric inclusions and show that our method reproduces the Mie resonant features and photonic band structure obtained from a multiple scattering approach, hence opening the possibility to study arbitrarily complex geometries for the design of resonance-based negative refractive metamaterials at optical wavelengths.
We demonstrate that the toroidal dipolar response can be realized in the optical regime by designing a feasible nanostructured metamaterial, comprising asymmetric double-bar magnetic resonators assembled into a toroid-like configuration. It is confirmed numerically that an optical toroidal dipolar moment dominates over other moments. This response is characterized by a strong confinement of an E-field component at the toroid center, oriented perpendicular to the H-vortex plane. The resonance-enhanced optical toroidal response can provide an experimental avenue for various interesting optical p…
We report on the fabrication and mid-infrared transmission properties of free-standing thin metal films, periodically patterned with holes at periods down to 2 microns and area of 3x3 mm2. Square grids were fabricated by electron beam lithography and deep-etching techniques and display substrateless holes, with the metal being supported by a patterned dielectric silicon nitride membrane. The mid-infrared transmission spectra of the substrateless grid display extraordinary transmission peaks and resonant absorption lines with a Q-factor up to 22. These spectral features are due to the interacti…
We introduce the concept of magnetoelastic metamaterials with electromagnetic properties depending on elastic deformation. We predict a strong nonlinear and bistable response of such metamaterials caused by their structural reshaping in response to the applied electromagnetic field. In addition, we demonstrate experimentally the feasibility of the predicted effect.
Toroidal dipole, first described by Ia. B. Zeldovich [Sov. Phys. JETP 33, 1184 (1957)], is a distinct electromagnetic excitation that differs both from the electric and the magnetic dipoles. It has a number of intriguing properties: static toroidal nuclear dipole is responsible for parity violation in atomic spectra; interactions between static toroidal dipole and oscillating magnetic dipole are claimed to violate Newton's Third Law while non-stationary charge-current configurations involving toroidal multipoles have been predicted to produce vector potential in the absence of electromagnetic …
As artificial structures, metamaterials are usually described by macroscopic effective medium parameters, which are named as "analog metamaterials". Here, we propose "digital metamaterials" in two steps. Firstly, we present "coding metamaterials" that are composed of only two kinds of unit cells with 0 and π phase responses, which we name as "0" and "1" elements. By coding "0" and "1" elements with controlled sequences (i.e., 1-bit coding), we can manipulate electromagnetic (EM) waves and realize different functionalities. The concept of coding metamaterial can be extended from 1-bit coding to…
We apply a rigorous eigenmode analysis to study the electromagnetic properties of linear and weakly nonlinear metamaterials. The nonlinear response can be totally described by the linear eigenmodes when weak nonlinearities are attributed to metamaterials. We use this theory to interpret intrinsic second-harmonic spectroscopy on metallic metamaterials. Our study indicates that metamaterial eigenmodes play a critical role in optimizing a nonlinear metamaterial response to the extent that a poorly optimized modal pattern overwhelms the widely recognized benefits of plasmonic resonant field enhanc…
We experimentally demonstrate at terahertz frequencies that a planar metamaterial exhibits a spectral response resembling electromagnetically induced transparency. The metamaterial unit cell consists of a split ring surrounded by another closed ring where their dimensions are such that their excitable lowest order modes have identical resonance frequencies but very different life times. Terahertz time-domain spectroscopy verifies that the interference of these two resonances results in a narrow transparency window located within a broad opaque region. In contrast to previous studies this enhan…
In this paper, we employ the properties of metamaterials to tailor the modes of metamaterial-dielectric waveguides operating at optical frequencies. We survey the effect of fishnet metamaterial structural parameters such as the magnetic oscillation strength, magnetic resonance frequency and magnetic damping on the double-negative refractive index frequency region in metamaterials and on the hybrid-modes in slab metamaterial-dielectric waveguides. To identify the robustness of the metamaterials to fluctuations in the metamaterial structural parameters, we investigate the behavior of metamateria…
We demonstrate that left-handed resonance transmission from metallic metamaterial, composed of periodically arranged double rings, can be extended to visible spectrum by introducing an active medium layer as the substrate. The severe ohmic loss inside metals at optical frequencies is compensated by stimulated emission of radiation in this active system. Due to the resonance amplification mechanism of recently proposed lasing spaser, the left-handed transmission band can be restored up to 610 nm wavelength, in dependence on the gain coefficient of the active layer. Additionally, threshold gains…
By harnessing the resonant nature of localized electromagnetic modes in a nanostructured silicon membrane, an all-dielectric metamaterial can act as nonlinear medium at optical telecommunications wavelengths. We show that such metamaterials provide extremely large optomechanical nonlinearities, operating at intensities of only a few μW per unit cell and modulation frequencies as high as 152 MHz, thereby offering a path to fast, compact and energy efficient all-optical metadevices.
We propose and design a new type of nonlinear metamaterials exhibiting a resonant electric response at microwave frequencies. By introducing a varactor diode as a nonlinear element within each resonator, we are able to shift the frequency of the electric mode stop-band by changing the incident power, without affecting the magnetic response. These elements could be combined with the previously developed nonlinear magnetic metamaterials in order to create negative index media with control over both electric and magnetic nonlinearities.
We identify a route towards achieving a negative index of refraction at optical frequencies based on coupling between plasmonic waveguides that support backwards waves. We show how modal symmetry can be exploited in metal-dielectric waveguide pairs to achieve negative refraction of both phase and energy. By properly controlling coupling between adjacent waveguides, a metamaterial consisting of a one-dimensional multilayer stack exhibiting an isotropic index of -1 can be achieved at a free-space wavelength of 400 nm. The general concepts developed here may inspire new low-loss metamaterial desi…
One route to create tunable metamaterials is through integration with "on-demand" dynamic quantum materials, such as vanadium dioxide (VO2). This enables new modalities to create high performance devices for historically challenging applications. Indeed, dynamic materials have often been integrated with metamaterials to imbue artificial structures with some degree of tunability. Conversely, metamaterials can be used to enhance and extend the natural tuning range of dynamic materials. Utilizing a complementary split ring resonator array deposited on a VO2 film, we demonstrate enhanced terahertz…
We demonstrated an ultra-broadband, polarization-insensitive and wide-angle metamaterial absorber for terahertz (THz) frequencies using arrays of truncated pyramid unit structure made of metal-dielectric multilayer composite. In our design each sub-layer behaving as an effective waveguide is gradually modified in their lateral width to realize a wideband response by effectively stitching together the resonance bands of different waveguide modes. Experimentally, our five layer sample with a total thickness 21um is capable of producing a large absorptivity above 80% from 0.7 to 2.3 THz up to the…
We propose a design for broadband waveguide mode conversion based on gradient index metamaterials (GIMs). Numerical simulations demonstrate that the zeroth order of transverse magnetic mode or the first order of transverse electric mode (TM0/TE1) can be converted into the first order of transverse magnetic mode or the second order of transverse electric mode (TM1/TE2) for a broadband of frequencies. As an application, an asymmetric propagation is achieved by integrating zero index metamaterials inside the GIM waveguide.
We theoretically investigate the electromagnetic response of a novel class of multi-layered metamaterials obtained by alternating graphene sheets and dielectric layers, the whole structure not exhibiting a plane of reflection symmetry along the stacking direction. We show that the electromagnetic response of the structure is characterized by a magneto-electric coupling described by an effective chiral parameter. Exploiting the intrinsic tunability of the graphene-light coupling, we prove that one can tune both the dielectric and the chiral electromagnetic response by varying the graphene chemi…
Metamaterials, artificial media structured on the subwavelength scale offer a rich paradigm for developing unique photonic functionalities ranging from negative index of refraction and directionally asymmetric transmission to slowing light. Here we demonstrate that a combination of carbon nanotubes with a photonic metamaterial offers a new paradigm for the development of nonlinear media with exceptionally strong ultrafast nonlinear response invaluable in photonic applications. It is underpinned by strong coupling between weakly radiating Fano-type resonant plasmonic modes and the excitonic res…
We demonstrate, for the first time, an all-dielectric metamaterial resonator in the mid-wave infrared based on high-index tellurium cubic inclusions. Dielectric resonators are desirable compared to conventional metallo-dielectric metamaterials at optical frequencies as they are largely angular invariant, free of ohmic loss, and easily integrated into three-dimensional volumes. With these low-loss, isotropic elements, disruptive optical metamaterial designs, such as wide-angle lenses and cloaks, can be more easily realized.
Artificially structured metamaterials have enabled unprecedented flexibility in manipulating electromagnetic waves and producing new functionalities, including the cloak of invisibility based on coordinate transformation. Here we present the design of a non-magnetic cloak operating at optical frequencies. The principle and structure of the proposed cylindrical cloak are analyzed, and the general recipe for the implementation of such a device is provided. The cloaking performance is verified using full-wave finite-element simulations.
Control of electromagnetic waves using engineered materials is very important in a wide range of applications, therefore there is always a continuous need for new and more efficient solutions. Known natural and artificial materials and surfaces provide a particular functionality in the frequency range they operate but cast a "shadow" and produce reflections at other frequencies. Here, we introduce a concept of multifunctional engineered materials that possess different predetermined functionalities at different frequencies. Such response can be accomplished by cascading metasurfaces (thin comp…
Designing broadband enhanced chirality is of strong interest to the emerging fields of chiral chemistry and sensing, or to control the spin orbital momentum of photons in recently introduced nanophotonic chiral quantum and classical optical applications. However, chiral light-matter interactions have an extremely weak nature, are difficult to be controlled and enhanced, and cannot be made tunable or broadband. In addition, planar ultrathin nanophotonic structures to achieve strong, broadband, and tunable chirality at the technologically important visible to ultraviolet spectrum still remain el…
e present a detailed study of the retrieved optical parameters, electrical permittivity, magnetic permeability and refractive index, of the coupled fishnet metamaterial structures as a function of the separation between layers. For the weak coupling case, the retrieved parameters are very close to the one-functional-layer results and converge relatively fast. For the strong coupling case, the retrieved parameters are completely different than the one unit fishnet results. We also demonstrate that the high value of the figure of merit (FOM=|Re(n)/Im(n)|) for the strongly coupled structures is d…
Polaritonic materials, owing to a strong phonon-polariton resonance in the THz and far-infrared parts of the electromagnetic spectrum, offer both high-index dielectric and metallic response in this regime. This complex response makes them suitable candidates for the design of metamaterial-related phenomena and applications. Here we show that one type of polaritonic-material-based structures that are particularly suitable for the achievement of a wide range of metamaterial properties are systems of polaritonic rods. To study the interplay between the material and the structural resonances in su…
Photonic metamaterials are man-made structures composed of tailored micro- or nanostructured metallo-dielectric sub-wavelength building blocks that are densely packed into an effective material. This deceptively simple, yet powerful, truly revolutionary concept allows for achieving novel, unusual, and sometimes even unheard-of optical properties, such as magnetism at optical frequencies, negative refractive indices, large positive refractive indices, zero reflection via impedance matching, perfect absorption, giant circular dichroism, or enhanced nonlinear optical properties. Possible applicat…
The toroidal response is numerically investigated in a multifold double-ring metamaterials at the antibonding magnetic-dipole mode (i.e., antiparallel magnetic dipoles in one double-ring fold). This intriguing toroidal resonance in metamaterials is considered as a result of the magnetoelectric effect due to the broken balance of the electric near-field environment. We demonstrate that the toroidal dipole response in metamaterials can improve the quality factor of the resonance spectrum. In viewing of the design flexibility on the double-ring geometry, such toroidal metamaterials will offer adv…
Using interplay between surface plasmons and metamaterials, we propose a new technique for novel metamaterial designs. We show that surface plasmons existing on thin metal surfaces can be used to "drive" non-resonant structures in their vicinity to provide new types of electric and magnetic resonators. These resonators strictly adhere to surface plasmon dispersion of the host metal film. The operating frequency of the resultant metamaterials can be scaled to extremely high frequencies, otherwise not possible with conventional split-ring-resonator-based designs. Our approach opens new possibili…
We estimate the dominating frequencies contributing to the Casimir energy in a cavity of metamaterials mimicking de Sitter space, by solving the eigenvalue problem of Maxwell equations. It turns out the dominating frequencies are the inverse of the size of the cavity, and the degeneracy of these frequencies also explains our previous result on the unusually large Casimir energy. Our result suggests that carrying out the experiment in laboratory is possible theoretically.
Strong diamagnetic response of wire medium with finite wire radius is reported. Contrary to the previous works where it was assumed that the wire medium exhibits only the electric response, we show that the non-zero magnetic susceptibility has to be taken into account for proper effective medium description of the wire medium. Analytical and numerical results are supported by the experimental measurements.
We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order. Specifically, by resorting to a suitable multiscale technique, we show that medium effective permittivity tensor and the first and second order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly-varying fields each satysifing electrostatic-like equations within the metamaterial unit cell. For metamaterials with ne…
Electromagnetic metamaterials offer a great avenue to engineer and amplify the nonlinear response of materials. Their electric, magnetic, and magneto-electric linear and nonlinear response are related to their structure, providing unprecedented liberty to control those properties. Both the linear and the nonlinear properties of metamaterials are typically anisotropic. While the methods to retrieve the effective linear properties are well established, existing nonlinear retrieval methods have serious limitations. In the present work, we generalize a nonlinear transfer matrix approach to account…
