Isofrequency Surfaces Research Articles

Collimated beam formation in 3D acoustic sonic crystals

We demonstrate strongly collimated beam formation, at audible frequencies, in a three-dimensional acoustic phononic crystal where the wavelength is commensurate with the crystal elements; the crystal is a seemingly simple rectangular cuboid constructed from closely-spaced spheres, and yet demonstrates rich wave phenomena acting as a canonical three-dimensional metamaterial. We employ theory, numerical simulation and experiments to design and interpret this collimated beam phenomenon and use a crystal consisting of a finite rectangular cuboid array of 4×10×10 polymer spheres 1.38 cm in diameter in air, arranged in a primitive cubic cell with the centre-to-centre spacing of the spheres, i.e. the pitch, as 1.5 cm. Collimation effects are observed in the time domain for chirps with central frequencies at 14.2 kHz and 18 kHz, and we deployed a laser feedback interferometer or Self-Mixing Interferometer – a recently proposed technique to observe complex acoustic fields—that enables experimental visualisation of the pressure field both within the crystal and outside of the crystal. Numerical exploration using a higher-order multi-scale finite element method designed for the rapid and detailed simulation of 3D wave physics further confirms these collimation effects and cross-validates with the experiments. Interpretation follows using High Frequency Homogenization and Bloch analysis whereby the different origin of the collimation at these two frequencies is revealed by markedly different isofrequency surfaces of the sonic crystal.

Topological hyperbolic metamaterials

Abstract Hyperbolic metamaterial (HMM) is a unique type of anisotropic material that can exhibit metal and dielectric properties at the same time. This unique characteristic results in it having unbounded isofrequency surface contours, leading to exotic phenomena such as spontaneous emission enhancement and applications such as super-resolution imaging. However, at optical frequencies, HMM must be artificially engineered and always requires a metal constituent, whose intrinsic loss significantly limits the experimentally accessible wave vector values, thus negatively impacting the performance of these applications. The need to reduce loss in HMM stimulated the development of the second-generation HMM, termed active HMM, where gain materials are utilized to compensate for metal’s intrinsic loss. With the advent of topological photonics that allows robust light transportation immune to disorders and defects, research on HMM also entered the topological regime. Tremendous efforts have been dedicated to exploring the topological transition from elliptical to hyperbolic dispersion and topologically protected edge states in HMM, which also prompted the invention of lossless HMM formed by all-dielectric material. Furthermore, emerging twistronics can also provide a route to manipulate topological transitions in HMMs. In this review, we survey recent progress in topological effects in HMMs and provide prospects on possible future research directions.

The diversity of isofrequency surface topologies in a hypercrystal composed of ferrite- and semiconductor-based metamaterials

Recent studies have centered on the potential for effectively controlling the topology state of iso-frequency surfaces in artificial photonic structures using external fields. This paper delves into the topological transitions and singularity states of the isofrequency surface of a highly anisotropic superlattice. This superlattice is composed of alternating layers of ferrite-dielectric and semiconductor-dielectric metamaterials. The superlattice is placed in an external magnetic field in the Voigt geometry that is parallel to the boundaries of the structure layers and perpendicular to the periodicity axis. Material properties of both constituent metamaterials are described in terms of effective components of permittivity and permeability in the long-wave approximation. An external magnetic field influences the properties of transverse electric (TE) waves in the ferrite-dielectric metamaterial, and the properties of transverse magnetic (TM) waves in the semiconductor-dielectric metamaterial. This results in the iso-frequency surface transition from a closed ellipsoid to an open hyperboloid for both TE and TM waves in various configurations. Furthermore, the superlattice can be identified as a hypercrystal under certain conditions, specifically when the constituent metamaterials possess a hyperbolic isofrequency surface state. This research demonstrates that the isofrequency surface properties of the studied hypercrystal can be effectively controlled by altering the external magnetic field, the fill factors of metamaterials, and frequency. Special attention is devoted to investigating the topological singularities that take place when iso-frequency surfaces of TE and TM polarized waves intersect. This intersection leads to the degeneracy of the hypercrystal’s isofrequency surface and the potential observation of unique phenomena such as conical refraction or the existence of surface states.

Controlling the dispersion of longitudinal waves via the affine deformation of the interlaced wire medium

We studied the dispersion properties of double interlaced wire metamaterials with geometry modified by affine transformation. That metamaterials were found to support eigenmodes with longitudinal polarization at low frequencies for all deformations. Due to spatial dispersion, the metamaterials’ isofrequency surfaces are centered at the Brillouin zone edges (rather than at Γ-point) and have the shape of ellipsoids. Their refractive indices corresponding to the ellipsoids were analyzed both analytically and numerically.

Negative refraction in multilayered metal-dielectric metamaterials with ellipse-like isofrequence surfaces

Negative refraction in multilayered metal-dielectric metamaterials is usually based on negative refractive indices or hyperbolic-like isofrequency surfaces. In this study, we reveal that ellipse-like isofrequency surfaces can also lead to negative refraction. This phenomenon is theoretically demonstrated by analyzing the group velocities of refracted beams based on the exact transfer-matrix method and verified by numerical simulation based on the finite-element method. The corresponding physics mechanism is investigated through the energy flow of the ellipse-like modes in the metallic and dielectric layers. The results are also compared with the case of energy flow of hyperbolic-like modes. Moreover, negative double refraction is realized because negatively refracted beams can be enabled by ellipse-like and hyperbolic-like isofrequency surfaces simultaneously.

Dispersion properties of van der Waals phonon polaritons modulated by Weyl semimetals

Surface phonon polaritons (SPhP) as an alternative constituent for mid-infrared (MIR) nanophotonic applications have attracted extensive attention and they maybe solve the intrinsic loss problem of plasmonics. SPhP arise in polar dielectrics due to IR-active phonon resonances, leading to negative permittivity within the Reststrahlen band. Although SPhP have great potential in enhancing the interaction between light and matter in the infrared region, it is still limited to enhance optical fields and fixed resonance band because of the existing Reststrahlen band. Moreover, active manipulating of phonon polaritons in MIR range remains elusive. The significant research progress of natural van der Waals (vdW) crystal and heterostructures have been made, which are characterized by an anisotropic polaritonic response, leading to elliptical, hyperbolic, or biaxial polaritonic dispersions. Among these structures, SPhP with hyperbolicity in <i>α</i>-MoO<sub>3</sub> are of particular interest, due to not only the strong field confinement, low losses, and long lifetimes, but also the natural in-plane anisotropic dispersion. A heterostructure composed of a biaxial vdW material (<i>α</i>-MoO<sub>3</sub>) and a Weyl semimetal (WSM) is proposed to study the active tunability of anisotropic SPhP. The control of polaritons can show more degrees of freedom, which has not yet been addressed. Under the incident condition of transverse magnetic incident wave, the reflection coefficient and field distribution in the heterogeneous system are accurately solved by the 4×4 transfer matrix method, and the dispersion properties of anisotropic SPhP are described in detail. Variation of dispersion spectrum with azimuthal angle and <i>α</i>-MoO<sub>3</sub> thickness is presented. The research results indicate that mode hybridization and dispersion manipulation can be realized by controlling the azimuth angle and the thickness of <i>α</i>-MoO<sub>3</sub>. More importantly, the Fermi level of WSM enable the adjustment of dynamic dispersion curve, which depends on the change of external temperature. Isofrequency curves of hybridized SPhP at different Fermi levels are also demonstrated. By chemically changing the Femi level of <i>α</i>-MoO<sub>3</sub>, the topology of polariton isofrequency surfaces transforms from open shape to closed shape as a result of polariton hybridization. Therefore, our research is helpful in further optimizing and designing active optoelectronic devices based on vdW materials, which have good application prospects in infrared heat radiation and biosensing.

Doping-driven topological polaritons in graphene/α-MoO3 heterostructures

Control over charge carrier density provides an efficient way to trigger phase transitions and modulate the optoelectronic properties of materials. This approach can also be used to induce topological transitions in the optical response of photonic systems. Here we report a topological transition in the isofrequency dispersion contours of hybrid polaritons supported by a two-dimensional heterostructure consisting of graphene and α-phase molybdenum trioxide. By chemically changing the doping level of graphene, we observed that the topology of polariton isofrequency surfaces transforms from open to closed shapes as a result of doping-dependent polariton hybridization. Moreover, when the substrate was changed, the dispersion contour became dominated by flat profiles at the topological transition, thus supporting tunable diffractionless polariton propagation and providing local control over the optical contour topology. We achieved subwavelength focusing of polaritons down to 4.8% of the free-space light wavelength by using a 1.5-μm-wide silica substrate as an in-plane lens. Our findings could lead to on-chip applications in nanoimaging, optical sensing and manipulation of energy transfer at the nanoscale.

The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas

The topological Langmuir-cyclotron wave (TLCW) is a recently identified topological surface excitation in magnetized plasmas. We show that TLCW originates from the topological phase transition at the Langmuir wave-cyclotron wave resonance. By isofrequency surface analysis and two- and three-dimensional time-dependent simulations, we demonstrate that the TLCW can propagate robustly along complex phase transition interfaces in a unidirectional manner and without scattering. Because of these desirable features, the TLCW could be explored as an effective mechanism to drive current and flow in magnetized plasmas. The analysis also establishes a close connection between the newly instituted topological phase classification of plasmas and the classical Clemmow-Mullaly-Allis (CMA) diagram of plasma waves.

Nanostructured multilayer hyperbolic metamaterials for high efficiency and selective solar absorption.

Highly efficient solar-to-thermal conversion is desired for the renewable energy technologies, such as solar thermo-photovoltaics and solar thermo-electric systems. In order to maximize the energy conversion efficiency, solar-selective absorbers are essential with its absorption characteristics specially tailored for solar applications. Here, we propose a wideband spectral-selective absorber based on three-dimensional (3D) nanostructured hyperbolic metamaterial (HMM), which can realize near-unity absorption across the UV and NIR spectral ranges. Moreover, the optical topological transition (OTT) of iso-frequency surface (IFS) is manipulated to selectively enhance light absorption in the entire solar spectrum, crucial for improved energy utilization. Impressive solar-to-thermal conversion efficiency of 95.5% has been achieved. Particularly, such superior properties can be retained well even over a wide range of incident angles. These findings open new avenues for designing high-performance solar thermal devices, especially in the fields related to solar energy harvesting.

Gyrotropy-governed isofrequency surfaces and photonic spin in gyromagnetic media

Topology of isofrequency surfaces plays a crucial role in characterizing the interaction of an electromagnetic wave with a medium. Thus, engineering the topology in complex media is leading to novel applications, ranging from super-resolution microscopy with hyperbolic metamaterials to sub-wavelength waveguiding structures. Here, we investigate the spin-governed nature of isofrequency surfaces in a general gyromagnetic medium. We show that gyrotropy also plays an important role in the topological properties of a medium, along with the anisotropic permeability and permittivity. Even though the topology primarily depends on permeability, gyrotropy can suppress or support the existence of certain topological surfaces. We reveal the connection between the gyrotropy imposed constraints and the photonic spin-profile of the topological surfaces. The spin-profile along the isofrequency surface is locked to the material, resulting in the non-reciprocity and breaking of the spin-momentum locking in the gyromagnetic medium. Further, we show that the conflict between spin-momentum locking and material locked spin leads to asymmetric mode profile and gyrotropy-induced cutoff in guided wave structures. Our work provides important insights into the underlying link between topology, spin, and non-reciprocity in gyrotropic media.

Topological Engineering of the Iso-Frequency Contours in Connection-Type Metamaterials

The topology of isofrequency surface governs the electromagnetic wave propagation and light–matter interaction in metamaterials. For most metamaterials with local medium description, the low-frequency isosurfaces are typical spheres or ellipsoids centered at zero momentum, which, to some extent, limits our manipulation ability on low-frequency wave. In this work, based on connection-type wire metamaterials, we propose a scheme to engineer the shapes of isofrequency surfaces. An equivalent circuit model is developed to analyze the low-frequency dispersion of connection-type metamaterials. It implies that the shape of index ellipsoids at quasistatic limit is determined by the equivalent inductances and capacitances of the metallic meshes. By adjusting these equivalent circuit parameters, we can achieve the isotropic or anisotropic index ellipsoids at quasistatic limit and, hence, a cruciform or bowtie-shaped isofrequency contours for the lowest-frequency band. Our results demonstrate a feasible platform for topological engineering of isofrequency surfaces, which may pave the way to novel devices for manipulating long-wavelength electromagnetic wave.

Beam steering with the enhanced semiconductor-based hyperprism

To the best of our knowledge topological change of the iso-frequency surface of hyperbolic metamaterials paves the way for the unique capabilities aiming to engineer propagation of the wave. Herein, an enhanced semiconductor-based hyperprism structure is presented aiming to seek for the optical switching and beam steering dependencies. Based on the outcomes of the numerical simulations one may conclude that by engineering the doping level of the semiconductor-based hyperprism, a maximum adjustable angle of 1.4 rad can be obtained. It has been concluded that changes in doping level allow for a variety of fascinating phenomenon.

Linear dynamics of spin waves in an array of YIG waveguides

The features of spin-wave transport in a system of coupled magnetic microwaveguides with perpendicular magnetization relative to the longitudinal axis of the system are considered. In this case, the system has uniaxial anisotropy, the horizontal and vertical coupling coefficients have different signs, and the isofrequency surfaces have a "saddle" shape. In the propagation of transversely limited beams of spin waves, the type of curvature of the wave fronts is determined by the direction of wave propagation relative to the external magnetic field. Keywords: spin waves, magnonics, microwaveguides, lateral structures.

Classification and materials realization of topologically robust nodal ring phonons

Nodal ring phonons with topologically nontrivial properties have triggered much interest in recent years. Unlike fermions inevitably affected by the spin-orbit interaction, nodal ring phonons are topologically robust. In this paper, we investigate the classification of nodal rings in phonon systems based on symmetry arguments and $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ models. We identify that all the nodal ring phonons can be categorized into three types, i.e., in-plane nodal rings protected by mirror symmetry, twisted nodal rings protected by inversion and time-reversal symmetries, and the hybrid type protected by a combination of these symmetries. On the basis of first-principles calculations, we propose that these three types of nodal ring phonons can emerge in two different phases of silver oxide. The calculation results also show clear drumheadlike surface states along high-symmetry paths and nontrivial arc states in the isofrequency surfaces. This work exposes various appearances of nodal rings and also promotes the development of topological phonons.

Hourglass phonons jointly protected by symmorphic and nonsymmorphic symmetries

Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the hourglass dispersion can be jointly protected by symmorphic and nonsymmorphic symmetries, instead of the conventional nonsymmorphic symmetry. Moreover, using first-principles calculations, we realize our proposal in the phonon spectra of realistic materials that share an antiperovskite structure with space group $P4$/nmm. Importantly, the neck points of these hourglass dispersions trace out two nodal rings tangential to four nodal lines, forming a unique hourglass nodal cage in the bulk Brillouin zone. The Berry phase analysis reveals the nontrivial topology of these nodal rings and nodal lines. Furthermore, nontrivial surface states and isofrequency surface arcs are visible, facilitating their experimental confirmation of such exotic quasiparticles. work not only offers different insights into the hourglass dispersion, but also expands aspects for studying promising topological quasiparticles in condensed-matter systems.

Anisotropic epsilon-near-pole (ENP) resonance leads to hyperbolic photonic dispersion in homologous (Bi2)m(Bi2Se3)n topological quantum materials

The hyperbolic iso-frequency surface (dispersion) of photons in materials that arise from extreme dielectric anisotropy is the latest frontier in nanophotonics with potential applications in subwavelength imaging, coherent thermal emission, photonic density of state engineering, negative refraction, thermal hyperconductivity, etc. Most hyperbolic materials utilize nanoscale periodic metal/dielectric multilayers (superlattices) or metallic nanowires embedded inside the dielectric matrix that require expensive growth techniques and possess significant fabrication challenges. Naturally occurring bulk materials that exhibit tunable hyperbolic photonic dispersion in the visible-to-near-IR spectral ranges will, therefore, be highly beneficial for practical applications. Due to the layered structure and extreme anisotropy, a homologous series of (Bi2)m(Bi2Se3)n could serve as a unique class of natural hyperbolic material with tunable properties derived from different stoichiometry. In this Letter, we demonstrate hyperbolic photonic dispersion in a single crystal of weak topological insulator BiSe (m = 1 and n = 2), where a Bi2 layer is inserted between Bi2Se3 (m = 0 and n = 1) quintuple layers in the visible (525–710 nm) and near-UV (210–265 nm) spectral range. The origin of hyperbolic dispersion in homologous (Bi2)m(Bi2Se3)n topological quantum materials arises from their anisotropic epsilon-near-pole resonance corresponding to the interband transitions that lead to different signs of its dielectric permittivity. The tunability of hyperbolic dispersion is further demonstrated by alloying Bi2Se3 with Mn that alters the interband transition positions and expands their hyperbolic spectral regime from 500–1045 to 500–1185 nm.

Experimental investigation of optically controlled topological transition in bismuth-mica structure

The hyperbolic materials are strongly anisotropic media with a permittivity/permeability tensor having diagonal components of different sign. They combine the properties of dielectric and metal-like media and are described with hyperbolic isofrequency surfaces in wave-vector space. Such media may support unusual effects like negative refraction, near-field radiation enhancement and nanoscale light confinement. They were demonstrated mainly for microwave and infrared frequency ranges on the basis of metamaterials and natural anisotropic materials correspondingly. For the terahertz region, the tunable hyperbolic media were demonstrated only theoretically. This paper is dedicated to the first experimental demonstration of an optically tunable terahertz hyperbolic medium in 0.2–1.0 THz frequency range. The negative phase shift of a THz wave transmitted through the structure consisting of 40 nm (in relation to THz wave transmitted through substrate) to 120 nm bismuth film (in relation to both THz waves transmitted through substrate and air) on 21 µm mica substrate is shown. The optical switching of topological transition between elliptic and hyperbolic isofrequency contours is demonstrated for the effective structure consisting of 40 nm Bi on mica. For the case of 120 nm Bi on mica, the effective permittivity is only hyperbolic in the studied range. It is shown that the in-plane component of the effective permittivity tensor may be positive or negative depending on the frequency of THz radiation and continuous-wave optical pumping power (with a wavelength of 980 nm), while the orthogonal one is always positive. The proposed optically tunable structure may be useful for application in various fields of the modern terahertz photonics.

Optical topological transition and refraction control in crystal quartz by tilting the optical axis

Optical topological transition of iso-frequency surfaces strongly modifies the propagation behavior within media. However, in most previous studies, optical topological transition was achieved by tuning the frequency. In this paper, we achieve optical topological transition at fixed frequencies by tuning the direction of the optical axis in crystal quartz. Also, according to the energy flow method, we calculate the refractive angle within the crystal quartz. The calculated results show that both positive and negative refraction can be realized by tuning the direction of the optical axis in the crystal quartz. This optical topological transition in crystal quartz by tilting the optical axis might have potential applications in refraction controlling, spontaneous emission engineering, thermal emission engineering, and phonon polariton engineering.

Линейная динамика спиновых волн в массив ЖИГ-волноводов

The features of spin-wave transport in a system of coupled magnetic microwaveguides with perpendicular magnetization relative to the longitudinal axis of the system are considered. In this case, the system has uniaxial anisotropy, the horizontal and vertical coupling coefficients have different signs, and the isofrequency surfaces have a "saddle" shape. In the propagation of transversely limited beams of spin waves, the type of curvature of the wave fronts is determined by the direction of wave propagation relative to the external magnetic field.

Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals

It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that in an AB-layer-stacked photonic crystal composed of anisotropic dielectrics, the unique photonic band connectivity leads to a new kind of symmetry-enforced triply degenerate points at the nexuses of two nodal rings and a Kramers-like nodal line. The emergence and intersection of the line nodes are guaranteed by a generalized 1/4-period screw rotation symmetry of Maxwell’s equations. The bands with a constant kz and iso-frequency surfaces near a nexus point both disperse as a spin-1 Dirac-like cone, giving rise to exotic transport features of light at the nexus point. We show that spin-1 conical diffraction occurs at the nexus point, which can be used to manipulate the charges of optical vortices. Our work reveals that Maxwell’s equations can have hidden symmetries induced by the fractional periodicity of the material tensor components and hence paves the way to finding novel topological nodal structures unique to photonic systems.