Hyperbolic Dispersion Relation Research Articles

Hyperbolic plasmons on natural biphenylene surface

Meta-surfaces constructed of patterned graphene nanoribbons on dielectric substrates have enabled in-plane propagation of surface plasmons with hyperbolic dispersion. However, the current size limitations of these meta-surface result in a restricted ceiling for the plasmon wave vector, highlighting the importance of exploring natural hyperbolic surfaces that do not require structuring. Here, we unveil a promising natural hyperbolic surface: the newly-synthesized graphene allotrope – biphenylene (BPN) [Fan et al., Science 372, 852–856 (2021)]. We demonstrate the anisotropic framework of π orbitals of BPN endows broadband hyperbolic plasmons on the BPN surface. Undamped plasmons emerge along the x-direction with a broadband spectrum from THz to the ultraviolet regime, whereas those along the y-direction are restricted to a low frequency region (<0.74 eV). Notably, hyperbolic regimes are observed within specific energy ranges, 1.21–2.44 eV and 3.35–3.51 eV, which facilitate the directional propagation of surface plasmons with hyperbolic dispersion relations. These results open an avenue for the use of graphene technique in advanced optics and offer a promising strategy for designing hyperbolic natural surfaces.

Probing hyperbolic and surface phonon-polaritons in 2D materials using Raman spectroscopy

The hyperbolic dispersion relation of phonon-polaritons (PhPols) in anisotropic van der Waals materials provides high-momentum states, directional propagation, subdiffractional confinement, large optical density of states, and enhanced light-matter interactions. In this work, we use Raman spectroscopy in the convenient backscattering configuration to probe PhPol in GaSe, a 2D material presenting two hyperbolic regions separated by a double reststrahlen band. By varying the incidence angle, dispersion relations are revealed for samples with thicknesses between 200 and 750 nm. Raman spectra simulations confirm the observation of one surface and two extraordinary guided polaritons and match the evolution of PhPol frequency as a function of vertical confinement. GaSe appears to provide relatively low propagation losses and supports confinement factors matching or exceeding those reported for other 2D materials. Resonant excitation close to the 1s exciton singularly exalts the scattering efficiency of PhPols, providing enhanced scattering signals and means to probe the coupling of PhPols to other solid-state excitations.

Broadband hyperbolic plasmons in aluminum disulfide monolayer and its analogues: The role of orbital anisotropy

Two-dimensional (2D) materials with high in-plane anisotropy offer promising candidates for hosting highly directional surface plasmons, but few of them have been demonstrated to reach this goal thus far. In this paper, we propose a design principle of 2D hyperbolic materials (2D-HMs) based on orbital anisotropy and predict from first-principles calculations a family of 2D-HMs: aluminum disulfide monolayer and its analogues $X{Y}_{2}$ $(X=\mathrm{Al},\mathrm{Ga},\mathrm{In};Y=\mathrm{S},\mathrm{Se},\mathrm{Te})$. These natural 2D-HMs exhibit broadband hyperbolic regimes across the near-infrared to ultraviolet spectrum, enabling the propagation of highly directional hyperbolic surface plasmons. Undamped plasmons emerge along the $x$ direction with the maximum wave vector of $\ensuremath{\sim}0.16\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$ and frequency of 4.6 eV, whereas the plasmons along the $y$ direction have low frequency $(&lt;0.6\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$ and decay rapidly to electron-hole pairs for the $\mathrm{Al}{\mathrm{S}}_{2}$ monolayer. By solving Maxwell's equation, we simulate the directional propagation of the surface waves with hyperbolic dispersion relations. We correlate the fascinating plasmonic properties with the unique electronic structures of these highly anisotropic 2D materials, which offers a promising strategy for the design of 2D-HMs.

Nano‐Optical Engineering of Anisotropic Phonon Resonances in a Hyperbolic α‐MoO3 Metamaterial

AbstractLow‐dimensional α‐phase molybdenum trioxide (α‐MoO3), a layered van‐der‐Waals (vdW) semiconductor, has emerged as an attractive natural hyperbolic material supporting mid‐infrared hyperbolic phonon polaritons (PhPs), which exhibit strong spatial confinement and low loss. With the advantages of strong in‐plane optical anisotropy, many efforts have been devoted to investigating the properties of hyperbolic PhPs in α‐MoO3 using scanning near‐field optical microscopy. However, the studies of far‐field controlling of hyperbolic PhPs in α‐MoO3 have been quite limited so far. This work reports the first experimental demonstration of far‐field excitation and manipulation of hyperbolic phonon resonances in metamaterial structures consisting of α‐MoO3 nanodisks and slabs. The excited phonon resonances show a maximum spatial confinement factor (free space wavelength/period) of 32 and a quality factor of 76. It is shown that the in‐plane phonon resonances in α‐MoO3 can be selectively excited in the two Reststrahlen bands featuring hyperbolic dispersion relations along its two crystal directions, by simply controlling the incident polarization. In addition, the relative strength of resonances along different in‐plane crystal directions and the resultant field distributions can be continuously reconfigured by varying the incident polarization angle. These findings pave the way for future development of novel nanophotonic devices based on hyperbolic PhPs in vdW materials.

Mechanism of emitters coupled with a polymer-based hyperbolic metamaterial.

We study a polymer-based hyperbolic metamaterial (HMM) structure composed of three Au-polymer bilayers with a hyperbolic dispersion relation. Using an effective refractive index retrieval algorithm, we obtain the effective permittivity of the experimentally fabricated polymer-based structure. In particular, the unique polymer-based HMM shows the existence of high-k modes that propagate in the metal-dielectric multilayered structure due to the excitation of bulk plasmon-polaritonic modes. Moreover, we compare the experimental luminescence and fluorescence lifetime results of the multilayered Au and a dye-doped polymer (PMMA) to investigate the dynamics of three different emitters, each incorporated within the unique polymer-based HMM structure. With emitters closer to the epsilon-near-zero region of the HMM, we observed a relatively high shortening of the average lifetime as compared to other emitters either close or far from the epsilon-near-zero region. This served as evidence of coupling between the emitters and the HMM as well as confirmed the increase in the non-radiative recombination rate of the different emitters. We also show that the metallic losses of a passive polymer-based HMM can be greatly compensated by a gain material with an emission wavelength close to the epsilon-near-zero region of the HMM. These results demonstrate the unique potential of an active polymer-based hyperbolic metamaterial in loss compensation, quantum applications, and sub-wavelength imaging techniques.

A high–order spectral algorithm for the numerical simulation of layered media with uniaxial hyperbolic materials

Electromagnetic metamaterials are artificial media assembled from components which have dimensions much smaller than the wavelength of the illuminating radiation. It has been demonstrated that these media can have properties beyond those found in conventional materials with important applications to many areas of science and engineering. Among the collection of such materials currently garnering significant attention are the Hyperbolic Metamaterials. These are highly anisotropic structures which have a hyperbolic dispersion relation due to the fact that one principal component of the relative permittivity or permeability tensor has the opposite sign of the other two. For such materials scattered wave information at all scales is transmitted far away which suggests a number of important applications, the most immediate of which is imaging objects below the diffraction limit (superlensing). Clearly it is of great current interest to have numerical simulation capabilities for these fascinating materials. As the hyperbolic response is quite strong and its nature is very sensitive, numerical simulations of these configurations should be robust and highly accurate. For this reason we focus on High–Order Spectral algorithms which efficiently produce high fidelity solutions. More specifically, we describe a High–Order Perturbation of Surfaces approach which enjoys the greatly reduced operation counts and memory savings of interfacial methods while avoiding the complexities and indefinite linear systems faced by Integral Equation algorithms. We give a full discussion of our formulation in terms of Impedance–Impedance Operators (which avoids spurious singularities of other formulations) and implementation details, followed by numerical validation and simulation of results which appear in the engineering literature.

The NV metamaterial: Tunable quantum hyperbolic metamaterial using nitrogen vacancy centers in diamond

We show that nitrogen-vacancy (NV) centers in diamond can produce a unique quantum hyperbolic metamaterial. We demonstrate that a hyperbolic dispersion relation in diamond with NV centers can be engineered and dynamically tuned by applying a magnetic field at 20 K. This quantum hyperbolic metamaterial with a tunable window for the negative refraction allows for the construction of a superlens beyond the diffraction limit. In addition to subwavelength imaging, this NV metamaterial can be used in spontaneous emission enhancement, heat transport, and acoustics, analog cosmology, and lifetime engineering. Therefore, our proposal interlinks the two hotspot fields, i.e., NV centers and metamaterials.

Hyperbolic Bismuth–Dielectric Structure for Terahertz Photonics

Hyperbolic medium is a special class of strongly anisotropic materials described by diagonal permittivity tensor with the principal components being of the opposite signs, which results in a hyperbolic shape of isofrequency contours. These media support propagating electromagnetic waves with extremely large wave vectors exhibiting unique optical properties and applications such as negative refraction, subwavelength imaging, radiative heat transfer manipulation, enhancing spontaneous emission rate (Purcell factor), biosensing, and nanoscale light confinement. Hyperbolic metamaterials have been experimentally realized for optical, infrared, and microwave frequency ranges. For the terahertz (THz) frequency range, graphene‐based and bismuth‐based media are only theoretically predicted to have a hyperbolic dispersion relation. Herein, the experimental evidence of such dispersion in bismuth–dielectric materials at THz frequencies is shown. THz waveforms transmitted through ultrathin bismuth film/dielectric substrate structures are measured and the negative time delay caused by transition between the elliptic and hyperbolic dispersion at bismuth thickness increase is revealed. In the hyperbolic regime, the switching between effective near‐zero and negative refractive index regime is demonstrated, which depends on the bismuth film thickness and dielectric substrate optical properties. The outcomes demonstrate the possibility for realizing easy planar hyperbolic media for THz photonics, sensing, imaging, and communication systems.

(Invited) Electroluminescent Hyperbolic Cooling of Graphene Field Effect Transistors

Heat management is critical for the performance of most modern electronic devices. It was recently proposed that radiative heat transfer - which is usually negligible in the solid state - could be increased in hyperbolic metamaterials, i.e., materials having a hyperbolic electromagnetic dispersion relation. [1] However, artificial metamaterials can be difficult to fabricate and integrate.Fortunately, most of Van der Waals materials are natural hyperbolic metamaterials. Indeed, due to their anisotropic layered structure, the in-plane and out-of-plane optical phonon energy splitting results in a hyperbolic dispersion of light in the Resstrahlen bands. As a consequence, in these materials, the strong light-matter coupling can give rise to a 102-105 increase in the e.m. local density of states, resulting in a dramatic enhancement of the radiative heat transfer. Moreover, the radiative character of heat exchange results in a propagative heat transport via hyperbolic phonon-polariton (HPhP) modes on micrometric scales.We have studied heat transfer in graphene on hexagonal boron nitride: a natural 2D hyperbolic material. In our devices, graphene is used as a versatile heat source in the near field of a hyperbolic material, and as a sensitive noise thermometer. [2] Using mono-, bi- and trilayer graphene, we demonstrate a strong increase of the electron gas cooling resulting in a large temperature drop when the emission of HPhP sets in. This process shares many analogies with electroluminescence, except that it involves near-field modes. We experimentally evidence that the case of graphene is unique, with cooling powers reaching few milliwatts per micron square [3], i.e., nine orders of magnitude larger than previously reported in the literature. Bibliography [1] S. Biehs, et al "Hyperbolic metamaterials as an analog of a blackbody in the near field." Phys. Rev. Lett. 109, 104301 (2012)[2] W. Yang, et al "A Graphene Zener–Klein Transistor Cooled by a Hyperbolic Substrate." Nat. Nanotech. 13, 47 (2018)[3] E. Baudin, et al "Hyperbolic Phonon Polariton Electroluminescence as an Electronic Cooling Pathway", Adv. Funct. Mat.1904783 (2019) Figure 1

Determination of the Lightest Strange Resonance K_{0}^{*}(700) or κ, from a Dispersive Data Analysis.

In this work we present a precise and model-independent dispersive determination from data of the existence and parameters of the lightest strange resonance κ/K_{0}^{*}(700). We use both subtracted and unsubtracted partial-wave hyperbolic and fixed-t dispersion relations as constraints on combined fits to πK→πK and ππ→KK[over ¯] data. We then use the hyperbolic equations for the analytic continuation of the isospin I=1/2 scalar partial wave to the complex plane, in order to determine the κ/K_{0}^{*}(700) and K^{*}(892) associated pole parameters and residues.

Hyperbolic metamaterial using chiral molecules

We theoretically investigate the intra-band transitions in M\"{o}bius molecules. Due to the weak magnetic response, the relative permittivity is significantly modified by the presence of the medium while the relative permeability is not. We show that there is hyperbolic dispersion relation induced by the intra-band transitions because one of the eigen-values of permittivity possesses a different sign from the other two, while all three eigen-values of permeability are positive. We further demonstrate that the bandwidth of negative refraction is 0.1952~eV for the $H$-polarized incident light, which is broader than the ones for inter-band transitions by 3 orders of magnitude. Moreover, the frequency domain has been shifted from ultra-violet to visible domain. Although there is negative refraction for the $E$-polarized incident light, the bandwidth is much narrower and depends on the incident angle.

Formation of nonlinearX-waves in condensed matter systems

X-waves are an example of a localized wave packet solution of the homogeneous wave equation, and can potentially arise in any area of physics relating to wave phenomena, such as acoustics, electromagnetism, or quantum mechanics. They have been predicted in condensed matter systems such as atomic Bose-Einstein condensates in optical lattices, and were recently observed in exciton-polariton condensates. Here we show that polariton X-waves result from an interference between two separating wave packets that arise from the combination of a locally hyperbolic dispersion relation and nonlinear interactions. We show that similar X-wave structures could also be observed in expanding spin-orbit coupled Bose-Einstein condensates.

Schrödinger formalism for a particle constrained to a surface in R13

In this work, the Schrödinger equation is studied for a non-relativistic particle restricted to move on a surface S in a three-dimensional Minkowskian medium R13, i.e., the space R3 equipped with the metric diag(−1, 1, 1). After establishing the consistency of the interpretative postulates for the new Schrödinger equation, namely, the conservation of probability and the hermiticity of the new Hamiltonian built out of the Laplacian in R13, we investigate the confining potential formalism in the new effective geometry. Like in the well-known Euclidean case, a geometry-induced potential acting on the dynamics VS=−ℏ22mεH2−K is found which, besides the usual dependence on the mean (H) and Gaussian (K) curvatures of the surface, has the remarkable feature of dependence on the signature of the induced metric of the surface: ε = +1, if the signature is (−, +), and ε = 1, if the signature is (+, +). Applications to surfaces of revolution in R13 are examined, and we provide examples, where the Schrödinger equation is exactly solvable, as well as possible impacts in optics. It is hoped that our formalism will prove useful in the modeling of novel materials such as hyperbolic metamaterials, which are characterized by a hyperbolic dispersion relation, in contrast to the usual spherical (elliptic) dispersion typically found in conventional materials.

Dispersive analysis of the κ/K0*(700) meson and other light strange resonances

We briefly review our recent works where we use dispersion relations to constrain fits to data on πK → πK and $ \pi \pi \to K\bar K $ providing a simple but consistent description of these processes. Then, simple analytic methods allow to extract parameters of poles associated to light strange resonances without assuming a particular model. We also present preliminary results on a model-independent determination of the controversial κ or $ K_0^*\left( {700} \right) $ resonance parameters, by using those constrained parameterizations as input for partial-wave hyperbolic dispersion relations that allow to perform a rigorous analytic continuation to determine its associated pole.

Pi pi rightarrow K {bar{K}} scattering up to 1.47 GeV with hyperbolic dispersion relations

In this work we provide a dispersive analysis of pi pi rightarrow K{bar{K}} scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from K{{bar{K}}} threshold up to 2 GeV, while being consistent with crossing symmetric partial-wave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region.

Hyperbolic Medium of Finite-Length Wires

An artificial medium in the form of a cubic uniaxial photonic crystal (PC) with periodically arranged conducting wire cylinders in a dielectric matrix and oriented along the PC axis is considered. Permittivity \(\tilde \varepsilon \) of the matrix is assumed to be constant, while the permittivity of the cylinders is described by the Drude–Lorentz model. The homogenization of such a medium, the methods of its description, the role of dissipation and spatial dispersion (SD), as well as the possibility of obtaining a hyperbolic dispersion relation are considered. The ambiguity of the PC description with the help of effective material parameters and the introduction of such parameters are demonstrated, as well as the effect of dissipation and SD on the hyperbolicity property under investigation.

Biaxial hyperbolic metamaterials using anisotropic few-layer black phosphorus.

Most of hyperbolic metamaterials (HMMs) investigated to date are based on isotropic materials resulting in uniaxial HMMs in which dielectric permittivities perpendicular to the propagation direction are the same. Using an anisotropic material constituent to form a HMM is a promising research direction providing opportunities to control the dielectric permittivity in all three directions independently. Herein, we propose and theoretically demonstrate novel biaxial HMMs composed of multilayer stacks of few-layer black phosphorus (BP) and Au thin films. Black phosphorus is an anisotropic material exhibiting crystal axis-dependent dielectric permittivity due to its puckered crystal structure. The proposed HMM provides previously unattained hyperbolic dispersion relations in which the dielectric permittivity in Z-direction of the structure shows opposite sign from that in X- and Y-directions in the most wavelengths from 400~900nm. Furthermore, we calculated the Purcell factor of the proposed biaxial HMMs using full-field electromagnetic simulations.

Tunable plasmon lensing in graphene-based structure exhibiting negative refraction

We propose a novel method to achieve tunable plasmon focusing in graphene/photonic-crystal hybrid structure exhibiting all-angle negative refraction at terahertz frequencies. A two-dimensional photonic crystal composed of a square lattice of dielectric rods is constructed on the substrate of a graphene sheet to provide the hyperbolic dispersion relations of the graphene plasmon, giving rise to the all-angle plasmonic negative refraction. Plasmon lensing induced from the negative refraction is observed. We show that the ultracompact graphene-based system can produce sub-diffraction-limited images with the resolution significant smaller than the wavelength of the incident terahertz wave. Moreover, by adjusting the Fermi energy of the graphene, the imaging performance of the proposed system can remain almost invariant for different frequencies. Our results may find applications in diverse fields such as subwavelength spatial light manipulation, biological imaging, and so forth.

Luminescent hyperbolic metasurfaces

When engineered on scales much smaller than the operating wavelength, metal-semiconductor nanostructures exhibit properties unobtainable in nature. Namely, a uniaxial optical metamaterial described by a hyperbolic dispersion relation can simultaneously behave as a reflective metal and an absorptive or emissive semiconductor for electromagnetic waves with orthogonal linear polarization states. Using an unconventional multilayer architecture, we demonstrate luminescent hyperbolic metasurfaces, wherein distributed semiconducting quantum wells display extreme absorption and emission polarization anisotropy. Through normally incident micro-photoluminescence measurements, we observe absorption anisotropies greater than a factor of 10 and degree-of-linear polarization of emission >0.9. We observe the modification of emission spectra and, by incorporating wavelength-scale gratings, show a controlled reduction of polarization anisotropy. We verify hyperbolic dispersion with numerical simulations that model the metasurface as a composite nanoscale structure and according to the effective medium approximation. Finally, we experimentally demonstrate >350% emission intensity enhancement relative to the bare semiconducting quantum wells.

Epsilon-near-zero behavior from plasmonic Dirac point: Theory and realization using two-dimensional materials

The electromagnetic response of a two-dimensional metal embedded in a periodic array of a dielectric host can give rise to a plasmonic Dirac point that emulates Epsilon-Near-Zero (ENZ) behavior. This theoretical result is extremely sensitive to tructural features like periodicity of the dielectric medium and thickness imperfections. We propose that such a device can actually be realized by using graphene as the 2D metal and materials like the layered semiconducting transition-metal dichalcogenides or hexagonal boron nitride as the dielectric host. We propose a systematic approach, in terms of design characteristics, for constructing metamaterials with linear, elliptical and hyperbolic dispersion relations which produce ENZ behavior, normal or negative diffraction.