Isofrequency Contours Research Articles

Toggling near-field directionality via manipulation of matter's anisotropy.

Near-field directional excitation of dipolar sources is crucial for many practical applications, such as quantum optics, photonic integrated circuits, and on-chip information processing. Based on theoretical analyses and numerical simulations, here we find that the near-field directionality of circularly polarized dipoles can be flexibly toggled by engineering the anisotropy of the surrounding matter, in which the dipolar source locates. To be specific, if the circularly polarized dipole is placed close to the interface between a hyperbolic matter and air, the main propagation direction of excited surface waves would be reversed when the location of the dipolar source is changed from the air region to the hyperbolic-matter region. The underlying mechanism is that the spatial-frequency spectrum of evanescent waves carried by the dipolar source in a homogeneous surrounding matter could be flexibly reshaped by the matter's anisotropy, especially when the isofrequency contour of the surrounding matter changes from the circular shape to the hyperbolic one.

Tailoring band gap properties of curved hexagonal lattices with nodal cantilevers

Metamaterials find applications across diverse domains such as electromagnetics, elasticity, and acoustics by creating band gaps. Lattice-based metamaterials also exhibit band gaps, which have a great potential to influence engineering design in vibration and noise reduction problems. The geometry of the repetitive unit cell in the lattice plays a crucial role in diversifying the location and number of stop bands across the frequency range. One of the key hurdles is devising unit cell architectures that can effectively suppress vibrations across diverse frequency ranges. This work proposes an innovative two-dimensional hexagonal lattice with tailored band gap characteristics through curved beam members and auxiliary cantilever beams at the nodes. We have thoroughly explored the impact of various design parameters on dispersion characteristics, wave directionality through iso-frequency contours of dispersion surfaces, and the transmission loss considering finite lattice. The investigation demonstrates an improvement in band gap characteristics, indicating the generation of more band gaps across the entire frequency range and the widening of the same. This study has the potential to serve as a future benchmark in the development of lattice-based elastic/acoustic metamaterials, particularly for addressing vibration reduction challenges at user-defined frequencies.

Back-focal plane scanning spectroscopy for investigating the optical dispersion of large-area two-dimensional photonic crystal fabricated by capillary force lithography

In this article, we introduce our custom-built back-focal plane (BFP) scanning spectroscopy to explore an angle-resolved optical dispersion in two-dimensional (2D) photonic crystal (PhC) constructed with hexagonal lattice of nano-scaled dielectric rods. We fabricated a uniformly large-area photonic crystal measuring 1 cm by 0.5 cm, featuring a polymer-based hexagonal lattice on a gold layer, using capillary force lithography. This precision enables the effective confinement of photonic modes, leading to enhanced optical interactions. We successfully map out the angle-resolved reflectance spectra by directly scanning BFP, revealing the structure's angle dependent optical response and providing insights into its iso-frequency contours. Our approach simplifies the exploration of advanced optical materials, highlighting the role of precise fabrication and measurement techniques in understanding and utilizing the optical properties of structured materials for various technological applications.

Tunable anisotropic van der Waals films of 2M-WS2 for plasmon canalization

In-plane anisotropic van der Waals materials have emerged as a natural platform for anisotropic polaritons. Extreme anisotropic polaritons with in-situ broadband tunability are of great significance for on-chip photonics, yet their application remains challenging. In this work, we experimentally characterize through Fourier transform infrared spectroscopy measurements a van der Waals plasmonic material, 2M-WS2, capable of supporting intrinsic room-temperature in-plane anisotropic plasmons in the far and mid-infrared regimes. In contrast to the recently revealed natural hyperbolic plasmons in other anisotropic materials, 2M-WS2 supports canalized plasmons with flat isofrequency contours in the frequency range of ~ 3000-5000 cm−1. Furthermore, the anisotropic plasmons and the corresponding isofrequency contours can be reversibly tuned via in-situ ion-intercalation. The tunable anisotropic and canalization plasmons may open up further application perspectives in the field of uniaxial plasmonics, such as serving as active components in directional sensing, radiation manipulation, and polarization-dependent optical modulators.

Topological design of hexagonal lattice phononic crystals for vibration attenuation combined fast plane wave expansion method with elite seed strategy genetic algorithm

The characteristics of manipulating elastic wave propagation in phononic crystals (PnCs) have been applied in various fields. A triangular element discrete method for two-dimensional (2D) hexagonal lattice PnCs is proposed, which combines with the fast plane wave expansion method (FPWEM) to obtain the band structure. As compared to the finite element method (FEM), time consumption is one order of magnitude faster while ensuring accuracy. To design the wider band gap (BG) of PnCs, the elite seed strategy genetic algorithm (ESS-GA) is used to optimize the topology of PnCs for in-plane mode and out-of-plane mode, and based on this, the proposed method is first applied to optimize hexagonal lattice PnCs, which is extended to the BG design of mixed mode. The relationship between the optimized individual under different propagate modes, and the volume fraction of PnCs at each BG is explained, physical mechanism of optimized unit cells is also estimated through iso-frequency contours and dynamic effective mass. The numerical and experimental results of a hexagonal lattice composed of optimized unit cells indicate that elastic waves can be suppressed within the BG, fully demonstrating the effectiveness of the method. In addition, this method is expected to explore its potential applications in the reverse design of PnCs.

Directional spontaneous emission in photonic crystal slabs

Abstract Spontaneous emission is one of the most fundamental out-of-equilibrium processes in which an excited quantum emitter relaxes to the ground state due to quantum fluctuations. In this process, a photon is emitted that can interact with other nearby emitters and establish quantum correlations between them, e.g., via super and subradiance effects. One way to modify these photon-mediated interactions is to alter the dipole radiation patterns of the emitter, e.g., by placing photonic crystals near them. One recent example is the generation of strong directional emission patterns – key to enhancing super and subradiance effects – in two dimensions by employing photonic crystals with band structures characterized by linear isofrequency contours and saddle points. However, these studies have predominantly used oversimplified toy models, overlooking the electromagnetic field’s intricacies in actual materials, including aspects like geometrical dependencies, emitter positions, and polarization. Our study delves into the interaction between these directional emission patterns and the variables mentioned above, revealing the untapped potential to fine-tune collective quantum optical phenomena.

Strain-Tunable Hyperbolic Exciton Polaritons in Monolayer Black Arsenic with Two Exciton Resonances.

Hyperbolic polaritons have been attracting increasing interest for applications in optoelectronics, biosensing, and super-resolution imaging. Here, we report the in-plane hyperbolic exciton polaritons in monolayer black-arsenic (B-As), where hyperbolicity arises strikingly from two exciton resonant peaks. Remarkably, the presence of two resonances at different momenta makes overall hyperbolicity highly tunable by strain, as the two exciton peaks can be merged into the same frequency to double the strength of hyperbolicity as well as light absorption under a 1.5% biaxial strain. Moreover, the frequency of the merged hyperbolicity can be further tuned from 1.35 to 0.8 eV by an anisotropic biaxial strain. Furthermore, electromagnetic numerical simulation reveals a strain-induced hyperbolicity, as manifested in a topological transition of iso-frequency contour of exciton polaritons. The good tunability, large exciton binding energy, and strong light absorption exhibited in the hyperbolic monolayer B-As make it highly suitable for nanophotonics applications under ambient conditions.

Manipulating hyperbolic transient plasmons in a layered semiconductor

Anisotropic materials with oppositely signed dielectric tensors support hyperbolic polaritons, displaying enhanced electromagnetic localization and directional energy flow. However, the most reported hyperbolic phonon polaritons are difficult to apply for active electro-optical modulations and optoelectronic devices. Here, we report a dynamic topological plasmonic dispersion transition in black phosphorus via photo-induced carrier injection, i.e., transforming the iso-frequency contour from a pristine ellipsoid to a non-equilibrium hyperboloid. Our work also demonstrates the peculiar transient plasmonic properties of the studied layered semiconductor, such as the ultrafast transition, low propagation losses, efficient optical emission from the black phosphorus’s edges, and the characterization of different transient plasmon modes. Our results may be relevant for the development of future optoelectronic applications.

Tunable bandgap characteristic of various hexagon-type elastic metamaterials for broadband vibration attenuation

Inspired by the advantages of the hexagon lattices and auxetic metamaterials, the typical two-dimensional (2D) hexagon-type elastic metamaterials (EMs), that is, the concave, the convex, and the rectangular hexagon-type EMs, are presented for investigating the dynamic behavior systematically. Firstly, the lumped mass-spring models are used to construct the band structures, and the eigenmodes are obtained by solving the eigenvalue problem of motion equations to unveil the formation mechanisms of bandgap (BG). Note that the specific dispersion branches are characterized by eigenfrequencies with the eigenmodes presenting similar vibrational forms, rather than just ranking the eigenfrequencies from low to high. Furthermore, the dependence on the main structural parameters of the lumped mass-spring models is investigated to achieve tunability of the bandgap characteristics. Then, the continuum models are also established to study the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission. The comprehensive study of the physical mechanics of the unit cells is carried out, encompassing the analysis of iso-frequency contours, deformation fields, and mesh-independent analysis. Finally, both the numerical analysis and experimental validation demonstrate the effect of vibration attenuation on in-plane elastic waves, which has the ideal great agreement with the prediction of the band structures (the values of the frequency response functions are much less than -20 dB within the ranges of BGs). This research is expected to provide valuable insight into the design of vibration isolators, beams, plates, and other devices that are being renewed.

Tunable Optical Forces Enabled by Bilayer van der Waals Materials

AbstractManipulation of nanoparticles by light induced forces is widely used in nanotechnology and bioengineering. In normal cases, when a nanoparticle is illuminated by light waves, the transfer of momentum from light to the nanoparticle can push it to move along the light propagation direction. On the other hand, the lateral optical force can transport an object perpendicular to the light propagation direction, and the optical pulling force can attract an object toward the light source. Although these optical forces have drawn growing attention, in situ tuning of them is rarely explored. In this paper, tuning of both lateral optical forces and optical pulling forces is numerically demonstrated via a graphene/α‐phase molybdenum trioxide (α‐MoO3) bilayer structure. Under plane‐wave illumination, both the amplitude and direction of the optical forces exerted on a nanoparticle above this bilayer structure can be tuned in the mid‐infrared range. The underlying mechanism can be understood by studying the corresponding isofrequency contours of the hybrid plasmon‐phonon polaritons supported by the graphene/α‐MoO3 bilayer. The analytical study using the dipole approximation method reproduces the numerical results, revealing the origin of the optical forces. This work opens a new avenue for engineering optical forces to manipulate various objects optically.

SURFACE PLASMON-POLARITONS IN THE VO<sub>2</sub>-DIELECTRIC-METASURFACE STRUCTURE BASED ON GRAPHENE IN AN EXTERNAL MAGNETIC FIELD

In this paper presents the results of a study of the behavior of surface plasmon polaritons in the layered structure of VO2–SiO2-graphene-based hyperbolic metasurface under the influence of an external magnetic field before and at the beginning of the phase transition of vanadium dioxide. As a result of calculations, it is shown how the Isofrequency contour of surface plasmons changes taking into account the different direction of the external magnetic field. It is also shown how an external magnetic field affects the direction of static magnetization caused by the inverse Faraday effect. This work can offer additional ways to control the behavior of surface plasmons, as well as become the basis for the study of new self-adjusting structures.

Guided Polaritons along the Forbidden Direction in MoO3 with Geometrical Confinement.

Highly anisotropic materials show great promise for spatial control and the manipulation of polaritons. In-plane hyperbolic phonon polaritons (HPhPs) supported by α-phase molybdenum trioxide (MoO3) allow for wave propagation with a high directionality due to the hyperbola-shaped isofrequency contour (IFC). However, the IFC prohibits propagations along the [001] axis, hindering information or energy flow. Here, we illustrate a novel approach to manipulating the HPhP propagation direction. We experimentally demonstrate that geometrical confinement in the [100] axis can guide HPhPs along the forbidden direction with phase velocity becoming negative. We further developed an analytical model to provide insights into this transition. Moreover, as the guided HPhPs are formed in-plane, modal profiles were directly imaged to further expand our understanding of the formation of HPhPs. Our work reveals a possibility for manipulating HPhPs and paves the way for promising applications in metamaterials, nanophotonics, and quantum optics based on natural van der Waals materials.

Actively Tunable Phonon Polaritons in Twisted α-MoO3 Slabs With Weyl Semimetal Interlayer

Hybrid phonon polaritons (PhPs) in polar van der Waals (vdW) layered materials are very appealing for the confinement of light at the nanoscale and have facilitated various applications. However, manipulation of in-plane anisotropic PhPs via external stimuli presents a significant challenge. Here, we offer a lithography-free avenue to create structure for the realization of hybridized PhPs from α-phase molybdenum trioxide (α-MoO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) vdW crystal with dependence on the chemical potential of Weyl semimetals (WSM). We demonstrate the distinct dispersion tunability of the strongly coupled PhPs and the optical topologic transitions from open to closed iso-frequency contours (IFCs). As the chemical potential is strongly temperature dependent, an alteration of the hybridization will be met by changing the temperature of surroundings, which enables an efficient way for the control of light-matter interaction at nanoscale in the mid-infrared (MIR) range.

Real-space observation of ultraconfined in-plane anisotropic acoustic terahertz plasmon polaritons.

Thin layers of in-plane anisotropic materials can support ultraconfined polaritons, whose wavelengths depend on the propagation direction. Such polaritons hold potential for the exploration of fundamental material properties and the development of novel nanophotonic devices. However, the real-space observation of ultraconfined in-plane anisotropic plasmon polaritons (PPs)-which exist in much broader spectral ranges than phonon polaritons-has been elusive. Here we apply terahertz nanoscopy to image in-plane anisotropic low-energy PPs in monoclinic Ag2Te platelets. The hybridization of the PPs with their mirror image-by placing the platelets above a Au layer-increases the direction-dependent relative polariton propagation length and the directional polariton confinement. This allows for verifying a linear dispersion and elliptical isofrequency contour in momentum space, revealing in-plane anisotropic acoustic terahertz PPs. Our work shows high-symmetry (elliptical) polaritons on low-symmetry (monoclinic) crystals and demonstrates the use of terahertz PPs for local measurements of anisotropic charge carrier masses and damping.

Mid-infrared analogue polaritonic reversed Cherenkov radiation in natural anisotropic crystals

Cherenkov radiation (CR) excited by fast charges can serve as on-chip light sources with a nanoscale footprint and broad frequency range. The reversed CR, which usually occurs in media with the negative refractive index or negative group-velocity dispersion, is highly desired because it can effectively separate the radiated light from fast charges thanks to the obtuse radiation angle. However, reversed CR at the mid-infrared remains challenging due to the significant loss of conventional artificial structures. Here we observe mid-infrared analogue polaritonic reversed CR in a natural van der Waals (vdW) material (i.e., α-MoO3), whose hyperbolic phonon polaritons exhibit negative group velocity. Further, the real-space image results of analogue polaritonic reversed CR indicate that the radiation distributions and angles are closely related to the in-plane isofrequency contours of α-MoO3, which can be further tuned in the heterostructures based on α-MoO3. This work demonstrates that natural vdW heterostructures can be used as a promising platform of reversed CR to design on-chip mid-infrared nano-light sources.

Topological Transitions Enhance the Performance of Twisted Thermophotovoltaic Systems

Twisted bilayer two-dimensional electronic systems give rise to many exotic phenomena and unveil a new frontier for the study of quantum materials. In photonics, twisted two-dimensional systems coupled via near-field interactions offer a platform to study localization and lasing. Here, we theoretically propose that twisting can be an unprecedented tool to tune the performance of near-field thermophotovoltaic systems. Remarkably, through twisting-induced photonic topological transitions, we achieve significant tuning of the thermophotovoltaic energy efficiency and power. The underlying mechanism is related to the change of the photonic isofrequency contours from elliptical to hyperbolic geometries in a setup where the hexagonal-boron-nitride metasurface serves as the heat source and the indium-antimonide $p$-$n$ junction serves as the cell. We find that a notably high energy efficiency, nearly 53 of the Carnot efficiency, can be achieved in our thermophotovoltaic system, while the output power can reach up to $1.1\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.2em}{0ex}}\mathrm{W}/{\mathrm{m}}^{2}$ without requiring a large temperature difference between the source and the cell. Our results indicate the promising future of twisted near-field thermophotovoltaics and paves the way towards tunable, high-performance thermophotovoltaics and infrared detection.

Visualization of photonic band structures via far-field measurements in SiNx photonic crystal slabs

Band structures of the photonic crystal slabs play a significant role in manipulating the flow of light and predicting exotic physics in photonics. In this Letter, we show that the key features of photonic band structures can be achieved experimentally by the polarization- and momentum-resolved photoluminescence spectroscopy utilizing the light emission properties of SiNx. The two-dimensional spectra clearly reveal the energy-momentum dispersion of band structures, which is in perfect agreement with the simulation results. The isofrequency contours can be measured easily by adding a bandpass filter with a desired photon energy. Furthermore, it is convenient to observe clearly and directly the optical singularity—the optical bound states in the continuum featured by dark point in three-dimensional photoluminescence spectra. The polarization-resolved isofrequency contours clearly show that this dark point is the center of an azimuthally polarized vortex. Finally, the helical topological edge states can be easily observed in photonic topological insulators with deformed hexagonal lattices. Our work provides a simple and effective approach for exploring topological photonics and other intriguing phenomena hidden in the photonic crystal slabs.

Active Tuning and Anisotropic Strong Coupling of Terahertz Polaritons in Van der Waals Heterostructures.

Electromagnetic field confinement is significant in enhancing light-matter interactions as well as in reducing footprints of photonic devices especially in Terahertz (THz). Polaritons offer a promising platform for the manipulation of light at the deep sub-wavelength scale. However, traditional THz polariton materials lack active tuning and anisotropic propagation simultaneously. In this paper, we design a graphene/α-MoO3 heterostructure and simulate polariton hybridization between isotropic graphene plasmon polaritons and anisotropic α-MoO3 phonon polaritons. The physical fundamentals for polariton hybridizations depend on the evanescent fields coupling originating from the constituent materials as well as the phase match condition, which can be severely affected by the α-MoO3 thickness and actively tuned by the gate voltages. Hybrid polaritons propagate with in-plane anisotropy that exhibit momentum dispersion characterized by elliptical, hyperboloidal and even flattened iso-frequency contours (IFCs) in the THz range. Our results provide a tunable and flexible anisotropic polariton platform for THz sensing, imaging, and modulation.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Filtering and Imaging of Frequency-Degenerate Spin Waves Using Nanopositioning of a Single-Spin Sensor.

Nitrogen-vacancy (NV) magnetometry is a new technique for imaging spin waves in magnetic materials. It detects spin waves by their microwave magnetic stray fields, which decay evanescently on the scale of the spin-wavelength. Here, we use nanoscale control of a single-NV sensor as a wavelength filter to characterize frequency-degenerate spin waves excited by a microstrip in a thin-film magnetic insulator. With the NV probe in contact with the magnet, we observe an incoherent mixture of thermal and microwave-driven spin waves. By retracting the tip, we progressively suppress the small-wavelength modes until a single coherent mode emerges from the mixture. In-contact scans at low drive power surprisingly show occupation of the entire isofrequency contour of the two-dimensional spin-wave dispersion despite our one-dimensional microstrip geometry. Our distance-tunable filter sheds light on the spin-wave band occupation under microwave excitation and opens opportunities for imaging magnon condensates and other coherent spin-wave modes.