Quasi‐Single‐Mode Polaritonic Crystal for Hyperbolic Phonon‐Polaritons

Phonon polaritons (PhPs) in van der Waals (vdW) crystal slabs enable nanoscale infrared light manipulation. Specifically, periodically structured vdW slabs behave as polaritonic crystals (vdW-PCs), where the polaritons form Bloch modes. Because the polariton wavelengths are smaller than that of light, conventional far-field spectroscopy does not allow for a complete characterization of vdW-PCs or for revealing their band structure. Here, we perform hyperspectral infrared nanoimaging and analysis of PhPs in a vdW-PC slab made of h-BN. We demonstrate that infrared spectra recorded at individual spatial positions within the unit cell of the vdW-PC can be associated with its band structure and local density of photonic states (LDOS). We thus introduce hyperspectral infrared nanoimaging as a tool for the comprehensive analysis of polaritonic crystals, which could find applications in the reconstruction of complex polaritonic dispersion surfaces in momentum-frequency space or for exploring exotic electromagnetic modes in topological photonic structures.

Hyperbolic phonon polaritons (HPhPs) in polar van der Waals crystals, such as α-MoO3 and α-V2O5, enable deep subwavelength light confinement and in-plane manipulation via hyperbolic dispersion, yet momentum mismatch hinders efficient excitation. We present a far-field method to excite in-plane HPhPs using plasmonic gold nanorods. Surface plasmon resonance (SPPR) in nanorods mediates strong interactions between free-space waves and HPhPs in α-MoO3. Excitation efficiency is highly sensitive to nanorod length and angular orientation relative to the [100] crystal axis of α-MoO3. Maximum HPhP near-field intensity is achieved when the nanorods are aligned to optimize coupling with the anisotropic polaritonic modes, with efficiency closely linked to the resonance conditions of the plasmonic antennas. Numerical designs are corroborated well with near-field optical characterizations. Therefore, our approach establishes a platform to study interactions between plasmonic antennas and anisotropic polaritons, advancing controlled manipulation of in-plane polaritonic modes in van der Waals materials.

Polaritons allow for strong light-matter coupling and for highly sensitive analysis of (bio)chemical substances and processes. Nanoimaging of the polaritons' evanescent fields is critically important for experimental mode identification and field confinement studies. Here we describe two setups for polariton nanoimaging and spectroscopy in liquid. We first demonstrate the mapping of localized plasmon polaritons in metal antennas with a transflection infrared scattering-type scanning near-field optical microscope (s-SNOM), where the tip acts as a near-field scattering probe. We then demonstrate a total internal reflection (TIR)-based setup, where the tip is both launching and probing ultraconfined polaritons in van der Waals materials (here phonon polaritons in hexagonal boron nitride flakes), laying the foundation for s-SNOM-based polariton interferometry in liquid. Our results promise manifold applications, for example, in situ studies of strong coupling between polaritons and molecular vibrations or chemical reactions at the bare or functionalized surfaces of polaritonic materials.

Sub-wavelength metal grating structures exhibit extraordinary transmission (EOT) due to constructive interference of surface plasmon polaritons (SPPs) tunneling. Phonon polaritons (PhPs) having several advantages over metal-supported plasmons, such as zero ohmic loss and larger propagation lengths, can further enhance the transmission. We propose the design of silver gratings filled with anisotropic Molybdenum Trioxide (α - MoO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) to exhibit EOT by utilizing PhPs. We also numerically demonstrate the tunability (amplitude) of EOT by introducing a layer of graphene nanoribbon in the proposed device and show its application as a mid-infrared switch with bandwidth of 650 nm. α-MoO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> /silver grating produces normalized transmission as high as ∼5.5 for [100] and ∼6 for [001] crystalline directions. This extraordinary effect is attributed to the formation of (i) hybrid modes, specifically cavity modes coupled with SPPs outside the reststrahlen band (RB) and (ii) cavity modes coupled with PhPs inside the RB. The reported work can be employed in diverse applications including molecular sensing, space communications, remote controlling and, imaging.

Body: Surface plasmon polariton (SPP), which result from the strong coupling of bound electromagnetic (EM) waves and collective charge oscillations, enable subwavelength manipulation of light and matter interaction. Conventional noble metals-based SPP excited in the visible and near-Infrared spectra ranges suffer from large energy losses and cannot be dynamically tuned. Thanks to its 2D nature, graphene has emerged as a promising alternative plasmonic material with well- confined SPPs in the mid-infrared (MIR) and terahertz (THz) ranges and remarkable tunability. On the other hand, polar dielectric materials support low optical losses and sub-wavelength mode in the MIR and THz regions via surface phonon polariton (SPhP)mode' stimulation within the Reststrahlen band, a narrow spectral range between transverse optical (TO) and longitudinal optical (LO) frequencies. Due to the excellent polaritonic responses in both graphene and silicon carbide in the MIR and THz regions, devices combining the two materials are inferred to greatly advance photonics and THz technologies. We have recently theoretically demonstrated the strong confinement and large propagation figures of merit (FOM) for hybrid surface plasmon and surface phonon polariton in the epitaxial graphene on silicon carbide. The ability to confine such MIR light into small volume through excitation of SPP and SPhP has many implications for optoelectronic technologies such as the MIR photodetection[2], sensing[3], and solar cells[4]. Epitaxial graphene(EG) grown on silicon carbide(SiC) on silicon(Si) has been investigated as a suitable platform for graphene growth on semiconductors to meet the prospective technologies [5]. Despite this platform being very advantageous, experimental and theoretical works demonstrating the potentials properties/applications of EG on SiC on Si are still missing. Here we combine electromagnetic simulations based on finite elements method (FEM) with attenuated total reflectance Fourier transformed infrared (ATR-FTIR) spectroscopy to indicate improved MIR absorption, E field enhancement, and tunability for graphene-coated SiC nanowires (NWs). As anticipated, low absorption was confirmed from both simulations and measurements on bare SiC NWs, further supported by the calculated weak electric field due to the thin size of SiC NWs being incapable of absorbing sufficient light. On the other hand, enhanced absorption for the SiC NWs was measured by ATR-FTIR after a conformal graphitization of NWs[6]. Our previous study of this material system revealed a low-density oxide layer formed between graphene and SiC NWs[6]. This oxide layer between EG and SiC NW has been implemented in the FEM model, leading to field enhancement of incident EM field and strongly confined in the thin oxide. This substantial absorption and field enhancement originates from the coupling between the incident MIR photon and the plasmon/ phonon in graphene and SiC, respectively, with the oxide layer acting as a coupling medium. Furthermore, we demonstrate the modes' tunability whereby tuning the graphene's Fermi energy, the modes' resonance frequencies can be shifted to ~ 100 cm-1. Lastly, we realize substantial field enhancement, which is achieved by carefully tuning the graphene's Fermi energy and adjusting the spectra position of mode 1(mode on the left of LO frequency) closer to TO frequency. These results hold promise for various photonic applications such as perfect absorber to improve solar cell, MIR photodetectors, and other tunable photonics. [1]P. Rufangura, et al., J. Phys. Mater., vol. 3, no. 3, p. 032005, 2020. [2]T. Low and P. Avouris, ACS nano, vol. 8, no. 2, pp. 1086-1101, 2014. [3]A. G. Brolo, Nat. Photon., vol. 6, no. 11, p. 709, 2012. [4]H. A. Atwater and A. Polman, Nat. Mater., vol. 9, no. 3, p. 205, 2010. [5] N. Mishra et al., Phys. Status Solidi (a), vol. 213, no. 9, pp. 2277-2289, 2016. [6]N. Mishra et al., J. Appl. Phys., vol. 126, no. 6, p. 065304, 2019.

A photonic bandgap (PBG) structure for a polaritonic photonic crystal (PPC) containing lithium tantalate (LiTaO3) in the negative refractive index (NRI) region has been theoretically investigated. This region consists of a narrow frequency range of anomalous dispersion and a wide range of normal dispersion. The result shows that such PPC has a multiple-PBG structure with one gap located in the anomalous dispersion region and others in the normal dispersion region. PBG in the anomalous region is invariant with filling factor and scaling. This gap is further proven to be independent of the angle of incidence for both TE and TM nodes, leading to the existence of an omnidirectional gap. BPGs within the normal dispersion region are, however, strongly affected by the above three factors, especially for gaps near the upper limit of the NRI region.

In this work, we reported a systemic study on the enhanced efficiency of launching hyperbolic phonon polaritons (PhPs) in stacked α-phase molybdenum trioxide (α-MoO3) flakes. By using the infrared photo-induced force microscopy (PiFM), real-space near-field images (PiFM images) of mechanically exfoliated α-MoO3 thin flakes were recorded within three different Reststrahlen bands (RBs). As referred with PiFM fringes of the single flake, PiFM fringes of the stacked α-MoO3 sample within the RB 2 and RB 3 are greatly improved with the enhancement factor (EF) up to 170%. By performing numerical simulations, it reveals that the general improvement in near-field PiFM fringes arises from the existence of a nanoscale thin dielectric spacer in the middle part between two stacked α-MoO3 flakes. The nanogap acts as a nanoresonator for prompting the near-field coupling of hyperbolic PhPs supported by each flake in the stacked sample, contributing to the increase of polaritonic fields, and verifying the experimental observations Our findings could offer fundamental physical investigations into the effective excitation of PhPs and will be helpful for developing functional nanophotonic devices and circuits.

We present a study of light-induced forces between two coupled plasmonic nano-particles above various slab geometries including a metallic half-space and a 280-nm thick negative index material (NIM) slab waveguide. We investigate optical forces by non-perturbatively calculating the scattered electric field via a Green function technique which includes the particle interactions to all orders. For excitation frequencies near the surface plasmon polariton and slow-light waveguide modes of the metal and NIM, respectively, we find rich light-induced forces and significant dynamical back-action effects. Optical quenching is found to be important in both metal and NIM planar geometries, which reduces the spatial range of the achievable inter-particle forces. However, reducing the loss in the NIM allows radiation to propagate through the slow-light modes more efficiently, thus causing the light-induced forces to be more pronounced between the two particles. To highlight the underlying mechanisms by which the particles couple, we connect our Green function calculations to various familiar quantities in quantum optics.

In 1968, Veselago posed that media with simultaneous negative values of the permittivity and permeability would exhibit a negative index of refraction (Soviet Physics Uspekhi, vol. 10, pp. 509-514, 1968.). Due to the left-handed relationship between the electric field, magnetic field, and wave vector in these materials he termed them left-handed media (LHM). These LHM are expected to have many unusual properties such as inverted Snell's law, Doppler shift and Cherenkov radiation. However, until recently, such materials were unavailable and these predictions remained uncorroborated for nearly thirty years. As with any new field, the topic of the LHM suffers from some misconceptions and misunderstandings. One such misconception has to do with the notion of negative group velocity which has been closely linked with these media (R.A. Shelby et al, Appl. Phys. Lett., vol. 78, pp. 489-91, 2001) and in fact has been used as equivalent to the term LHM. In this paper, the existence and meaning of negative group velocity in LHM are discussed. It is shown that similar to normal right-handed media (RHM), LHM can also exhibit a negative group velocity and group delay within the region of anomalous dispersion (/spl delta/n//spl delta//spl omega/<0). On the other hand, in the experiments presented so far, the researchers have only measured positive group velocity and negative phase velocity corresponding to so called backward waves (BWs).

The terahertz (THz) frequency range is key to studying collective excitations in many crystals and organic molecules. However, due to the large wavelength of THz radiation, the local probing of these excitations in smaller crystalline structures or few-molecule arrangements requires sophisticated methods to confine THz light down to the nanometer length scale, as well as to manipulate such a confined radiation. For this purpose, in recent years, taking advantage of hyperbolic phonon polaritons (HPhPs) in highly anisotropic van der Waals (vdW) materials has emerged as a promising approach, offering a multitude of manipulation options, such as control over the wavefront shape and propagation direction. Here, we demonstrate the THz application of twist-angle-induced HPhP manipulation, designing the propagation of confined THz radiation between 8.39 and 8.98 THz in the vdW material α-molybdenum trioxide (α-MoO3), hence extending twistoptics to this intriguing frequency range. Our images, recorded by near-field optical microscopy, show the frequency- and twist-angle-dependent changes between hyperbolic and elliptic polariton propagation, revealing a polaritonic transition at THz frequencies. As a result, we are able to allocate canalization (highly collimated propagation) of confined THz radiation by carefully adjusting these two parameters, i.e. frequency and twist angle. Specifically, we report polariton canalization in α-MoO3 at 8.67 THz for a twist angle of 50°. Our results demonstrate the precise control and manipulation of confined collective excitations at THz frequencies, particularly offering possibilities for nanophotonic applications.

Phonons are important lattice vibrations that affect the thermal, electronic, and optical properties of materials. In this work, we studied infrared phonon resonance in a prototype van der Waals (vdW) material—hexagonal boron nitride (hBN)—with the thickness ranging from monolayers to bulk, especially on ultra-thin crystals with atomic layers smaller than 20. Our combined experimental and modeling results show a systematic increase in the intensity of in-plane phonon resonance at the increasing number of layers in hBN, with a sensitivity down to one atomic layer. While the thickness-dependence of the phonon resonance reveals the antenna nature of our nanoscope, the linear thickness-scaling of the phonon polariton wavelength indicates the preservation of electromagnetic hyperbolicity in ultra-thin hBN layers. Our conclusions should be generic for fundamental resonances in vdW materials and heterostructures where the number of constituent layers can be conveniently controlled. The thickness-dependent phonon resonance and phonon polaritons revealed in our work also suggest vdW engineering opportunities for desired thermal and nanophotonic functionalities.

Strongly coupled phonon polaritons in patterned polar dielectric nano-resonators give rise to the formation of hybridized energy states with intriguing properties. However, direct observation of mode coupling in these periodic nanostructures is still challenging for momentum-matching-required far-field spectroscopies. Here, we explore the near-field response of strong coupling between propagating and localized polariton modes sustained in SiC phonon polaritonic crystals (PhPCs) to reveal the evolution of Rabi splittings with the change of lattice constant in the near-field perspective. The near-field nano-spectra of PhPCs show distinct Rabi splitting near the forbidden bands of ∼16 cm−1 in the band structures. In particular, an exotic three-polariton-coupling effect is observed with three splitting peaks in the nano-spectra induced by the interaction between local monopolar modes in nano-pillars and zone-folded phonon polaritons. Furthermore, sharp dips indicating weak near-field scatterings appear in nano-spectra at the intrinsic frequencies of the monopolar modes with strong local-field enhancement, which are estimated to be bright scattering peaks intuitively. These results would inspire the dispersion engineering and characterization of coupled phononic nano-resonators for diverse nanophotonic applications.

Guided modes in nanometer thick anisotropic van der Waals materials are experimentally investigated and their refractive indices in visible wavelengths are extracted. Our method involves near-field scanning optical microscopy of waveguide (transverse electric) and surface plasmon polariton (transverse magnetic) modes in h-BN/SiO2/Si and Ag/h-BN stacks, respectively. We determine the dispersion of these modes and use this relationship to extract anisotropic refractive indices of h-BN flakes. In the wavelength interval 550–700 nm, the in-plane and out-of-plane refractive indices are in the range 1.98–2.12 and 1.45–2.12, respectively. Our approach of using near-field scanning optical microscopy allows for the direct study of the interaction between light and two-dimensional van der Waals materials and heterostructures.

Generation and manipulation of phonon polaritons are of paramount importance for understanding the interaction between an electromagnetic field and dielectric materials and furthering their application in mid-infrared optical communication. However, the formation of tunable one-dimensional phonon polaritons has been rarely realized in van der Waals layered structures. Here we report the discovery of curvature-induced phonon polaritons localized at the crease of folded hexagonal boron nitrides (h-BNs) with a few atomic layers using monochromated electron energy-loss spectroscopy. Compared to bulk regions, the creased-localized signals undergo an abnormal blue-shift of 1.4 meV. First-principles calculations reveal that the energy shift arises from the optical phonon hardening in the curled region. Interestingly, the curvature-induced phonon polariton can also be controllably achieved via an electron-beam etching approach. This work opens an avenue of tailoring local electromagnetic response and creating unique phonon polariton modes in van der Waals layered materials for diverse applications.

We present a detailed analysis for the existence of dark and bright solitary waves as also fractional-transform solutions in a nonlinear Schrödinger equation model for competing cubic–quintic and higher-order nonlinearities with dispersive permittivity and permeability. Parameter domains are delineated in which these ultrashort optical pulses exist in negative-index materials (NIMs). For example, dark solitons exist for the case of normal second-order dispersion, anomalous third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities, while the bright solitons exist for the case of anomalous second-order dispersion, normal third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities. This is contrary to the situation in ordinary materials.