Phonon Polariton Modes Research Articles

ModulatioAn of Hybrid Plasmon Phonon Polaritons Mode in Circular Cylindrical Three-Layer Graphene Waveguide

In this present research article, we have investigated analytically the characteristics of the fundamental mode of hybrid surface plasmon phonon polariton (HSPPhPs) mode in a circular cylindrical three-layer graphene (CTLG) waveguide structure. The dispersion equation of HSPPhPs is derived by using Maxwell’s equations and continuity conditions of tangential components of electric and magnetic fields in cylindrical geometry. The dispersion curve has been illustrated and thoroughly examined in relation to the effects of temperature and chemical potential (μc) of graphene, as well as variations in the thickness of silicon dioxide (SiO2) and hexagonal boron nitride (hBN) layers, and found that in the presence of hBN, the effective mode index exhibits hyperbolic behavior with wave number. Up to the first Reststrahlen band (∼830.57cm⁻¹), it varies slightly with graphene temperature; increasing graphene's (μc) lowers the index, while a thicker hBN layer reduces it, whereas the index increases with SiO₂ layer thickness. Also, we looked at how the CTLG waveguide structure is affected by the electric field distribution, phase speed, and propagation length.

Landau-phonon polaritons in Dirac heterostructures.

Polaritons are light-matter quasiparticles that govern the optical response of quantum materials at the nanoscale, enabling on-chip communication and local sensing. Here, we report Landau-phonon polaritons (LPPs) in magnetized charge-neutral graphene encapsulated in hexagonal boron nitride (hBN). These quasiparticles emerge from the interaction of Dirac magnetoexciton modes in graphene with the hyperbolic phonon polariton modes in hBN. Using infrared magneto-nanoscopy, we reveal the ability to completely halt the LPP propagation in real space at quantized magnetic fields, defying the conventional optical selection rules. The LPP-based nanoscopy also tells apart two fundamental many-body phenomena: the Fermi velocity renormalization and field-dependent magnetoexciton binding energies. Our results highlight the potential of magnetically tuned Dirac heterostructures for precise nanoscale control and sensing of light-matter interaction.

Highly Confined Hybridized Polaritons in Scalable van der Waals Heterostructure Resonators.

The optimization of nanoscale optical devices and structures will enable the exquisite control of planar optical fields. Polariton manipulation is the primary strategy in play. In two-dimensional heterostructures, the ability to excite mixed optical modes offers an additional control in device design. Phonon polaritons in hexagonal boron nitride have been a common system explored for the control of near-infrared radiation. Their hybridization with graphene plasmons makes these mixed phonon polariton modes in hexagonal boron nitride more appealing in terms of enabling active control of electrodynamic properties with a reduction of propagation losses. Optical resonators can be added to confine these hybridized plasmon-phonon polaritons deeply into the subwavelength regime, with these structures featuring high quality factors. Here, we show a scalable approach for the design and fabrication of heterostructure nanodisc resonators patterned in chemical vapor deposition-grown monolayer graphene and h-BN sheets. Real-space mid-infrared nanoimaging reveals the nature of hybridized polaritons in the heterostructures. We simulate and experimentally demonstrate localized hybridized polariton modes in heterostructure nanodisc resonators and demonstrate that those nanodiscs can collectively couple to the waveguide. High quality factors for the nanodiscs are measured with nanoscale Fourier transform infrared spectroscopy. Our results offer practical strategies to realize scalable nanophotonic devices utilizing low-loss hybridized polaritons for applications such as on-chip optical components.

Enhancing mid-infrared surface phonon polariton modes: optimization of structural parameters in Nb-doped SrTiO3 with hole array structures for advanced infrared sensors

This study utilized the finite difference time domain method to investigate the mid infrared surface phonon polaritons and localized surface phonon resonances in undoped and niobium (Nb)-doped SrTiO3 (STO) with planar and holes array structures. Research has shown that Nb-doped STO operates in the Reststrahlen band of 8.06–18.48 µm, providing a wider spectral response than undoped STO (12.58–18.26 µm) and effectively covering the atmospheric window of long wave infrared. This indicates that the increase in virtual permittivity has the least impact on spectral broadening, indicating that the new infrared sensor technology has broad prospects. The optimization of structural parameters, including the period, filling factor, and depth of STO holes array, as well as the response to changes in incident light angle, is crucial for guiding the design of high-performance optoelectronic devices. In addition, this study explored the excitation of four resonant modes within a holes array and analyzed their relationship with array parameters to enhance the design of optoelectronic applications.

Greatly Enhanced Radiative Transfer Enabled by Hyperbolic Phonon Polaritons in α‐MoO3

AbstractOrthorhombic molybdenum trioxide (α‐MoO3) is a highly anisotropic hyperbolic material in nature. Within its wide Reststrahlen bands, α‐MoO3 has hyperboloidal dispersion that supports bulk propagation of high‐k phonon polariton modes. These modes can serve as energy transport channels to greatly enhance radiative heat transfer inside the material. In this work, large radiative transfer enabled by phonon polaritons in α‐MoO3 is demonstrated. The study first determines the temperature‐dependent permittivity of α‐MoO3 from polarized Fourier‐Transform Infrared (FTIR) spectroscopy measurements and then uses a many‐body radiative heat transfer model to predict the equivalent radiative thermal conductivity of hyperbolic phonon polariton. Contribution of radiative transfer to the total thermal transport is experimentally determined from the Time‐Domain Thermoreflectance (TDTR) measurements in a temperature range from −100 to 300 °C. It is found that radiative transfer can account for ≈60% of the total thermal transport at a temperature of 300 °C. That is, conductive thermal transport is enhanced by >100% by radiative transfer, or radiation inside α‐MoO3 is greater than that of conduction. These additional energy pathways will have important implications in thermal management in new materials and devices.

Lifetime and Molecular Coupling in Surface Phonon Polariton Resonators.

Surface phonon polariton (SPhP) modes in polar semiconductors offer a low-loss platform for infrared nanophotonics and sensing. However, the efficient design of polariton-enhanced sensors requires a quantitative understanding of how to engineer the frequency and lifetime of SPhPs in nanophotonic structures. Here, we study organ-pipe resonances in 4H-SiC trenches as a prototype system for infrared sensing. We use a transmission line framework that accounts for the field distribution within the trench, accurately predicting mode frequency and lifetime when compared against finite element method (FEM) electromagnetic calculations. Accounting for the electric field profile across the gap is critical in our model to accurately predict mode frequencies, quality factor (Q factor), and reflectance, outperforming previous circuit models developed in the literature. Beyond structural simulation, our model can provide insights into the frequency ranges in the Reststrahlen band where enhanced sensor activity should be present. The radiative lifetime is significantly enlarged close to the longitudinal optic phonon, restricting sensor efficiency at this wavelength range. This pushes the optimal frequency for sensing closer to the center of the Reststrahlen band than might be naively expected. This model ultimately demonstrates the primary challenge of designing SPhP-based sensors: only a relatively narrow region of the Reststrahlen band offers efficient sensing, guiding future designs for infrared spectroscopy.

Tailoring intrinsic chiroptical responses via twisted bilayer α-MoO3 separated by a VO2 film

Flexible control of intrinsic chiroptical responses within compact nanostructures is crucial for flat optics, topological photonics, and chiroptics. However, previous approaches require complicated patterns with both in-plane and out-of-plane mirror symmetry breaking to achieve intrinsic chirality, and their chiroptical responses cannot be dynamically controlled as well. Herein, we demonstrated that near-perfect intrinsic circular dichroism (CD) can be achieved within a lithography-free structure consisting of the twisted bilayer α-MoO3 separated by a vanadium dioxide (VO2) film. By twisting the bilayer α-MoO3, dual-band intrinsic chiroptical responses can be realized due to the excitations of the hyperbolic phonon polaritons modes in the mid-infrared. It is the spin-selected average electric-field enhancement instead of the chiral absorption that is responsible for the intrinsic CD of the device. In addition, the chiroptical responses are insensitive to the variation of the thickness of the structure as well as the incident angle, and high contrast CD can be dynamically tuned by varying the volume fraction of VO2.

Near-unity nonreciprocal thermal radiation in biaxial van der Waals material-Weyl semimetal heterostructures

Polaritons in natural van der Waals (vdW) materials have drawn significant attention as the unique optical properties and have opened doors for various potential applications. α-phase molybdenum trioxide (α-MoO3) has been revealed as a semiconducting anisotropic vdW material that holds great promise for manipulating orthogonal in-plane phonon polariton (PhP) modes in infrared (IR). Here, we consider an attenuated total reflection (ATR) geometry consisting of an α-MoO3 layer and a Weyl semimetal (WSM) interlayer sitting on a silver (Ag) substrate. The incorperated coupling prism is selected as KRS5 (thallium bromide-iodide) that can provide a larger wavevector. The spectral responses of the proposal have been investigated using electromagnetic (EM) simulations that utilize the anisotropic rigorous coupled-wave analysis (aRCWA). Our results demonstrate that the α-MoO3 thin layer can boost the constrast between the emissivity and absorptivity in a broad range of wavelength as compared to an uncoated device. The nonreciprocity at resonance wavelength can reach near-unity for both transverse electric (TE) and transverse magnetic (TM) wave incidence. The proposed α-MoO3/WSM heterostructure suggests great potentials for thermal radiation management with different demands.

A high figure of merit of phonon-polariton waveguide modes with hbn/SiO2/graphene /hBN ribs waveguide in mid-infrared range

Natural hyperbolic materials can confine electromagnetic waves at the nanoscale. In this study, we propose a waveguide design that combines a high quality factor (FOM) with low loss, utilizing hexagonal boron nitride and graphene and gold substrate. The waveguide consists of a dielectric rib with a graphene layer sandwiched between two hBN ribs. Numerical simulations demonstrate the existence of two guided modes in the proposed waveguide within the second reststrahlen band (1360.0 cm−1<ω < 1609.8 cm−1) of hBN. These modes are formed by coupling the hyperbolic phonon polariton (HPhP) of two hBN rib in the middle dielectric rib and are subsequently modulated by a graphene layer. Interestingly, we observe variations in four transmission parameters, namely effective length, figure of merit, device length, and propagation loss of the guided modes, with respect to the operation frequency and gate voltage. By optimizing the waveguide's geometry parameters and dielectric permittivity, the modal properties were analyzed. Simulation results indicate that optimizing the waveguide size parameters enables us to achieve a high FOM of 4.0 × 107. The proposed waveguide design offers a promising approach for designing tunable mid infrared range waveguides on photonic chips, and this concept can be extended to other 2D materials and hyperbolic materials.

Lithography-free high sensitivity perfect absorption based on Graphene/α-MoO3/SiC and Tamm plasmonic structure

In this paper, we propose a tunable perfect-absorption lithography-free refractive index sensor structure, which couples the Tamm phonon polariton (TPhP) mode and Graphene/α-MoO3/SiC (GMS) mode. By aligning the modal frequencies of TPhP and GMS, the coupling of the two modes is realized with perfect absorption. We utilize the transfer matrix method (TMM), resonance equation and coupled mode theory (CMT) to theoretically analyze the absorption of different modes and apply the structure to refractive index sensor. By modulating the structure parameter, the sensitivity of the sensor can be as high as 6 μm/RIU. This work could contribute to several fields such as refractive index sensors, photodetectors, absorbers, and energy harvesting devices.

Ghost surface polaritons in naturally uniaxial hyperbolic materials

We investigated ghost surface phonon polaritons localized in a naturally uniaxial hyperbolic material, where the longitudinal axis (optical axis) is at any angle with respect to the surface plane. Two ghost surface phonon polaritons (GSPs) were found in the two Reststrahlen frequency bands, respectively. They are two TM surface waves, and their electromagnetic fields not only attenuate but also oscillate with the distance away from the surface. Unlike conventional surface phonon polaritons, GSPs are virtual surface phonon-polariton modes without electrostatic limit. The numerical simulations of the GSP dispersion and polarization properties were based on the hexagonal boron nitride, and the numerical simulation of the attenuated total reflection (ATR) experiment demonstrates the existence of the GSPs and prove their excitability and observability.

High-field 1/f noise in hBN-encapsulated graphene transistors

$1/f$ electronic noise is a conductance fluctuation, expressed in terms of a mobility ``$\ensuremath{\alpha}$-noise'' by Hooge and Kleinpenning. Understanding this noise in graphene is key for high-performance electronics. Early investigations pointed out a deviation from the standard Hooge formula, with the free-carrier density substituted by a constant density ${n}_{\mathrm{\ensuremath{\Delta}}}\ensuremath{\sim}{10}^{12}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Here we investigate hBN-encapsulated graphene transistors where high mobility gives access to the velocity-saturation regime. We show that $\ensuremath{\alpha}$-noise is still accounted for by the Hooge formula on substituting conductance by differential conductance $G$, resulting in a bell-shaped dependence of flicker noise with bias voltage. The same analysis holds in the Zener regime at even larger bias, with two main differences. The first one is a strong enhancement of the Hooge parameter reflecting the hundred-times larger coupling of interband excitations to the hyperbolic phonon-polariton (HPhP) modes of the midinfrared Reststrahlen (RS) bands of hBN, which is supported by microwave noise thermometry measurements. The second is an exponential suppression of this coupling at large fields, which we attribute to decoherence effects. The phenomenology of $1/f$ noise in graphene supports a quantum-coherent bremsstrahlung interpretation of $\ensuremath{\alpha}$-noise.

Strong coupling in an Au plasmonic antenna– SiO2 layer system: A hybrid-mode analysis

A detailed analysis of the optical response of a system accommodating several coupled modes is needed for the complete understanding of the strong coupling effect. In this paper, we report on the analysis of scattering cross-section spectra of Au antennas on a ${\mathrm{SiO}}_{2}$ layer on a Si substrate in the IR region. A classical model of coupled oscillators is used for determining the resonant energies, damping rates, and coupling strengths of four phonon polariton modes in the ${\mathrm{SiO}}_{2}$ layer coupled to a localized surface plasmon mode in a Au antenna. The calculated Hopfield mixing coefficients then show the contribution of the individual uncoupled modes to the hybrid modes of the coupled system.

Selective excitation of hyperbolic phonon polaritons-induced broadband absorption via α-MoO3 square pyramid arrays

Optical anisotropy of α-MoO3 in its reststrahlen (RS) bands provides exciting opportunities for constructing the polarization-dependent devices. However, achieving broadband anisotropic absorptions through the same α-MoO3 arrays is still challenging. In this study, we demonstrate that selective broadband absorption can be achieved by using the same α-MoO3 square pyramid arrays (SPAs). For both the x and y polarizations, the absorption responses of the α-MoO3 SPAs calculated by using the effective medium theory (EMT) agreed well with those of the FDTD, indicating the excellent selective broadband absorption of the α-MoO3 SPAs are associated with the resonant hyperbolic phonon polaritons (HPhPs) modes assisted by the anisotropic gradient antireflection (AR) effect of the structure. The near-field distribution of the absorption wavelengths of the α-MoO3 SPAs shows that the magnetic-field enhancement of the lager absorption wavelength tends to shift to the bottom of the α-MoO3 SPAs due to the lateral Fabry–Pérot (F–P) resonance, and the electric-field distribution exhibits the ray-like light propagation trails due to the resonance nature of the HPhPs modes. In addition, broadband absorption of the α-MoO3 SPAs can be maintained if the width of the bottom edge of the α-MoO3 pyramid is large than 0.8 μm, and excellent anisotropic absorption performances are almost immune to the variations of the thickness of the spacer and the height of the α-MoO3 pyramid.

Hyperbolic whispering-gallery phonon polaritons in boron nitride nanotubes.

Light confinement in nanostructures produces an enhanced light-matter interaction that enables a vast range of applications including single-photon sources, nanolasers and nanosensors. In particular, nanocavity-confined polaritons display a strongly enhanced light-matter interaction in the infrared regime. This interaction could be further boosted if polaritonic modes were moulded to form whispering-gallery modes; but scattering losses within nanocavities have so far prevented their observation. Here, we show that hexagonal BN nanotubes act as an atomically smooth nanocavity that can sustain phonon-polariton whispering-gallery modes, owing to their intrinsic hyperbolic dispersion and low scattering losses. Hyperbolic whispering-gallery phonon polaritons on BN nanotubes of ～4 nm radius (sidewall of six atomic layers) are characterized by an ultrasmall nanocavity mode volume (Vm ≈ 10-10λ03 at an optical wavelength λ0 ≈ 6.4 μm) and a Purcell factor (Q/Vm) as high as 1012. We posit that BN nanotubes could become an important material platform for the realization of one-dimensional, ultrastrong light-matter interactions, with exciting implications for compact photonic devices.

Effects of anisotropy, morphology, and interparticle coupling on the far-infrared optical modes of randomly oriented ZnO nanoparticles

Polar dielectric nanoparticles (NPs) with uniaxial anisotropy support two-surface phonon polariton modes inside a reststrahlen band. The effective permittivity of a randomly orientated ensemble of NPs is usually assumed to be isotropic due to averaging of the optical response over all orientations. In this work, we demonstrate that this assumption is not valid for ZnO nanoparticles, and the resultant absorption of a nanoparticle film can be tailored by the nanoparticle morphology. We measure distinct features in the absorption spectrum for films or ensembles of interacting polar dielectric NPs, which we attribute to the excitation of SPhP modes due to anisotropy in the dielectric permittivity of the NPs. We identify and characterize these modes in elliptical and rod-like ZnO NPs prepared by solvothermal synthesis and dispersed within an optically transparent matrix. Localized optical modes are identified using Fourier transform infrared absorption spectroscopy and confirmed by finite element simulations. The broadening and maxima of the modes are shown to be governed by the effects of anisotropy, nanoparticle morphology, and interparticle coupling within nanoparticle ensembles.

Extraordinary optical transmittance generation on Si3N4 membranes.

Metamaterials are attracting increasing attention due to their ability to support novel and engineerable electromagnetic functionalities. In this paper, we investigate one of these functionalities, i.e. the extraordinary optical transmittance (EOT) effect based on silicon nitride (Si3N4) membranes patterned with a periodic lattice of micrometric holes. Here, the coupling between the incoming electromagnetic wave and a Si3N4 optical phonon located around 900 cm-1 triggers an increase of the transmitted infrared intensity in an otherwise opaque spectral region. Different hole sizes are investigated suggesting that the mediating mechanism responsible for this phenomenon is the excitation of a phonon-polariton mode. The electric field distribution around the holes is further investigated by numerical simulations and nano-IR measurements based on a Scattering-Scanning Near Field Microscope (s-SNOM) technique, confirming the phonon-polariton origin of the EOT effect. Being membrane technologies at the core of a broad range of applications, the confinement of IR radiation at the membrane surface provides this technology platform with a novel light-matter interaction functionality.

Curvature-Induced One-Dimensional Phonon Polaritons at Edges of Folded Boron Nitride Sheets.

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.

Near-field radiative heat transfer modulated by nontrivial topological surface states

Three-dimensional topological insulators (3D TIs), such as Bi2Se3 and Bi2Te3, possessing insulating bulk states and nontrivial topological surface states protected by time-reversal symmetry, have attracted considerable attention. In this paper, we investigate the near-field radiative heat transfer in 3D TIs, which can be strongly modulated by the non-trivial surface states. Full 3D TI properties including both the bulk and surface states are considered in our theoretical study. We show that the hybrid polaritons in single-material TI films, resulting from the coupling of Dirac plasmons on the top and bottom surfaces with the multiple phonon polariton modes supported by the bulk states including hyperbolic phonon polaritons (HPP), surface phonon polaritons (SPhP) and epsilon-near-pole (ENP) modes, can strongly mediate and enhance the near-field thermal radiation. The dispersions of hybrid polaritons intensely depend on the chemical potential of the surface and the film thickness, and by tuning both separately, we can control the coupling and competition between the surface and bulk modes, and thus modulate the radiative spectrum and heat flux. In addition, the nonlocal optical response of the surface states has a remarkable impact on the mode hybridization. This work demonstrates the potential of 3D TIs in manipulating near-field thermal radiation, which may provide a useful platform for energy conversion and thermal management.

Transition from Phononic to Geometrical Mie Modes Measured in Single Subwavelength Polar Dielectric Spheres

Spherical dielectric resonators are highly attractive for light manipulation, thanks to their intrinsic electric and magnetic resonances. Here, we present measurements of the mid-infrared far-field thermal radiation of single subwavelength dielectric spheres deposited on a gold substrate, of radii ranging from 1 to 2.5 μm, which agree quantitatively with simulated absorption cross sections. For SiO2 microspheres, we evidence the excitation of both surface phonon-polariton (SPhP) modes and geometrical electric and magnetic Mie modes. The transition from a phonon-mode-dominated to a Mie-mode-dominated emission spectrum is observed, with a threshold radius of ∼1.5 μm. We also show that the presence of the metallic substrate augments the computed spheres absorption cross-section due to increased local field enhancement, arising from the near-field interaction of the spheres oscillating charges with their image in the metallic mirror. In contrast, measurements of single subwavelength SPhP-inactive PTFE spheres reveal that the mid-infrared response of such lossy spheres is dominated by their bulk absorption. Our results demonstrate how engineering the geometrical and dielectric properties of subwavelength scatterers can enable the control of thermal emission near room temperature, with exciting perspectives for applications such as radiative cooling.