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Keywords = phonon polariton

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9 pages, 1789 KiB  
Communication
Near-Field Imaging of Hybrid Surface Plasmon-Phonon Polaritons on n-GaN Semiconductor
by Vytautas Janonis, Adrian Cernescu, Pawel Prystawko, Regimantas Januškevičius, Simonas Indrišiūnas and Irmantas Kašalynas
Materials 2025, 18(12), 2849; https://doi.org/10.3390/ma18122849 - 17 Jun 2025
Viewed by 384
Abstract
Near-field imaging of the hybrid surface plasmon-phonon polaritons on the n-GaN semiconductor was performed using a scattering scanning near-field optical microscope at the selected frequencies of 920 cm−1 and 570 cm−1. The experimental measurements and numerical modeling data were in [...] Read more.
Near-field imaging of the hybrid surface plasmon-phonon polaritons on the n-GaN semiconductor was performed using a scattering scanning near-field optical microscope at the selected frequencies of 920 cm−1 and 570 cm−1. The experimental measurements and numerical modeling data were in good agreement, revealing the large propagation distances on the n-GaN semiconductor and other insights which could be obtained by analyzing the dispersion characteristics of hybrid polaritons. In particular, the decay lengths of polaritons at the excitation frequency of 920 cm−1 were measured to be up to 25 and 30 µm in experiment and theory, respectively. In the case of excitation at the frequency of 570 cm−1, the surface plasmon-phonon polaritons’ decay distances were 25 µm and 105 µm, respectively, noting the limitations of the near-field optical microscope setups used. Dispersion characteristics of the resonant frequency and the damping rate of hybrid polaritons were numerically modeled and compared with the analytical calculations, validating the need for further experiment improvements. The launch conditions for the near-field observation of extraordinary coherence of the surface plasmon-phonon polaritons were also discussed. Full article
(This article belongs to the Topic Wide Bandgap Semiconductor Electronics and Devices)
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19 pages, 1403 KiB  
Review
Nonlinear Dielectric Metasurfaces for Terahertz Applications
by Forouzan Habibighahfarokhi, Olga Sergaeva, Luca Carletti, Paolo Franceschini, Andrea Tognazzi, Andrea Locatelli, Unai Arregui Leon, Giuseppe Della Valle, Costantino De Angelis and Davide Rocco
Photonics 2025, 12(4), 370; https://doi.org/10.3390/photonics12040370 - 12 Apr 2025
Cited by 1 | Viewed by 1057
Abstract
The terahertz (THz) region of the electromagnetic spectrum, spanning from 0.1 to 30 THz, represents a prospering area in photonics, with transformative applications in imaging, communications, and material analysis. However, the development of efficient and compact THz sources has long been hampered by [...] Read more.
The terahertz (THz) region of the electromagnetic spectrum, spanning from 0.1 to 30 THz, represents a prospering area in photonics, with transformative applications in imaging, communications, and material analysis. However, the development of efficient and compact THz sources has long been hampered by intrinsic material limitations, inefficient conversion processes, and complex phase-matching requirements. Recent breakthroughs in nonlinear optical mechanisms, resonant metasurface engineering, and advances in the fabrication processes for materials such as lithium niobate (LN) and aluminum gallium arsenide (AlGaAs) have paved the way for innovative THz generation techniques. This review article explores the latest theoretical advances, together with key experimental results and outlines perspectives for future developments. Full article
(This article belongs to the Special Issue Photonics Metamaterials: Processing and Applications)
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21 pages, 3704 KiB  
Article
Effective Polarizability in Near-Field Microscopy of Phonon-Polariton Resonances
by Viktoriia E. Babicheva
Nanomaterials 2025, 15(6), 458; https://doi.org/10.3390/nano15060458 - 18 Mar 2025
Cited by 1 | Viewed by 555
Abstract
We investigate the resonant characteristics of planar surfaces and distinct edges of structures with the excitation of phonon-polaritons. We analyze two materials supporting phonon-polariton excitations in the mid-infrared spectrum: silicon carbide, characterized by an almost isotropic dielectric constant, and hexagonal boron nitride, notable [...] Read more.
We investigate the resonant characteristics of planar surfaces and distinct edges of structures with the excitation of phonon-polaritons. We analyze two materials supporting phonon-polariton excitations in the mid-infrared spectrum: silicon carbide, characterized by an almost isotropic dielectric constant, and hexagonal boron nitride, notable for its pronounced anisotropy in a spectral region exhibiting hyperbolic dispersion. We formulate a theoretical framework that accurately captures the excitations of the structure involving phonon-polaritons, predicts the response in scattering-type near-field optical microscopy, and is effective for complex resonant geometries where the locations of hot spots are uncertain. We account for the tapping motion of the probe, perform analysis for different heights of the probe, and demodulate the signal using a fast Fourier transform. Using this Fourier demodulation analysis, we show that light enhancement across the entire apex is the most accurate characteristic for describing the response of all resonant excitations and hot spots. We demonstrate that computing the demodulation orders of light enhancement in the microscope probe accurately predicts its imaging. Full article
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11 pages, 3754 KiB  
Article
Low Dielectric Medium for Hyperbolic Phonon Polariton Waveguide in van der Waals Heterostructures
by Byung-Il Noh, Salvio Reza, Cassie Hardy, Jiahan Li, Adib Taba, Masoud Mahjouri-Samani, James H. Edgar and Siyuan Dai
Nanomaterials 2024, 14(16), 1344; https://doi.org/10.3390/nano14161344 - 14 Aug 2024
Cited by 2 | Viewed by 2371
Abstract
Polar van der Waals (vdW) crystals, composed of atomic layers held together by vdW forces, can host phonon polaritons—quasiparticles arising from the interaction between photons in free-space light and lattice vibrations in polar materials. These crystals offer advantages such as easy fabrication, low [...] Read more.
Polar van der Waals (vdW) crystals, composed of atomic layers held together by vdW forces, can host phonon polaritons—quasiparticles arising from the interaction between photons in free-space light and lattice vibrations in polar materials. These crystals offer advantages such as easy fabrication, low Ohmic loss, and optical confinement. Recently, hexagonal boron nitride (hBN), known for having hyperbolicity in the mid-infrared range, has been used to explore multiple modes with high optical confinement. This opens possibilities for practical polaritonic nanodevices with subdiffractional resolution. However, polariton waves still face exposure to the surrounding environment, leading to significant energy losses. In this work, we propose a simple approach to inducing a hyperbolic phonon polariton (HPhP) waveguide in hBN by incorporating a low dielectric medium, ZrS2. The low dielectric medium serves a dual purpose—it acts as a pathway for polariton propagation, while inducing high optical confinement. We establish the criteria for the HPhP waveguide in vdW heterostructures with various thicknesses of ZrS2 through scattering-type scanning near-field optical microscopy (s-SNOM) and by conducting numerical electromagnetic simulations. Our work presents a feasible and straightforward method for developing practical nanophotonic devices with low optical loss and high confinement, with potential applications such as energy transfer, nano-optical integrated circuits, light trapping, etc. Full article
(This article belongs to the Special Issue Nano-Optics and Light-Matter Interactions)
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11 pages, 374 KiB  
Communication
Numerical Algorithms in III–V Semiconductor Heterostructures
by Ioannis G. Tsoulos and V. N. Stavrou
Algorithms 2024, 17(1), 44; https://doi.org/10.3390/a17010044 - 19 Jan 2024
Viewed by 2014
Abstract
In the current research, we consider the solution of dispersion relations addressed to solid state physics by using artificial neural networks (ANNs). Most specifically, in a double semiconductor heterostructure, we theoretically investigate the dispersion relations of the interface polariton (IP) modes and describe [...] Read more.
In the current research, we consider the solution of dispersion relations addressed to solid state physics by using artificial neural networks (ANNs). Most specifically, in a double semiconductor heterostructure, we theoretically investigate the dispersion relations of the interface polariton (IP) modes and describe the reststrahlen frequency bands between the frequencies of the transverse and longitudinal optical phonons. The numerical results obtained by the aforementioned methods are in agreement with the results obtained by the recently published literature. Two methods were used to train the neural network: a hybrid genetic algorithm and a modified version of the well-known particle swarm optimization method. Full article
(This article belongs to the Special Issue Algorithms in Data Classification (2nd Edition))
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14 pages, 3805 KiB  
Article
Significant Substrate Effects on Electromagnetic Scattering by Particles in the Infrared Atmospheric Window
by Feifei Gao, Shangyu Zhang, Wenjie Zhang, Lanxin Ma and Linhua Liu
Photonics 2023, 10(4), 476; https://doi.org/10.3390/photonics10040476 - 21 Apr 2023
Cited by 1 | Viewed by 2209
Abstract
Particle-dispersed coatings emerged as a promising approach to regulate the apparent radiative properties of underlying substrates in various applications, including but not limited to radiative cooling, thermal management, and infrared stealth. However, most research efforts in this field overlooked the dependent scattering mechanisms [...] Read more.
Particle-dispersed coatings emerged as a promising approach to regulate the apparent radiative properties of underlying substrates in various applications, including but not limited to radiative cooling, thermal management, and infrared stealth. However, most research efforts in this field overlooked the dependent scattering mechanisms between the particles and the substrate, which can impact the optical properties of the particles. In this study, we explored the particle-substrate interactions within the atmospheric radiative window of 8–14 µm. Using the T-matrix method, we calculated the scattering and absorption efficiencies of a dielectric/metallic particle situated above a metallic/dielectric substrate, considering the different gap sizes. Near the small gaps (<0.5a with a the sphere radius), we found that the strong local fields induced by the interaction between the induced and image charges largely enhanced the absorption and scattering efficiencies of the particles. With the increasing gap sizes, the absorption and scattering efficiencies presented a significant oscillation with a period of about 4.5a, which was attributed to the interference (standing wave) between the scattered fields from the sphere and the reflected fields from the substrate. Our findings identify a crucial role of the particle–substrate interactions in the infrared properties of particles, which may guide a comprehensive insight on the apparent radiative properties of the particle composite coatings. Full article
(This article belongs to the Section Optical Interaction Science)
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13 pages, 3349 KiB  
Article
Fano Resonance in Near-Field Thermal Radiation of Two-Dimensional Van der Waals Heterostructures
by Huihai Wu, Xiaochuan Liu, Keyong Zhu and Yong Huang
Nanomaterials 2023, 13(8), 1425; https://doi.org/10.3390/nano13081425 - 20 Apr 2023
Cited by 4 | Viewed by 2345
Abstract
Two-dimensional (2D) materials and their vertically stacked heterostructures have attracted much attention due to their novel optical properties and strong light-matter interactions in the infrared. Here, we present a theoretical study of the near-field thermal radiation of 2D vdW heterostructures vertically stacked of [...] Read more.
Two-dimensional (2D) materials and their vertically stacked heterostructures have attracted much attention due to their novel optical properties and strong light-matter interactions in the infrared. Here, we present a theoretical study of the near-field thermal radiation of 2D vdW heterostructures vertically stacked of graphene and monolayer polar material (2D hBN as an example). An asymmetric Fano line shape is observed in its near-field thermal radiation spectrum, which is attributed to the interference between the narrowband discrete state (the phonon polaritons in 2D hBN) and a broadband continuum state (the plasmons in graphene), as verified by the coupled oscillator model. In addition, we show that 2D van der Waals heterostructures can achieve nearly the same high radiative heat flux as graphene but with markedly different spectral distributions, especially at high chemical potentials. By tuning the chemical potential of graphene, we can actively control the radiative heat flux of 2D van der Waals heterostructures and manipulate the radiative spectrum, such as the transition from Fano resonance to electromagnetic-induced transparency (EIT). Our results reveal the rich physics and demonstrate the potential of 2D vdW heterostructures for applications in nanoscale thermal management and energy conversion. Full article
(This article belongs to the Special Issue Next-Generation Infrared Optoelectronic Nanomaterials and Devices)
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7 pages, 29623 KiB  
Article
Magnetical Manipulation of Hyperbolic Phonon Polaritons in Twisted Double-Layers of Molybdenum Trioxide
by Hongjing Li and Gaige Zheng
Micromachines 2023, 14(3), 648; https://doi.org/10.3390/mi14030648 - 13 Mar 2023
Cited by 1 | Viewed by 1845
Abstract
Controlling the twist angle between double stacked van der Waals (vdW) crystals holds great promise for nanoscale light compression and manipulation in the mid-infrared (MIR) range. A lithography-free geometry has been proposed to mediate the coupling of phonon polaritons (PhPs) in double-layers of [...] Read more.
Controlling the twist angle between double stacked van der Waals (vdW) crystals holds great promise for nanoscale light compression and manipulation in the mid-infrared (MIR) range. A lithography-free geometry has been proposed to mediate the coupling of phonon polaritons (PhPs) in double-layers of vdW α-MoO3. The anisotropic hyperbolic phonon polaritons (AHPhPs) are further hybridized by the anisotropic substrate environment of magneto-optic indium arsenide (InAs). The AHPhPs can be tuned by twisting the angle between the optical axes of the two separated layers and realize a topological transition from open to closed dispersion contours. Moreover, in the presence of external magnetic field, an alteration of the hybridization of PhPs will be met, which enable an efficient way for the control of light-matter interaction at nanoscale in the MIR region. Full article
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17 pages, 6463 KiB  
Review
Hexagonal Boron Nitride for Photonic Device Applications: A Review
by Shinpei Ogawa, Shoichiro Fukushima and Masaaki Shimatani
Materials 2023, 16(5), 2005; https://doi.org/10.3390/ma16052005 - 28 Feb 2023
Cited by 36 | Viewed by 10480
Abstract
Hexagonal boron nitride (hBN) has emerged as a key two-dimensional material. Its importance is linked to that of graphene because it provides an ideal substrate for graphene with minimal lattice mismatch and maintains its high carrier mobility. Moreover, hBN has unique properties in [...] Read more.
Hexagonal boron nitride (hBN) has emerged as a key two-dimensional material. Its importance is linked to that of graphene because it provides an ideal substrate for graphene with minimal lattice mismatch and maintains its high carrier mobility. Moreover, hBN has unique properties in the deep ultraviolet (DUV) and infrared (IR) wavelength bands owing to its indirect bandgap structure and hyperbolic phonon polaritons (HPPs). This review examines the physical properties and applications of hBN-based photonic devices that operate in these bands. A brief background on BN is provided, and the theoretical background of the intrinsic nature of the indirect bandgap structure and HPPs is discussed. Subsequently, the development of DUV-based light-emitting diodes and photodetectors based on hBN’s bandgap in the DUV wavelength band is reviewed. Thereafter, IR absorbers/emitters, hyperlenses, and surface-enhanced IR absorption microscopy applications using HPPs in the IR wavelength band are examined. Finally, future challenges related to hBN fabrication using chemical vapor deposition and techniques for transferring hBN to a substrate are discussed. Emerging techniques to control HPPs are also examined. This review is intended to assist researchers in both industry and academia in the design and development of unique hBN-based photonic devices operating in the DUV and IR wavelength regions. Full article
(This article belongs to the Special Issue Research Progress on Two-Dimensional Materials)
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9 pages, 3012 KiB  
Article
Active Tuning and Anisotropic Strong Coupling of Terahertz Polaritons in Van der Waals Heterostructures
by Shaopeng Li, Junhao Xu and Yajie Xie
Micromachines 2022, 13(11), 1955; https://doi.org/10.3390/mi13111955 - 11 Nov 2022
Cited by 1 | Viewed by 2036
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Processing and Applications of Novel Optical Metamaterials)
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12 pages, 2037 KiB  
Article
Quantum Interference in Spontaneous Decay of a Quantum Emitter Placed in a Dimer of Bismuth-Chalcogenide Microparticles
by Nikolaos Kyvelos, Georgios Tsigaridas, Emmanuel Paspalakis and Vassilios Yannopapas
Photonics 2022, 9(9), 596; https://doi.org/10.3390/photonics9090596 - 23 Aug 2022
Cited by 6 | Viewed by 2965
Abstract
We investigate the phenomenon of quantum interference in spontaneous emission for a three-level V-type quantum emitter placed between two bismuth-chalcogenide (Bi2Te3, Bi2Se3) microspheres. In particular, we find that the degree of quantum interference can become [...] Read more.
We investigate the phenomenon of quantum interference in spontaneous emission for a three-level V-type quantum emitter placed between two bismuth-chalcogenide (Bi2Te3, Bi2Se3) microspheres. In particular, we find that the degree of quantum interference can become as high as 0.994, a value which is attributed to the strong dependence of the spontaneous emission rate on the orientation of an atomic dipole relative to the surfaces of the microspheres, at the excitation frequencies of phonon-polariton states of the bismuth-chalcogenide microspheres (anisotropic Purcell effect). As a consequence of the high degree of quantum interference, we observe the occurrence of strong population trapping in the quantum emitter. To the best of our knowledge, the reported values of the degree of quantum interference are record values and are obtained for a relatively simple geometrical setup such as that of a microparticle dimer. Full article
(This article belongs to the Section Quantum Photonics and Technologies)
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13 pages, 5674 KiB  
Article
Modulation of Casimir Force between Graphene-Covered Hyperbolic Materials
by Ge Song, Zhixiang Liu, Lingchun Jia, Cong Li and Yingli Chang
Nanomaterials 2022, 12(13), 2168; https://doi.org/10.3390/nano12132168 - 23 Jun 2022
Cited by 6 | Viewed by 2409
Abstract
A flexible method for modulating the Casimir force is proposed by combining graphene and hyperbolic materials (HMs). The proposed structure employs two candidates other than graphene. One is hexagonal boron nitride (hBN), a natural HM. The other is porous silicon carbide (SiC), which [...] Read more.
A flexible method for modulating the Casimir force is proposed by combining graphene and hyperbolic materials (HMs). The proposed structure employs two candidates other than graphene. One is hexagonal boron nitride (hBN), a natural HM. The other is porous silicon carbide (SiC), which can be treated as an artificial HM by the effective medium theory. The Casimir force between graphene-covered hBN (porous SiC) bulks is presented at zero temperature. The results show that covering HM with graphene increases the Casimir force monotonically. Furthermore, the force can be modulated by varying the Fermi level, especially at large separation distances. The reflection coefficients are thoroughly investigated, and the enhancement is attributed to the interaction of surface plasmons (SPs) supported by graphene and hyperbolic phonon polaritons (HPhPs) supported by HMs. Moreover, the Casimir force can be controlled by the filling factor of porous SiC. The Casimir force can thus be modulated flexibly by designing desired artificial HMs and tuning the Fermi level. The proposed models have promising applications in practical detection and technological fields. Full article
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10 pages, 4581 KiB  
Article
Selective Properties of Mid-Infrared Tamm Phonon-Polaritons Emitter with Silicon Carbide-Based Structures
by Chengxuan Gong and Gaige Zheng
Micromachines 2022, 13(6), 920; https://doi.org/10.3390/mi13060920 - 10 Jun 2022
Cited by 9 | Viewed by 2455
Abstract
Electromagnetic (EM) absorbers and emitters have attracted much interest because of their versatile applications. A photonic heterostructure composed of silicon carbide (SiC) layer/germanium (Ge) cavity/distributed Bragg reflector (DBR) has been proposed. Selective emission properties have been investigated through rigorous coupled wave analysis (RCWA) [...] Read more.
Electromagnetic (EM) absorbers and emitters have attracted much interest because of their versatile applications. A photonic heterostructure composed of silicon carbide (SiC) layer/germanium (Ge) cavity/distributed Bragg reflector (DBR) has been proposed. Selective emission properties have been investigated through rigorous coupled wave analysis (RCWA) method. The results illustrate that Tamm phonon-polaritons can be excited, and the magnetic field is partially centralized at the junction of Ge cavity and SiC film, aimed to improve the interactions of photon–phonon. The absorptivity/emissivity of the structure can be better optimized by controlling the coupling of surface modes with the incident wave. Near-unity absorption can be achieved through optimizing the SiC grating/Ge cavity/distributed Bragg reflector (DBR) multilayer structure with geometrical parameters of ds = 0.75 μm, dg = 0.7 μm, d1 = 1.25 μm and d2 = 0.75 μm, respectively. Physical mechanism of selective emission characteristics is deliberated. In addition, the simulation results demonstrate that the emitter desensitizes to the incidence angle and polarization state in the mid-infrared (MIR) range. This research ameliorates the function of the selective emitters, which provides more efficient design for SiC-based systems. Full article
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13 pages, 5557 KiB  
Article
Enhancement of Casimir Friction between Graphene-Covered Topological Insulator
by Ting Yu, Rong Luo, Tongbiao Wang, Dejian Zhang, Wenxing Liu, Tianbao Yu and Qinghua Liao
Nanomaterials 2022, 12(7), 1148; https://doi.org/10.3390/nano12071148 - 30 Mar 2022
Cited by 6 | Viewed by 2377
Abstract
Casimir friction is theoretically studied between graphene-covered undoped bismuth selenide (Bi2Se3) in detail. In the graphene/Bi2Se3 composite structure, the coupling of the hyperbolic phonon polaritons supported by Bi2Se3 with the surface plasmons supported [...] Read more.
Casimir friction is theoretically studied between graphene-covered undoped bismuth selenide (Bi2Se3) in detail. In the graphene/Bi2Se3 composite structure, the coupling of the hyperbolic phonon polaritons supported by Bi2Se3 with the surface plasmons supported by graphene can lead to the hybrid surface plasmon–phonon polaritons (SPPPs). Compared with that between undoped Bi2Se3, Casimir friction can be enhanced by more than one order of magnitude due to the contribution of SPPPs. It is found that the chemical potential that can be used to modulate the optical characteristic of SPPPs plays an important role in Casimir friction. In addition, the Casimir friction between doped Bi2Se3 is also studied. The friction coefficient between doped Bi2Se3 can even be larger than that between graphene-covered undoped Bi2Se3 for suitable chemical potential due to the contribution of unusual electron surface states. The results obtained in this work are not only beneficial to the study of Casimir frictions but also extend the research ranges of topological insulators. Full article
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9 pages, 2432 KiB  
Article
Multi-Channel High-Performance Absorber Based on SiC-Photonic Crystal Heterostructure-SiC Structure
by Jing Han, Jijuan Jiang, Tong Wu, Yang Gao and Yachen Gao
Nanomaterials 2022, 12(2), 289; https://doi.org/10.3390/nano12020289 - 17 Jan 2022
Cited by 15 | Viewed by 2362
Abstract
The multi-channel high-efficiency absorber in the mid-infrared band has broad application prospects. Here, we propose an SiC-photonic crystal (PhC) heterostructure-SiC structure to realize the absorber. The absorption characteristics of the structure are studied theoretically. The results show that the structure can achieve high-efficiency [...] Read more.
The multi-channel high-efficiency absorber in the mid-infrared band has broad application prospects. Here, we propose an SiC-photonic crystal (PhC) heterostructure-SiC structure to realize the absorber. The absorption characteristics of the structure are studied theoretically. The results show that the structure can achieve high-efficiency multi-channel absorption in the mid-infrared range. The absorption peaks come from the coupling of the dual Tamm phonon polariton (TPhP) mode formed at the interface between the two SiC layers and the photonic crystal, and the optical Tamm state (OTS) mode formed in the PhC heterostructure. By adjusting the thickness of the air dielectric layer and the period of the PhC in the heterostructure, the mode coupling intensity can be regulated; thereby, the position and intensity of the absorption peak can be adjusted. In addition, the absorption peaks of TE and TM polarized light can be controlled by changing the incident angle. Adjusting the incident angle can also control the excitation and intensity of the epsilon-near-zero (ENZ) phonon polariton mode produced by TM polarized light. This kind of light absorber may have potential applications in sensors, filters, modulators, switches, thermal radiators, and so on. Full article
(This article belongs to the Section Theory and Simulation of Nanostructures)
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