Lujun Huang

Lujun Huang
East China Normal University | ECNU

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122
Publications
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3,041
Citations

Publications

Publications (122)
Article
Full-text available
The ultimate goal of artificial intelligence (AI) is to mimic the human brain to perform decision-making and control directly from high-dimensional sensory input. Diffractive optical networks (DONs) provide a promising solution for implementing AI with high speed and low power-consumption. Most reported DONs focus on tasks that do not involve envir...
Article
Full-text available
Most reported thermal emitters to date employing photonic nanostructures to achieve narrow bandwidth feature the rainbow effect due to the steep dispersion of the involved high-Q resonances. In this work, we propose to realize thermal emissions with high temporal coherence but free from rainbow effect, by harnessing a novel flat band design within...
Data
The Supplemental Material provides the refractive index of Sb2S3; the simulation methods; the transmission spectrum for quasi-BIC; the fabrication procedure of the nanostructured Sb2S3 metasurface; the nonlocal wavefront-shaping of the proposed beam deflection metasurface; the nonlocal 1D focusing of the proposed radial metalens; the narrowband spa...
Article
Full-text available
Recent advances in nonlocal metasurfaces have enabled unprecedented success in shaping the wave front of light with spectral selectivity, offering alternative solutions for many emerging nanophotonics applications. The ability to tune both the spectral and spatial properties of such a class of metasurfaces is highly desirable, but the dynamic nonvo...
Article
Full-text available
Harnessing the power of symmetry‐protected bound states in the continuum (SP BICs) has become a focal point in scientific exploration, promising many interesting applications in nanophotonics. However, the practical realization of ultrahigh quality (Q) factor quasi‐BICs (QBICs) is hindered by the fabrication imperfections. In this work, an easy app...
Article
Acoustic resonances in open systems, which are usually associated with resonant modes characterized by complex eigenfrequencies, play a fundamental role in manipulating acoustic wave radiation and propagation. Notably, they are accompanied by considerable feld enhancement, boosting interactions between waves and matter, and leading to various...
Article
Full-text available
Bound states in the continuum (BICs) have emerged as an efficient tool for trapping light at the nanoscale, promising several exciting applications in photonics. Breaking the structural symmetry has been proposed as an effective way of exciting quasi-BlCs (QBICs) and generating high-Q resonances. Herein, we demonstrate that QBICs can be excited in...
Article
Full-text available
Quasi-bound states in the continuum (QBICs) coupling into the propagating spectrum manifest themselves as high-quality factor (Q) modes susceptible to perturbations. This poses a challenge in predicting stable Fano resonances for realistic applications. Besides, where and when the maximum field enhancement occurs in real acoustic devices remains el...
Article
Achieving perfect absorption in few-layer two-dimensional (2D) materials plays a crucial role in applications such as optoelectronics and sensing. However, the underlying mechanisms of all reported works imply a strongly inherent dependence of the central wavelength on the structural parameters. Here, we propose a structure-parameter-deviation immu...
Preprint
Full-text available
Recent advances in nonlocal metasurfaces have enabled unprecedented success in shaping the wavefront of light with spectral selectivity, offering new solutions for many emerging nanophotonics applications. The ability to tune both the spectral and spatial properties of such a novel class of metasurfaces is highly desirable, but the dynamic nonvolat...
Article
In recent years, the formation of exciton-polaritons in semiconductor materials has attracted major interest because of their exotic optical properties, allowing the study of many interesting physical phenomena, such as superfluids and Bose-Einstein condensation. Here, we demonstrate a double strong coupling regime in a perovskite and tungsten disu...
Article
Full-text available
High quality(Q) factor optical resonators are indispensable for many photonic devices. While very large Q-factors can be obtained theoretically in guided-mode settings, free-space implementations suffer from various limitations on the narrowest linewidth in real experiments. Here, we propose a simple strategy to enable ultrahigh-Q guided-mode reson...
Article
Exciton polaritons in metallic nanocavities and transition-metal dichalcogenide monolayers has led to striking discoveries, ranging from Bose-Einstein condensation to slowing light. Although plasmonic nanocavities offer small mode volumes, the intrinsic losses of plasmonic nanocavities remain an open challenge in exciton-polariton devices. Conseque...
Article
Full-text available
Advanced sensing devices, highly sensitive, and reliable in detecting ultralow concentrations of circulating biomarkers, are extremely desirable and hold great promise for early diagnostics and real‐time progression monitoring of diseases. Nowadays, the most commonly used clinical methods for diagnosing biomarkers suffer from complicated procedures...
Article
Full-text available
Symmetry-protected bound states in the continuum (SP-BICs) are one of the most intensively studied BICs. Typically, SP-BICs must be converted into quasi-BICs (QBICs) by breaking the unit cell’s symmetry so that they can be accessed by the external excitation. The symmetry-broken usually results in a varied resonance wavelength of QBICs which are al...
Article
Full-text available
Bound states in the continuum (BICs) have been demonstrated as a powerful tool for trapping acoustic fields in an acoustic resonator. It has been widely recognized that symmetry-protected (SP) BICs result from symmetry incompatibility of some eigenmodes of a resonator with propagating modes of waveguides. The most typical example of SP BIC is the o...
Article
Full-text available
Active devices play a critical role in modern electromagnetic and photonics systems. To date, the epsilon ( $\varepsilon$ ε )-near-zero (ENZ) is usually integrated with the low Q-factor resonant metasurface to achieve active devices, and enhance the light-matter interaction significantly at the nanoscale. However, the low Q-factor resonance may lim...
Article
Resonant Metasurface In article number 2200564, Lujun Huang, Guanhai Li, Andrey E. Miroshnichenko, and colleagues demonstrate accidental bound states in the continuum (BIC)s at Γ‐point in an asymmetric dielectric metasurface. The measured Q‐factor is up to 4.99 × 103. This work may enrich the library of BICs and find exciting applications in develo...
Preprint
Full-text available
The ultimate goal of artificial intelligence is to mimic the human brain to perform decision-making and control directly from high-dimensional sensory input. Diffractive optical networks provide a promising solution for implementing artificial intelligence with high-speed and low-power consumption. Most of the reported diffractive optical networks...
Article
It is well established that for symmetry‐protected bound states in the continuum (BICs), introducing the broken geometry symmetry in a dielectric metasurface transforms such a BIC into a quasi‐BIC (QBIC) with high‐quality factor (Q‐factor). Typically, the smaller the asymmetry parameter, the larger the Q‐factor. However, it is very challenging to f...
Preprint
Full-text available
Bound states in the continuum (BICs) are a well known phenomenon in physics, particularly in quantum physics and wave physics. Since BICs are local states, their existence typically manifests as Fano resonances in the transmission or reflection spectrum. However, to date no direct or visual proof of an acoustic BIC has been reported. We demonstrate...
Article
Full-text available
Bound states in the continuum (BICs) provide a viable way of achieving high-Q resonances in both photonics and acoustics. In this work, we propose a general method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a coupled acoustic waveguide-resonator system. We demonstrate that FW BICs can be achieved with arbitrary two degenerat...
Article
To date, second-harmonic generation (SHG) at nanoscale has concentrated on employing high-refractive-index nanostructures, owing to the strong field confinement at deep subwavelength scales based on optically resonant effects. However, nanostructures with lower index contrast between the structures and the surroundings generally exhibit weaker reso...
Article
Full-text available
We consider square and equilateral triangular open acoustic resonators with the $C_{4v}$ and $C_{3v}$ symmetries, respectively. There is an unique property of square and triangular resonators of accidental number four-fold degeneracy of eigenstates that gives rise to two-fold degenerate Friedrich-Wintgen (FW) BICs. Compared to usual FW BICs the deg...
Article
Exciton-polariton arising from strong light-matter interaction between exciton and optical cavity has attracted considerable attention due to its potential applications in Bose-Einstein condensation, low-threshold lasing, and slow light. In recent years, two-dimensional lead halide perovskite has emerged as an ideal candidate for realizing exciton...
Preprint
Full-text available
We consider square and equilateral triangular open acoustic resonators with the $C_{4v}$ and $C_{3v}$ symmetries, respectively. There is an unique property of square and triangular resonators of accidental number four-fold degeneracy of eigenstates that gives rise to two-fold degenerate Friedrich-Wintgen (FW) BICs. Compared to usual FW BICs the deg...
Article
Full-text available
Monolayer transition metal dichalcogenides (TMDCs), like MoS2, MoSe2, WS2, and WSe2, feature direct bandgaps, strong spin–orbit coupling, and exciton–polariton interactions at the atomic scale, which could be harnessed for efficient light emission, valleytronics, and polaritonic lasing, respectively. Nevertheless, to build next-generation photonic...
Preprint
Full-text available
Bound states in the continuum (BICs) provide a viable way of achieving high-Q resonances in both photonics and acoustics. In this work, we proposed a general method of constructing Friedrich-Wintgen (FW) BICs and accidental BICs in a coupled acoustic waveguide-resonator system. We demonstrated that FW BICs can be achieved with arbitrary two degener...
Preprint
Monolayer transition metal dichalcogenides (TMDCs), like MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, feature direct bandgaps, strong spin-orbit coupling, and exciton-polariton interactions at the atomic scale, which could be harnessed for efficient light emission, valleytronics, and polaritonic lasing, respectively. Nevertheless, to build next-generati...
Preprint
Full-text available
High quality (Q) factor optical resonators are indispensable for many photonic devices. While very large Q-factors can be obtained theoretically in guided mode settings, free-space implementations suffer from various limitations on the narrowest possible linewidth in real experiments. In these devices, the largest Q-factors are hindered by radiatio...
Preprint
To date, second-harmonic generation (SHG) at nanoscale has been concentrated on employing high-refractive-index nanostructures, owing to the strong field confinement at deep subwavelength scales based on optically resonant effects. However, low-index nanostructures generally exhibit weaker resonant effects and lower field confinement. To address th...
Article
Full-text available
Acoustic resonant cavities play a vital role in modern acoustical systems. The ultrahigh quality‐factor resonances are highly desired for some applications such as high‐resolution acoustic sensors and acoustic lasers. Here, a class of supercavity resonances is theoretically proposed and experimentally demonstrated in a coupled acoustic resonator sy...
Article
Full-text available
The optical anapole state resulting from interference of the electric and toroidal moments is of much interest due to its nonradiating nature. Interference of optical modes supported by a diverse range of Mie-resonant structures has found many applications, such as in biosensors and optical communication. This review provides an overview of the rec...
Article
Full-text available
Oligomer metasurfaces have attracted a lot of attention in recent years because of their ability to drive strong resonance effects. In this work, by perturbing the symmetry of the structure, we find that there are a large number of resonance modes in the oligomer metasurfaces associated with the optical bound states in the continuum (BICs) near the...
Article
The strong light-matter interaction between the exciton of atomically thin transition metal dichalcogenides (TMDCs) and photonic nanocavities leads to the formation of unique hybrid light-matter quasiparticles known as exciton-polaritons (EPs). The newly formed mixed state has the advantages of the photonic part such as rapid propagation and low ef...
Article
Full-text available
Two dimensional (2D) transition metal dichalcogenide (TMDC) materials, such as MoS2, WS2, MoSe2, and WSe2, have received extensive attention in the past decade due to their extraordinary electronic, optical and thermal properties. They evolve from indirect bandgap semiconductors to direct bandgap semiconductors while their layer number is reduced f...
Article
In the field of nonlinear optics, graphene has shown astounding nonlinear properties, including the generation of harmonics across a wide frequency range. Harmonic generation (HG) is a frequency conversion process that serves as the basis for a number of modern disciplines including materials science and nanotechnology. This field also holds great...
Article
Full-text available
As an elementary particle, a photon that carries information in frequency, polarization, phase, and amplitude, plays a crucial role in modern science and technology. However, how to retrieve the full information of unknown photons in an ultracompact manner over broad bandwidth remains a challenging task with growing importance. Here, we demonstrate...
Article
Due to the large binding energy and direct bandgap, transition-metal dichalcogenides (TMDCs) monolayers have been considered a perfect platform for realising strong coupling at room temperature. It is well established that the quality factor (Q-factor) plays a crucial role in enhancing strong coupling. In this work, we demonstrate the improved stro...
Preprint
Full-text available
Acoustic resonant cavities play a vital role in modern acoustical systems. They have led to many essential applications for noise control, biomedical ultrasonics, and underwater communications. The ultrahigh quality-factor resonances are highly desired for some applications like high-resolution acoustic sensors and acoustic lasers. Here, we theoret...
Conference Paper
Germanium is the proper material for fiber-optic communication due to low-intrinsic dissipative losses at the telecommunication C-band. But specific applications need stronger absorption. We demonstrate super-absorbing germanium metasurfaces designed by quasi-bound states in the continuum.
Article
Full-text available
Bound states in the continuum (BICs) correspond to a particular leaky mode with an infinitely large quality-factor (Q-factor) located within the continuum spectrum. To date, most of the research work reported focuses on the BIC-enhanced light matter interaction due to its extreme near-field confinement. Little attention has been paid to the scatter...
Article
Full-text available
Light absorption plays a vital role in governing the performance of optoelectronic devices, such as solar cells and photodetectors. However, it is quite challenging to realize perfect absorption for materials with low intrinsic dissipative losses and requires the careful design of nanoscale structures. This study theoretically proposes a polarizati...
Preprint
Full-text available
Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised of different parts, it is common to describe the dynamics of a subsystem of interest by making an adiabatic el...
Article
Transition‐metal dichalcogenides (TMDCs) monolayers have been considered a perfect platform for realizing exciton‐polariton at room temperature due to their direct bandgap and large binding energy of exciton. It is well established that strong coupling depends on the field enhancement induced by optical nanocavity with a high‐quality factor (Q‐fact...
Article
Full-text available
Recently developed halide perovskite semiconductors are viewed as an excellent platform to realize exciton‐polariton at room temperature due to their large oscillation strength. Here, the optimized strong coupling between the exciton of perovskite and quasi‐bound state in the continuum (QBIC) with high‐quality factor (Q‐factor), supported by all‐pe...
Article
Full-text available
The ability of sound energy confinement with high-quality factor resonance is of vital importance for acoustic devices requiring high intensity and hypersensitivity in biological ultrasonics, enhanced collimated sound emission (i.e. sound laser) and high-resolution sensing. However, structures reported so far have been experimentally demonstrated w...
Article
Full-text available
Geometrical symmetry plays a significant role in implementing robust, symmetry-protected, bound states in the continuum (BICs). However, this benefit is only theoretical in many cases since fabricated samples’ unavoidable imperfections may easily break the stringent geometrical requirements. Here we propose an approach by introducing the concept of...
Article
Metasurface provides a powerful platform to correct the chromatic aberration of conventional lenses in a flexible, integratable, and ultra‐compact manner. Mid‐wavelength infrared has promised many exciting applications ranged from molecular fingerprint detection to low‐light‐level night vision. Developing broadband achromatic metalens in mid‐wavele...
Article
Full-text available
We propose a universal strategy to realize a broadband control on arbitrary scatterers, through multiple coherent beams. By engineering the phases and amplitudes of incident beams, one can suppress the dominant scattering partial waves, making the obstacle lose its intrinsic responses in a broadband spectrum. The associated coherent beams generate...
Poster
Full-text available
Since the milestone work reporting the first exfoliation of monolayer graphene in 2004, two-dimensional (2D) materials have attracted extensive attention from both scientific and industrial communities. Compared with their bulky parental materials, these atomically thin layered materials exhibit many exceptional electrical and optical properties, a...
Preprint
Full-text available
Two dimensional (2D) transition metal dichalcogenide (TMDC) materials, such as MoS2, WS2, MoSe2, and WSe2, have received extensive attention in the past decade due to their extraordinary physical properties. The unique properties make them become ideal materials for various electronic, photonic and optoelectronic devices. However, their performance...
Preprint
Full-text available
The ability of extreme sound energy confinement with high-quality factor (Q-factor) resonance is of vital importance for acoustic devices requiring high intensity and hypersensitivity in biological ultrasonics, enhanced collimated sound emission (i.e. sound laser) and high-resolution sensing. However, structures reported so far demonstrated a limit...
Preprint
Full-text available
Geometrical symmetry plays a significant role in realizing robust, symmetry-protected, bound states in the continuum (BICs). However, this benefit is only theoretical in many cases since the unavoidable imperfections of fabricated samples may easily break the stringent geometrical requirements. Here we propose an essentially new approach by introdu...
Conference Paper
We perform multipolar analysis of second-harmonic generation (SHG) from gallium arsenide (GaAs) nanoantennas grown along different crystallographic directions and discuss their specifics. In particular, analysis of the nonlinear response of nanoantennas grown along the (110) axis based on the Lorentz lemma shows that such nanoantennas generate mult...
Article
Full-text available
Metasurfaces provide a compact, flexible, and efficient platform to manipulate the electromagnetic waves. However, chromatic aberration imposes severe restrictions on their applications in broadband polarization control. Here, we propose a broadband achromatic methodology to implement polarization-controlled multifunctional metadevices in mid-wavel...
Article
Full-text available
We put forward the multipolar model which captures the physics behind linear and nonlinear response driven by high-quality (high- Q ) supercavity modes in subwavelength particles. We show that the formation of such trapped states associated with bound states in the continuum (quasi-BIC) can be understood through multipolar transformations of couple...
Chapter
Full-text available
Deep learning has become a vital approach to solving a big-data-driven problem. It has found tremendous applications in computer vision and natural language processing. More recently, deep learning has been widely used in optimising the performance of nanophotonic devices, where the conventional computational approach may require much computation t...
Article
We elucidate the dependence of the in-plane and interfacial thermal conduction of two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials (including MoS2, WS2, and WSe2) on the materials’ physical features, such as size, layer number, composition, and substrates. The in-plane thermal conductivity k is measured at suspended 2D TMDC mat...
Preprint
Full-text available
We propose a universal strategy to realize a broadband control on arbitrary scatterers, through multiple coherent beams. By engineering the phases and amplitudes of incident beams, one can suppress the dominant scattering partial waves, making the obstacle lose its intrinsic responses in a broadband spectrum. The associated coherent beams generate...
Article
Full-text available
In this review, the nexus of nanophotonics and quantum science is considered. This nexus offers a wealth of applications and novel fundamental effects. Such an interdisciplinary approach may serve as a starting point for developing groundbreaking technologies. Several new directions in quantum nanophotonics are addressed, including strong light–mat...
Preprint
Full-text available
Multimode interference and multipolar interplay govern functionalities of optical nanoresonators and nonlinear nanoantennas. Recently, excitation of the high-quality supercavity modes (quasi-BIC states) in individual subwavelength dielectric particles has been predicted to boost the nonlinear frequency conversion at the nanoscale. Here, we put forw...
Conference Paper
Switching forward-to-backward linear scattering of nanoantennas is a process of major importance. Here, we demonstrate the first nonlinear switching of forward to backward second harmonic generation, via engineering the nonlinear-tensors of the (110)-GaAs nanoantennas.
Conference Paper
We show that the addition of an array of silicon nitride nanowire resonator can boost the absorbance of a monolayer of WS 2 from around 5-10% to 62% at the exciton wavelength of 620 nm.
Article
High-index III-V semiconductor nanoantennas have gained great attention for enhanced nonlinear light-matter interactions, in the last few years. However, the complexity of nonlinear emission profiles imposes severe constraints on practical applications, such as in optical communications and integrated optoelectronic devices. These complexities incl...
Preprint
A key concept underlying the specific functionalities of metasurfaces, i.e. arrays of subwavelength nanoparticles, is the use of constituent components to shape the wavefront of the light, on-demand. Metasurfaces are versatile and novel platforms to manipulate the scattering, colour, phase or the intensity of the light. Currently, one of the typica...
Preprint
High index dielectric nanostructure supports different types of resonant modes. However, it is very challenging to achieve high-Q factor in a single subwavelength dielectric nanoresonator due to non-hermtian property of the open system. Here, we present a universal approach of finding out a series of high-Q resonant modes in a single nonspherical d...
Article
Full-text available
Dynamical tuning of the nonlinear optical wavefront allows for a specific spectral response of predefined profiles, enabling various applications of nonlinear nanophotonics. This study experimentally demonstrates the dynamical switching of images generated by an ultrathin silicon nonlinear metasurface supporting a high‐quality leaky mode, which is...
Article
Full-text available
The presence of a substrate is one of the most important limitations of the real application of the directional conditions. These conditions allow the control of the spatial distribution of light scattering of nanoparticles. While the zero-forward condition is quite sensitive to any change of the surrounding medium, like the substrate, the zero-bac...
Article
Full-text available
Recent progress in nanoscale optical physics is associated with the development of a new branch of nanophotonics exploring strong Mie resonances in dielectric nanoparticles with high refractive index. The high-index resonant dielectric nanostructures form building blocks for novel photonic meta-devices with low losses and advanced functionalities....
Article
Full-text available
In this work, a single gallium nitride (GaN) nanowire has been examined by our previously reported technique parametric indirect microscopic imaging (PIMI). Mapping of the nanoscale scattering signals from GaN nanowire has been achieved with PIMI system. A comparison with classical far field microscopy and FDTD simulations is included to show the r...
Preprint
The presence of a substrate is one of the most important limitations of the real 14 application of the directional conditions. These conditions allow control of the spatial distribution 15 of light scattering of nanoparticles. While the zero-forward condition is quite sensitive to any change 16 of the surrounding medium, like the substrate, the zer...
Article
Full-text available
We report that the refractive index of transition metal dichacolgenide (TMDC) monolayers, such as MoS2, WS2, and WSe2, can be substantially tuned by > 60% in the imaginary part and > 20% in the real part around exciton resonances using CMOS-compatible electrical gating. This giant tunablility is rooted in the dominance of excitonic effects in the r...
Article
Transition metal dichalcogenide (TMDC) monolayers present a remarkable multifunctional material with potential to enable the development of a wide range of novel devices. However, the functionalities observed often fall short of the expectation, which hinders the device development. Here we demonstrate that the optical, catalytic, and thermal funct...
Article
We present a combined theoretical and experimental effort to enable strong light absorption (>70%) in atomically thin MoS2 films (≤ 4 layers) for either narrowband incidence with arbitrarily pre-specified wavelengths or broadband incidence like solar radiation. This is achieved by integrating the films with resonant photonic structures that are det...
Article
Full-text available
We present an approach of deterministic phase engineering that can enable the rational design of optical Fano resonances with arbitrarily pre-specified lineshapes. Unlike all the approaches previously used to design optical Fano resonances, which fall short of designing the resonances with arbitrary lineshapes because of the lack of information for...
Article
Full-text available
Semiconductor heterostructures provide a powerful platform to engineer the dynamics of excitons for fundamental and applied interests. However, the functionality of conventional semiconductor heterostructures is often limited by inefficient charge transfer across interfaces due to the interfacial imperfection caused by lattice mismatch. Here we dem...
Article
The microwave-induced dc response has been investigated in an in-plane magnetized permalloy strip. The spin wave resonances (SWRs) are observed. The SWR signals get anomalously suppressed when the direction of the specimen or the amplitude of the microwave frequencies is changed. Such suppression occurs at frequencies of less than 11 GHz, while the...
Article
Enabling perfect light absorption in ultrathin materials promises the development of exotic photonic devices. Here we demonstrate new strategies that can provide capabilities to rationally design ultrathin (thickness < {\lambda}/10~{\lambda}/5) semiconductor perfect absorbers for arbitrary wavelengths, including those at which the intrinsic absorpt...
Article
Full-text available
Semiconductor heterostructures provide a powerful platform for the engineering of excitons. Here we report the excitonic properties of two-dimensional (2D) heterostructures that consist of monolayer MoS2 and WS2 stacked epitaxially or non-epitaxially in the vertical direction. We find similarly efficient interlayer relaxation and transition of exci...
Article
Based on transformation optics (TO), we present and experimentally realize a new thermal carpet cloak. The device, which we call a "thermal carpet", provides a considerable cloaking effect. The device is designed, fabricated and measured to verify the thermal cloaking performance. In comparison with previous experimental work, the advantage of this...
Article
Full-text available
Understanding the maximal enhancement of solar absorption in semiconductor materials by light trapping promises the development of affordable solar cells. However, the conventional Lambertian limit is only valid for idealized material systems with weak absorption, and cannot hold for the typical semiconductor materials used in solar cells due to th...
Conference Paper
We propose a novel infrared nanofilter of localized enhanced field with multiband resonant frequencies. Compared to the resonant wavelength, the structure size is very subwavelength. We establish the effective medium theory to illustrate the light field distribution of the fractals. The loss factor is used to retrieve relative permittivity which is...

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