Effective Dielectric Constants of Photonic Crystal of Aligned Anisotropic Cylinders: Application to the Optical Response of Periodic Array of Carbon Nanotubes
We calculate the static dielectric tensor of a periodic system of aligned anisotropic dielectric cylinders. Exact analytical formulas for the effective dielectric constants for the E- and H- eigenmodes are obtained for arbitrary 2D Bravais lattice and arbitrary cross-section of anisotropic cylinders. It is shown that depending on the symmetry of the unit cell photonic crystal of anisotropic cylinders behaves in the low-frequency limit like uniaxial or biaxial natural crystal. The developed theory of homogenization of anisotropic cylinders is applied for calculations of the dielectric properties of photonic crystals of carbon nanotubes.
We theoretically study the role of nonlinear surface plasmoms on the optical bistability of graphene-wrapped dielectric cylinders, within the framework of both full-wave scattering theory and the quasistatic limit. Typical hysteresis curves are observed in both near-field and far-field spectra. Moreover, we demonstrate that introducing the full wave theory results in another bistable behavior with a high applied electromagnetic field, suggesting a more explicit way in analyzing the unstable behavior of the graphene-wrapped dielectric cylinder. Furthermore, optical stable region and the switchi…
We study behavior of resonant modes under change of the distance between two parallel dielectric cylinders. The processes of mutual scattering of Mie resonant modes by cylinders result in an interaction between the cylinders which lifts a degeneracy of resonances of the isolated cylinders. There are two basic scenarios of evolution of resonances with the distance. For strong interaction of cylinders resonances are unbound with avoided crossings from the of the Mie resonances with increasing of the distance. That scenario is typical for low exciting resonances (monopole and dipole). For weak in…
A rigorous analytical approach is applied to solve the eigenvalue problem for a pair of circular dielectric cylinders with complex permittivity. This approach relies on field expansion in terms of two sets of orthogonal azimuthal modes, which are coupled due to finite distance between the cylinders. We investigate the ability of a gain-dielectric cylinder operated in the fundamental TM mode to compensate material losses of a larger cylinder operated in the higher-order radial TM mode. To achieve such a loss compensation phenomenon, a simple design strategy is developed. It is shown that this p…
Wood's anomalies and excitation of cyclic Sommerfeld resonances under plane wave scattering from a single dielectric cylinder at oblique incidence of light
Exceptional points (EPs) are special parameter values of a non-Hermitian eigenvalue problem where eigenfunctions corresponding to a multiple eigenvalue coalesce. In optics, EPs are associated with a number of counter-intuitive wave phenomena, and have potential applications in lasing, sensing, mode conversion and spontaneous emission processes. For open photonic structures, resonant states are complex-frequency solutions of the Maxwell's equations with outgoing radiation conditions. For open dielectric structures without material gain or loss, the eigenvalue problem for resonant states can hav…
We investigate numerically Fano resonances excited in periodic arrays of dielectric, metallic and left-handed cylinders. Of particular interest are Fano resonances excited in the linear array of cylin- ders. We analyze spatial distribution and symmetry of electromagnetic field and discuss the relation between observed Fano resonances and frequency spectra of two-dimensional arrays of cylinders.
Highly-anisotropic plasmonic nanotubes exhibit a dramatic drop of the scattering cross section in the transition regime from hyperbolic to elliptic dispersion. The characterization of a realistic multilayered metamaterial is typically carried out by means of an effective medium approach providing average components of the permittivity tensor and wave fields. Here, the edge effects of the metal-dielectric stratified nanotube for different combinations were thoroughly analyzed. We show how the boundary layers, which in principle remain fully irrelevant in the estimation of the effective permitti…
Light confinement induced by resonant states in aperiodic photonic structures are interesting for many applications. A particular case of these resonances can be found in 2D quasi-crystalline arrangements of dielectric cylinders. These systems present a rather isotropic band gap as well as isolated in-gap photonic states (as a result of spatially localized resonances). These states are built by high symmetry polygonal clusters that can be regarded as photonic molecules. In this paper we study the transmission properties of a slab of glass cylinders arranged in approximants of decagonal quasi-c…
Eigenvalue problems for electromagnetic resonant states on open dielectric structures are non-Hermitian and may have exceptional points (EPs) at which two or more eigenfrequencies and the corresponding eigenfunctions coalesce. EPs of resonant states for photonic structures give rise to a number of unusual wave phenomena and have potentially important applications. It is relatively easy to find a few EPs for a structure with parameters, but isolated EPs provide no information about their formation and variation in parameter space, and it is always difficult to ensure that all EPs in a domain of…
Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with step boundaries. The Green function for a 2-dimensional homogeneous dielectric cylinder is obtained. As an example, the formulas are derived for scattered field of two parallel cylinders. The polar diagram is shown to agree with numerical calculation by the known methods of discrete dipoles and boundary elements.
In this paper we explored the scattering behavior of thin cylinders made of LHM and coated by a monoatomic graphene layer. A spectral tunability of the resonance peaks is evidenced by altering the chemical potential of the graphene coating, a fact that occurs at any state of polarization of the incident plane wave in opposition to the case of scatterers of dielectric core. On the contrary, no invisibility condition can be satisfied for dielectric environments. A singular performance is also found for cylinders with permittivity and permeability near zero. Practical implementations of our resul…
Electromagnetic wave extinction by the very long but finite dielectric needle is compared with that by the infinite dielectric cylinder for an oblique incidence of the electromagnetic wave. It is shown that the renormalized Hankel functions without the logarithmic terms should be used for the calculation of the extinction per unit length of the infinite dielectric cylinder to apply it for extinction calculations by the finite dielectric cylinder.
2D dielectric photonic quasicrystals can be designed to show isotropic band gaps. The system here studied is a quasiperiodic lattice made of silicon dielectric cylinders arranged as periodic unit cell based on a decagonal approximant of a quasiperiodic Penrose lattice. We analyze the bulk properties of the resulting lattice as well as the bright states excited in the gap which correspond to localized resonances of the electromagnetic field in specific cylinder clusters of the lattice. Then we introduce a controlled shear deformation which breaks the decagonal symmetry and evaluate the width re…
Radiation processes in dielectric cylindrical waveguides
Yerevan State University（耶烈万国立大学）；Institute of Physics, Yerevan State University（耶烈万国立大学物理研究所）；Institute of Applied Problems of Physics NAS RA（亚美尼亚国家科学院应用物理问题研究所）
We investigate the radiation from a charged particle rotating around a dielectric cylinder with a negative real part of dielectric permittivity. For the general case of frequency dispersion in dielectric permittivity, expressions are derived for the electric and magnetic fields and for the angular density of the radiation intensity on a given harmonic. Compared with the case of a cylinder with positive real part of the permittivity, new interesting features arise in the nonrelativistic limit and for the radiation at small angles with respect to the cylinder axis. Another feature is the appeara…
We present a novel differential refractive index sensor based on arrays of photonic molecules (PM) of dielectric cylinders and two structural defect cavities. The transmission spectrum of the photonic proposed structure as sensor shows a wide photonic stop band with two localized states. One of them, the reference state, is bound to a decagonal ring of cylinders and the other, the sensing state, to the defect cavities of the lattice. It is shown that defect mode is very sensitive to the presence of materials with dielectric permittivity different from that of the surrounding cylinders while th…
Insights into the need for ab-initio calculations to accurately predict the optical properties of metallic carbon nanotubes based on experimental confrontation
Wave scattering from a cylinder with a tensor impedance surface is investigated based on the Lorentz-Mie theory. A practical example of such a cylinder is a subwavelength metallic rod with helical dielectric-filled corrugations. The investigation is performed with the aim to maximize scattering cross-section by tailoring the surface impedance of cylindrical scatterers. For the normally incident TEz and TMz waves the required surface impedance of a subwavelength cylinder can be produced by longitudinal (axial) and transverse (circumferential) corrugations, respectively. It is shown that such co…
Electromagnetic cloaking of cylindrical objects by multilayer or uniform dielectric claddings
我们表明，介电，甚至完全导电的圆柱体可以通过均匀或分层的电介质包覆，而不需要任何外来的或磁性材料的参数。特别是，我们首先提出了一个简单的分析概念，可以准确地描述在可见光谱中的锥形银盘获得的隐身效果。模型结构最初在[S. A. Tretyakov，P. Alitalo，O.卢科宁角R. Simovski，Phys. Rev. Lett. Vol.103，p.103905，2009]，其中仅数值地研究了其在光学频率中作为斗篷的操作。我们严格地模拟这种配置作为一个多层介质覆盖周围的隐形物体，与实际设备的模拟结果非常吻合。使用均匀或多层介质覆盖的概念，相对介电常数大于1，然后成功地扩展到不可穿透的对象，如导电圆柱体的隐身。
With the rise of artificial magnetism and metamaterials, the toroidal family recently attracts more attention for its unique properties. Here we propose an all-dielectric pentamer metamolecule consisting of nano-cylinders with two toroidal dipolar resonances, whose frequencies, EM distributions and Q factor can be efficiently tuned due to the additional electric dipole mode offered by a central cylinder. To further reveal the underlying coupling effects and formation mechanism of toroidal responses, the multiple scattering theory is adopted. It is found that the first toroidal dipole mode, whi…
