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 interaction of cylinders the resonances are bound around highly excited Mie resonances. Both scenarios demonstrate a significant enhancement of the $Q$ factor compared to the case of isolated cylinder.
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 propertie…
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…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible overlapping. The results are compared with that for the case when a regularity at the cylinder placement exists.
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…
In this paper we consider a process of plane wave scattering from a single dielectric cylinder at oblique incidence under which it is possible to excite long range cyclic Sommerfeld waves (CSWs) and consequently cyclic Sommerfeld resonances (CSRs) of different orders. It is shown that the CSRs are analogous to Wood's anomalies occurred under plane wave scattering from one dimensional (1D) metallic diffraction gratings. The conditions which are necessary for an effective excitation of CSWs and CSRs with high quality factors are analyzed.
We investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The frequency band structure is computed using the standard plane-wave expansion method, while the propagation and scattering of the electromagnetic waves are calculated by the multiple scattering theory. It is shown that within partial bandgaps, the waves tend to bend away from the forbidden directions. Such a property may render novel applications in manipulating optical flows. In addition, the relevance with the imaging by flat photonic crys…
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.
In this paper, we establish the full-wave electromagnetic scattering theory to study the electromagnetic scattering from infinitely long cylinders with radially anisotropic coatings. We show that the total effective scattering width can be dramatically reduced by the suitable adjustment of the dielectric anisotropy of the shell, while it is not the case for tuning the dielectric anisotropy of the core. Furthermore, we could make the cylindrical objects invisible when both dielectric and magnetic anisotropies are adjusted. In the long wavelength limit, we develop effective medium theory to deri…
We present and analyze a dielectric cluster based on subwavelength LiTaO3 polaritonic cylinders for demonstrating toroidal response in THz regime due to mutual coupling of Mie- resonance modes of the cylinders. Based on this cluster, we demonstrate a low-loss metamaterial with the dominant toroidal response, which plays a key role in achieving resonant total transmission.
Two-dimensional problem of evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved numerically by boundary integral equations method. A special Green function was proposed to avoid the infinite integration. A pattern with a circular and a prolate elliptic cylinders, respectively, is suggested to simulate the sample and the probe in near-field optical microscopy. The energy flux in the midplane of the probe-cylinder is calculated as a function of its position.
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…
We consider boundary integral equations (BIEs) met in the scattering by dielectric cylinders and compare numerical algorithms based on elementary and Muller's BIEs near the "numerical resonances". A procedure of partial removal of well-known defect of elementary BIEs related to the loss of their unique solvability is discussed.
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.
The whispering-gallery mode (WGM) excitation and Luneburg lens (LL) effect are studied for a lossy circularly-layered dielectric cylinder illuminated by a beam field. The latter is simulated by the Complex Source-Point (CSP) beam. Exact series solution to the wave scattering problem is used to obtain the far-field patterns and directivity. The WG mode effect is shown to undermine the LL performance. Index Terms: Layered circular dielectric cylinder, Complex source point beam, Whispering-gallery modes, Luneburg lens.
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）
The electromagnetic modes and their field distributions are evaluated for a dielectric cylindrical structure embedded in another dielectric, with a thin metallic film at the cylinder/dielectric interface. These modes provide energy relaxation channels for excited dipole emitters located inside or outside the cylinder. Significantly, we find that the emission rate is sensitive to the magnitude of the electron density of the metallic film coating. For typical parameter values, we find large enhancements of the emission rate, which can be in excess of three orders of magnitude, relative to the ca…
In the absence of external excitation, light trapped within a dielectric medium generally decays by leaking out (and also by getting absorbed within the medium). We analyze the leaky modes of a parallel-plate slab, a solid glass sphere, and a solid glass cylinder, by examining those solutions of Maxwell's equations (for dispersive as well as non-dispersive media) which admit of a complex-valued oscillation frequency. Under certain circumstances, these leaky modes constitute a complete set into which an arbitrary distribution of the electromagnetic field residing inside a dielectric body can be…
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…
Recently, it was shown that an infinite perfectly conducting (PEC) cylinder can be nearly perfectly cloaked from normally incident electromagnetic waves using a single-layer homogeneous dielectric cladding. Here we study the electromagnetic response of such structures with the goal to understand the main mechanisms underpinning this cloaking phenomenon. We introduce a simple model of the cloaked PEC cylinder, replacing it by an omnidirectional electric-line scatterer and a bipolar magnetic one; accordingly, the far field is determined in a compact closed form. The analysis of the results shows…
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…
The hybrid plasmonic waveguide consists of a high-permittivity dielectric nanofiber embedded in a low-permittivity dielectric near a metal surface. This architecture is considered as one of the most perspective candidates for long-range subwavelength guiding. We present qualitative analysis and numerical results which reveal advantages of the special waveguide design when dielectric constant of the cylinder is greater than the absolute value of the dielectric constant of the metal. In this case the arbitrary subwavelength mode size can be achieved by controlling the gap width. Our qualitative …
We investigate the behaviour of a three-phase composite, structured as a hexagonal array of coated cylinders, when the sum of the dielectric constants of the core and shell equals zero. In such cases, the absorption of the composite is the same as the absorption of a periodic array of solid cylinders of core material and radius equal to the outer radius of the original coated cylinder. When the sum of the dielectric constants of the shell and matrix equals zero, the composite has the same absorption as a periodic array of solid cylinders of core material, and radius exceeding the shell radius.
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…
We show that dielectric or even perfectly conducting cylinders can be cloaked by a uniform or a layered dielectric cladding, without the need of any exotic or magnetic material parameters. In particular, we start by presenting a simple analytical concept that can accurately describe the cloaking effect obtained with conical silver plates in the visible spectrum. The modeled structure has been originally presented in [S. A. Tretyakov, P. Alitalo, O. Luukkonen, C. R. Simovski, Phys. Rev. Lett., vol. 103, p. 103905, 2009], where its operation as a cloak in the optical frequencies was studied only…
In this study, we used parallel plane mirror resonator analogy to design all-dielectric optical resonator that is performed with the objective-first inverse design algorithm. Confinement of the light is succeeded via predefined objective function to create symmetric mirror regions for the fundamental transverse-electric polarization mode. The algorithm creates bandgap in random structure to obtain resonance peak at the desired wavelength without any intuitive scanning of the parameter space. The first order mode is confined on the cavity region at pre-defined wavelength. The obtained structure…
When an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Haenchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted…
We consider cloaking by a coated cylindrical system using plasmonic resonance, and extend previous quasistatic treatments to include the effect of finite wavelength. We show that a probe cylinder can still be cloaked at finite wavelengths, but the cloaking cylinder develops a non-zero scattering cross-section. We show that this latter effect is dominated by a monopole term in the case of an ideal (lossless) cloaking material, and by a dipole term in the case of a realistic (lossy) material. It can be reduced but not eliminated by variations of geometric or dielectric parameters of the cloaking…
Nonreciprocal optical devices have broad applications in light manipulations for communications and sensing. Non-magnetic mechanisms of optical nonreciprocity are highly desired for high-frequency on-chip applications. Here, we investigate the nonreciprocal properties of light propagation in a dielectric waveguide induced by a subwavelength spinning cylinder. We find that the chiral modes of the cylinder can give rise to unidirectional coupling with the waveguide via the transverse spin-orbit interaction, leading to different transmissions for guided wave propagating in opposite directions and…
The plasmon resonance has found important application in various systems, e.g., nanoantennas, solar panels, refractive index sensors. Unfortunately, a few analytical solutions for such systems are known. The work aims to find a solution for scattering by a plane electromagnetic wave on two parallel cylinders. When their diameters and the gap between them are less than the radiation wavelength, the quasistatic approximation is valid. We build up a conformal transformation that maps Cartesian into bipolar orthogonal coordinates and represent the scattered field as a decomposition by eigenfunctio…
Exceptional points (EPs), i.e., non-Hermitian degeneracies at which eigenvalues and eigenvectors coalesce, can be realized by tuning the gain/loss contrast of different modes in non-Hermitian systems or by engineering the asymmetric coupling of modes. Here we demonstrate a mechanism that can achieve EPs of arbitrary order by employing the non-reciprocal coupling of spinning cylinders sitting on a dielectric waveguide. The spinning motion breaks the time-reversal symmetry and removes the degeneracy of opposite chiral modes of the cylinders. Under the excitation of a linearly polarized plane wav…
Dielectric microcavities based on cylindrical and deformed cylindrical shapes have been employed as resonators for microlasers. Such systems support spiral resonances with finite momentum along the cylinder axis. For such modes the boundary conditions do not separate and simple TM and TE polarization states do not exist. We formulate a theory for the dispersion relations and polarization properties of such resonances for an infinite dielectric rod of arbitrary cross-section and then solve for these quantities for the case of a circular cross-section (cylinder). Useful analytic formulas are obt…
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…
We show that the frequency spectrum of two dimensional photonic crystals is strongly influenced by Fano resonances which can be excited already in the linear array of dielectric cylinders. To support this claim, we calculate the transmission of electromagnetic wave through linear array of dielectric cylinders and show that frequencies of observed Fano resonances coincides with position of narrow frequency bands found in the spectra of corresponding two-dimensional photonic crystals. Split of frequency band or overlap of two bands, observed in the band structure of photonic structures are also …
The spectrum of guided modes of linear chain of dielectric and left-handed cylinders is analyzed. The structure of eigenfrequences is much more richer if cylinders are made from the left-handed material with both permittivity and permeability negative. he number of guided modes is much larger, and their interaction with incident electromagnetic wave is much stronger. For some value of the wave vector, no guided modes were found. We discuss how these specific properties of guided modes correspond to folded bands, observed recently in photonic structureswith left-handed components.
Polaritonic materials, owing to a strong phonon-polariton resonance in the THz and far-infrared parts of the electromagnetic spectrum, offer both high-index dielectric and metallic response in this regime. This complex response makes them suitable candidates for the design of metamaterial-related phenomena and applications. Here we show that one type of polaritonic-material-based structures that are particularly suitable for the achievement of a wide range of metamaterial properties are systems of polaritonic rods. To study the interplay between the material and the structural resonances in su…
We discuss optical forces exerted on particles, either dielectric or metallic, near a subwavelength slit illuminated by a photonic nanojet. We compare those cases in which the Mie resonances are or are not excited. The configurations on study are 2D, hence those particles are infinite cylinders and, in order to obtain extraordinary transmission, the illuminating beam is p-polarized. We show the different effects of these particle resonances on the optical forces: while whispering gallery modes under those illumination conditions weaken the force strength, this latter is enhanced by localized p…
Controlling the near field optical binding force can be a key factor for particle clustering, aggregation and localized surface plasmon sensors. So far there is no generic way to reverse the near field optical binding force for plasmonic or dielectric nano-dimers of distinct shapes (cube, cylinder, ring, sphere). In this article, for both plasmonic and dielectric objects, we have demonstrated a general way to control the reversal of near field binding force for different shaped dimer sets. The force reversal is achieved by simple breaking of symmetry, considering the nano particles are half or…
We present all-dielectric polaritonic metasurfaces consisting of properly sculptured cylinders to sustain the dynamic anapole, i.e. a non-radiating alternating current distribution. One way for the anapole to emerge, is by combining modes based on the first and the fourth Mie resonance of a cylinder made of high permittivity LiTaO$_3$ for operation in the low THz. The circular cross-section of each cylinder varies periodically along its length in a binary way, from small to large, while its overall circular symmetry has to be broken in order to remove parasitic magnetic modes. Small cross-sect…
Subwavelength structures demonstrate many unusual optical properties which can be employed for engineering functional metadevices, as well as scattering of light and invisibility cloaking. Here we demonstrate that the suppression of light scattering for any direction of observation can be achieved for an uniform dielectric object with high refractive index, in a sharp contrast to the cloaking with multilayered plasmonic structures suggested previously. Our finding is based on the novel physics of cascades of Fano resonances observed in the Mie scattering from a homogeneous dielectric rod. We o…
We study an optical response of a system of two parallel close metallic cylinders having nanoscale dimensions. Surface plasmon excitation in the gap between the cylinders are specifically analyzed. In particular, resonance frequencies and field enhancement were investigated as functions of geometrical characteristics of the system and Ohmic losses in the metal. The results of numerical simulations were systematically compared with the analytical theory, obtained in the quasi-static limit. The analytical method was generalized in order to take into account the retardation effects. We also prese…
We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, and whose dielectric properties are complex-valued. Efficient formulas are provided to determine the effective complex permittivity tensor which are in excellent agreement with numerical calculations. We also show that in contrast to the real-valued case, the real and imaginary parts of the effective complex-valued tensor can exhibit non-monotonic behavior as functions of volume fraction of cylinders, and can b…
In this article, we examine plasmon induced transparency (PIT) effect in a parallel plate waveguide (PPWG) comprising of two similar pyramidal shaped grooves. One of the grooves is filled with air, while the other is filled with a dielectric material whose refractive index can be varied. The resonant frequencies corresponding to the air and dielectric grooves in the proposed configuration results in the transparency window which can be modulated with the refractive index of the dielectric material. The approach provides flexibility to actively control transparency effect in a waveguide configu…
The propagation of electromagnetic waves trapped within dielectric and magnetic layers is considered. The description within the three-dimensional theory is compared with the simplified analysis in two dimensions. Two distinct media configurations with different topology are dealt with: a plane slab and a hollow cylinder. Choosing the appropriate values for the geometrical parameters (layer thickness, radius of the cylinder) and for the electromagnetic properties of the media one can trap exactly one mode corresponding to that obtained within the two-dimensional electromagnetism. However, the …
Open subwavelength cylindrical resonators of finite height are widely used in various photonics applications. Circular cylindrical resonators are particularly important in nanophotonics, since they are relatively easy to fabricate and can be designed to exhibit different resonance effects. In this paper, an efficient and robust numerical method is developed for computing resonant modes of circular cylinders which may have a few layers and may be embedded in a layered background. The resonant modes are complex-frequency outgoing solutions of the Maxwell's equations with no sources or incident w…
The objective of the paper is the assessment of the accuracy of a conventional FDTD code in the computation of the near and far-field scattering characteristics of a circular dielectric cylinder. We excite the cylinder with an electric or magnetic line current and demonstrate the failure of the two-dimensional FDTD algorithm to characterize accurately the emission rate and the field patterns near high-Q whispering-gallery-mode resonances. This is proven by comparison with the exact series solutions. The computational errors in the emission rate are then studied at the resonances still detectab…
We describe an event-based approach to simulate the propagation of an electromagnetic plane wave through dielectric media. The basic building block is a deterministic learning machine that is able to simulate a plane interface. We show that a network of two of such machines can simulate the propagation of light through a plane parallel plate. With properly chosen parameters this setup can be used as a beam splitter. The modularity of the simulation method is illustrated by constructing a Mach-Zehnder interferometer from plane parallel plates, the whole system reproducing the results of wave th…
