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 reduction of the gap together with the evolution of the resonances, for all shear values compatible with physical constraints (cylinder collision). The gap is reduced up to a 18.5 % while different states change their frequency in different ways. Realistic analysis about the actual transmission of the electromagnetic radiation, often missing in the literature, have been performed for a finite slice of the proposed quasicrystals structure. Two calculation procedures based on MIT Photonic Bands (MPB) and Finite Integration Technique (FIT) are used for the bulk and the finite structures finding an extremely good agreement among them.
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…
All-dielectric photonic quasicrystals may act as zero-refractive-index homogeneous materials despite their lack of translational symmetry and periodicity, stretching wavelengths to infinity and offering applications in light wavefront sculpting and optical cloaking.
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…
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…
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.
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.
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 present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12-fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency regions. However, contrary to the original interpretation, such focusing effects turn out to be critically associated to local symmetry points in the PQC slab, and strongly dependent on its thickness a…
One of the most intriguing problems of light transport in solids is the localization that has been observed in various disordered photonic structures1-11. The light localization in defect-free icosahedral quasicrystals has recently been predicted theoretically without experimental verification10. Here we report on the fabrication of submicron-size dielectric icosahedral quasicrystals and demonstrate the results of detailed studies of the photonic properties of these structures. Here, we present the first direct experimental observation of intrinsic light localization in defect-free quasicrysta…
Topological physics in photonic systems have attracted great attentions in recent years. In this work, we theoretically study the one and two dimensional photonic quasicrystal resonator lattices characterized by the first and second Chern number, which show exotic boundary states within the photonic energy band gap. In particular, the second Chern number protected edge states has opened up new possibilities for realizing topological physics of dimensions higher than three in photonic systems, which is highly sought for. Such photonic systems can be easily experimentally realized in regular pho…
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.
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.
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 report on the formation and development of the photonic band gap in two-dimensional 8-, 10- and 12-fold symmetry quasicrystalline lattices of low index contrast. Finite size structures made of dielectric cylindrical rods were studied and measured in the microwave region, and their properties compared with a conventional hexagonal crystal. Band gap characteristics were investigated by changing the direction of propagation of the incident beam inside the crystal. Various angles of incidence from 0 \degree to 30\degree were used in order to investigate the isotropic nature of the band gap. The…
In this paper, we study the radiation from embedded sources in two-dimensional finite-size "photonic-quasicrystal" (PQC) slabs made of dielectric rods arranged according to a 12-fold symmetric aperiodic tiling. The results from our investigation, based on rigorous full-wave simulations, show the possibility of achieving broadside radiation at multiple frequencies, with high-directivity (e.g., 15 dB) and low-sidelobes (e.g., -12 dB). We also show that leaky waves are supported by a PQC slab, and that the beamwidth is directly proportional to the leaky-wave attenuation constant, which provides a…
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.
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…
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…
Nanostructured magneto-optical materials sustaining optical resonances open very efficient way for light control via magnetic field, which is of prime importance for telecommunication and sensing applications. However, usually their response is narrowband due to its resonance character. Here we demonstrate and investigate a novel type of the magnetoplasmonic structure, the magnetoplasmonic quasicrystal, which demonstrates unique magneto-optical response. It consists of the magnetic dielectric film covered by a thin gold layer perforated by slits forming a Fibonacci-like binary sequence. The tr…
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…
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…
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.
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…
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…
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 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…
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…
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…
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 …
We report the first experimental demonstration of a TE-polarization photonic band gap (PBG) in a 2D isotropic hyperuniform disordered solid (HUDS) made of dielectric media with a index contrast of 1.6:1, very low for PBG formation. The solid is composed of a connected network of dielectric walls enclosing air-filled cells. Direct comparison with photonic crystals and quasicrystals permitted us to investigate band-gap properties as a function of increasing rotational isotropy. We present results from numerical simulations proving that the PBG observed experimentally for HUDS at low index contra…
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…
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.
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…
Photonic Molecules made of dielectric cylinders assembled as two-dimensional octagons and decagons have been studied. These structures exhibit resonance states that change their intensity depending on the incident radiation angle. While most part of spectra present small or even null variation, one of the resonances in both structures presents a high-sensibility to the incidence angle. This strong variation is well described in terms of the electric field intensity distribution of this resonant state, which is composed of maxima with alternate polarities inside each cylinder. Experimental meas…
The possibility of overcoming the critical condition for localized photonic nanojet upon plane optical wave diffraction at mesoscale dielectric particle, which is commonly known as "the refractive index contrast is less than two", was recently reported in our works. To this end, the novel geometrical scheme of photonic nanojet generation in "reflection mode" was proposed based on a super-contrast microparticle (n~2) placed near a flat mirror. In this paper, through the numerical FDTD calculations of optical near-field structure of 2D and 3D dielectric microparticles (cylinder, sphere) we exten…
Novel hollow-core THz waveguides featuring hyperuniform disordered reflectors are proposed, fabricated, and characterized. The reflector comprise aperiodically positioned dielectric cylinders connected with dielectric bridges. The proposed waveguides are fabricated using a 3D stereolithography printer. Optical properties of the fabricated waveguide are investigated numerically using finite element method, as well as experimentally using THz-TDS spectroscopy. The results confirm that proposed waveguides exhibit sizable photonic band gaps (20%) even when relatively low refractive index contrast …
We derive in the present work topological photonic states purely based on silicon, a conventional dielectric material, by deforming a honeycomb lattice of silicon cylinders into a triangular lattice of cylinder hexagons. The photonic topology is associated with a pseudo time reversal (TR) symmetry constituted by the TR symmetry respected in general by the Maxwell equations and the $C_6$ crystal symmetry upon design, which renders the Kramers doubling in the present photonic system with the role of pseudo spin played by the circular polarization of magnetic field in the transverse magnetic mode…
We experimentally verified the phenomena of photonic jets generated by plane-electromagnetic-wave-illuminated dielectric micro-cylinders with diameter comparable to the corresponding wavelength at microwave frequencies. Using a home-made 2D spatial field mapping system, we carried out a point-by-point measurement of both phase and intensity of spatial electric field distribution inside and around scattering cylinders, providing a clear complete electromagnetic field picture for these phenomena. Correspondingly, the theoretically predicted super-enhancement of the backscattering induced by smal…
We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving the eigenvalue problem with a non-Hermitian operator. The analogy with $\cal{PT}$-symmetric Hamiltonians reveals that the operator corresponds to the momentum as a physical quantity and the singularities at the band edges are related to the branch points and responses for the features on the band edges. The method is realized using plane wave expansion techniq…
