We have investigated bound modes in finite linear chains of dielectric particles of various lengths, interparticle spacing and particle materials. Through a unique application of the multisphere Mie scattering formalism, we have developed numerical methods to calculate eigen-optical modes for various arrays of particles. These numerical methods involve the use of the multisphere scattering formalism as the entries in NxN matrices where N represents the number of particles in the chain. Eigenmodes of these matrices correspond to the eigen-optical modes of interest. We identified the eigenmodes with the highest quality factor by the application of a modified version of the Newton-Raphson algorithm. We found that convergence is strong using this algorithm for linear chains of up to several hundreds of particles. By comparing the dipolar approach with the more complex approach which utilizes a combination of both dipolar and quadrupolar approaches, we demonstrated that the dipolar approach has an accuracy of approximately 99%. We found that the quality factor Q of the mode increases with the cubed value of the number of particles in chain in agreement with the previously developed theory, the effects of disordering of particle sizes and inter-particle distances will be discussed.
Nonmagnetic and spherically symmetric dielectric material media are investigated in their generality as analogue models, in the domains of geometrical optics, for a few relevant static and spherically symmetric solutions of gravitation, including black holes and wormholes. Typic and desirable gravitational features are systematically linked to the nonlinear properties of the phenomenological dielectric permittivity of the medium. From this, the limitations of such analogies are explored in terms of their corresponding geometric flexibility, dielectric configurations and causal structure.
Two point charges are placed in a spherical dielectric core-shell embedded in a dielectric environment, one of the charges being located in the core and the other in the shell. The core, shell, and environment are characterized by different dielectric constants. Analytical solutions for the electrostatic energy of the system and the polarization charge density at the core-shell and shell-environment interfaces are obtained by a classical approach.
Effective Dielectric Constants of Photonic Crystal of Aligned Anisotropic Cylinders: Application to the Optical Response of Periodic Array of Carbon Nanotubes
Small form-factor, narrowband, and highly directive antennas are of critical importance in a variety of applications spanning wireless communications, remote sensing, Raman spectroscopy, and single photon emission enhancement. Surprisingly, we show that the classical directivity limit can be appreciably surpassed for electrically small multilayer spherical antennas excited by a point electric dipole even if limiting ourselves to purely dielectric materials. Experimentally feasible designs of superdirective antennas are established by using a stochastic optimization algorithm combined with a ri…
We consider E polarized bound states in the radiation continuum (BICs) in circular periodical arrays of $N$ infinitely long dielectric rods. We find that each true BIC which occurs in an infinite linear array has its counterpart in the circular array as a near-BIC with extremely large quality factor. We argue analytically as well as numerically that the quality factor of the symmetry protected near-BICs diverges as $e^{λN}$ where $λ$ is a material parameter dependent on the radius and the refraction index of the rods. By tuning of the radius of rods we also find numerically non-symmetry protec…
The optical anapole resonances in nanostructures display strong field confinement and substantially suppressed scattering. In this study using three-dimensional finite-difference time-domain simulations, it is shown that high refractive index dielectric nanohole array metasurfaces having different profiles of the holes can possess the anapole state. The multipole decomposition including the dipole electric toroidal moment for the lattice elements of the arrays is provided. The anapole state in the lattice elements is illustrated by time-averaged distributions of the energy. As a result, high-i…
Dielectric spheres of various sizes may sustain electromagnetic whispering-gallery modes resonating at optical frequencies with very narrow linewidths. Arbitrary small deviations from the spherical shape typically shift and broaden such resonances. Our goal is to determine these shifted and broadened resonances. A boundary-condition perturbation theory for the acoustic vibrations of nearly circular membranes was developed by Rayleigh more than a century ago. We extend this theory to describe the electromagnetic excitations of nearly spherical dielectric cavities. This approach permits us to av…
We designed and simulated freestanding dielectric optical metasurfaces based on arrays of etched nanoholes in a silicon membrane. We showed $2π$ phase control and high forward transmission at mid-infrared wavelengths by tuning the dimensions of the holes. We also identified the mechanisms responsible for high forward scattering efficiency and showed that these conditions are connected with the well-known Kerker conditions already proposed for isolated scatterers. A beam deflector was designed and optimized through sequential particle swarm and gradient descent optimization to maximize transmis…
Plasmonic structures interacting with light provide electromagnetic resonances which result in a high degree of local field confinement enabling the enhancement of light-matter interaction. Plasmonic structures typically consist of metals which, however, suffer from very high ohmic losses and heating. High-index dielectrics, on the other hand, can serve as an alternative material due to their low-dissipative nature and strong scattering abilities. We study the optical properties of a system composed of all-dielectric nanoparticle arrays covered with a film of organic dye molecules (IR-792), an…
The strong electric and magnetic resonances in dielectric subwavelength structures have enabled unique opportunities for efficient manipulation of light-matter interactions. Besides, the dramatic enhancement of nonlinear light-matter interactions near so-called bound states in the continuum (BICs) has recently attracted enormous attention due to potential advancements in all-optical and quantum computing. However, the experimental realizations and the applications of high- Q factor resonances in dielectric resonances in the visible regime have thus far been considerably limited. In this work, …
Directional lasing, with a low threshold and high quality factor, in active dielectric nanoantenna arrays is demonstrated. This is achieved through a leaky resonance excited in coupled gallium arsenide (GaAs) nanopillars. The leaky resonance is formed by partially breaking a bound state in the continuum (BIC) generated by the collective, vertical electric dipole resonances excited in the nanopillars for sub-diffractive arrays. By opening an unprotected, diffractive channel along one of the periods of the array one can control the directionality of the emitted light without sacrificing the high…
We consider optical response induced by bound states in the continuum (BICs) in arrays of dielectric spheres. By combining quasi-mode expansion technique with coupled mode theory (CMT) we put forward a theory of the optical response by high-Q resonance surrounding BICs in momentum space. The central result are analytical expressions for the CMT parameters, which can be easily calculated from the eigenfrequencies and eigenvectors of the interaction matrix of the scattering systems. The results obtained are verified in comparison against exact numerical solutions to demonstrate that the CMT appr…
To define and characterize optical systems, obtaining information on the amplitude, phase, and polarization profile of optical beams is of utmost importance. Polarimetry using bulk optics is well established to characterize the polarization state. Recently, metasurfaces and metalenses have successfully been introduced as compact optical components. Here, we take the metasurface concept to the system level by realizing arrays of metalens 2*3 sub-arrays, allowing to determine the polarization profile of an optical beam. We use silicon-based metalenses with a numerical aperture of 0.32 and a mean…
Herein, we investigate the symmetry-protected toroidal dipole resonances and conditions of their excitation in a new type of electromagnetic metamaterials. These metamaterials are all-dielectric planar periodic arrays of dielectric disks disposed on a dielectric substrate. The elementary building blocks of the array are trimers which are distributed in hexagonal unit supercells. The highest geometrical symmetry of the unit supercell is C6v. The analysis is fulfilled by using the representation theory of groups with the application of the magnetic group theory, which is a new approach in solvin…
Photonic band structure and effective medium properties of doubly-resonant core-shell metallo-dielectric nanowire arrays: low-loss, isotropic optical negative-index behavior
The absorption to mass ratio of the infrared arrays is enhanced to approximately 1.33 to 7.33 times larger than the previously reported structures by incorporating two design characteristics: first, the coupling of evanescent fields in the air gaps around pixels to create effectively larger pixel sizes, and, second, the use of guided mode resonance (GMR) within the subwavelength metal-dielectric gratings. The bilayer Ti-Si3N4 gratings achieve broadband long-wave infrared (LWIR, 8 to 12 um) absorption by the combined effects of free carrier absorption by the thin Ti films and vibrational phonon…
Metasurfaces have attracted a great deal of attention from researchers due to their prominent optical properties. In particular, metasurfaces may consist of structures possessing optical anapole resonances with strong field confinement and substantially suppressed scattering. As a result, such nanostructures display enhanced nonlinear optical properties. In this paper by means of three-dimensional finite-difference time-domain simulations, the ability of anapole modes in high-index dielectric metasurfaces with circular nanopores is shown. In the vicinity of the anapole state, the effective opt…
We study the interplay between disorder and topology for the localized edge states of light in topological zigzag arrays of resonant dielectric nanoparticles. We characterize topological properties by the winding number that depends on both zigzag angle and spacing between nanoparticles in the array. For equal-spacing arrays, the system may have two values of the winding number $ν=0$ or $1$, and it demonstrates localization at the edges even in the presence of disorder, being consistent with experimental observations for finite-length nanodisk structures. For staggered-spacing arrays, the syst…
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…
Radiation of charged particles moving in the presence of dielectric targets is of significant interest for various applications in the accelerator and beam physics. The size of these targets is typically much larger than the wavelengths under consideration. This fact gives us an obvious small parameter of the problem and allows developing approximate methods for analysis. We develop two methods, which are called the "ray optics method" and the "aperture method". In the present paper, we apply these methods to analysis of Cherenkov radiation from a charge moving through a vacuum channel in a so…
Thermonanophotonics, i.e. the study of photothermal effects in optical nanoantennas, has recently attracted growing interest. While thermoplasmonic structures enable a broad range of applications, from imaging and optofluidics devices to medical and photochemical systems, dielectric nanoantennas open new opportunities for thermo-optical modulation and reconfigurable metasurfaces. However, computing both photo-thermal and thermo-optical effects in large arrays of nanoantennas remains a challenge. In this work, we implement a fast numerical method to compute the temperature increase of multi-dim…
We consider dielectric cavities whose radiation space is restricted by two parallel metallic planes. The TM solutions of the Maxwell equations of the system are equivalent to the solutions of periodical arrays of dielectric cavities. The system readily allows to achieve bound states in the continuum (BICs) of any type including topological BICs as dependent on position and orientation of the cavities relative to the planes. That extremely facilitates experimental studies in comparison to infinite arrays of the cavities. We show the effect of merging of topologically protected BICs that pushes …
Digital imaging has been steadily improving over the past decades and we are moving towards a wide use of multi- and hyperspectral cameras. A key component of such imaging systems are color filter arrays, which define the spectrum of light detected by each camera pixel. Hence, it is essential to develop a variable, robust and scalable way for controlling the transmission of light. Nanostructured surfaces, also known as metasurfaces, offer a promising solution as their transmission spectra can be controlled by shaping the wavelength-dependent scattering properties of their constituting elements…
The nonlinear optical properties of the high index nanoparticles are boosted at the anapole state. Researchers intensively study this phenomenon as promising for various applications. In this work, the nonlinear optical Kerr effect of disordered and square lattice metasurfaces of GaP nanodisks is investigated as a function of the disk size in the vicinity of the anapole state at the wavelength of 532 nm. When the sizes of the nanodisks are close to the anapole state, the effective second order refractive index of the metasurface increases exponentially. On approaching the anapole state, the si…
Mesa-top quantum dot single photon emitter arrays: growth, optical characteristics, and the simulated optical response of integrated dielectric nanoantenna-waveguide systems
While various nanophotonic structures applicable to relatively thin crystalline silicon-based solar cells were proposed to ensure effective light in-coupling and light trapping in the absorber, it is of great importance to evaluate their performance on the solar module level under realistic irradiation conditions. Here, we analyze the annual energy yield of relatively thin heterojunction (HJT) solar module architectures when optimized anti-reflective and light trapping titanium dioxide (TiO$_2$) nanodisk square arrays are applied on the front and rear cell interfaces. Our numerical study shows…
