The study of resonant dielectric nanostructures with a high refractive index is a new research direction in the nanoscale optics and metamaterial-inspired nanophotonics. Because of the unique optically induced electric and magnetic Mie resonances, high-index nanoscale structures are expected to complement or even replace different plasmonic components in a range of potential applications. We study a strong coupling between modes of a single subwavelength high-index dielectric resonator and analyze the mode transformation and Fano resonances when the resonator’s aspect ratio varies. We demonstrate that strong mode coupling results in resonances with high-quality factors, which are related to the physics of bound states in the continuum when the radiative losses are almost suppressed due to the Friedrich–Wintgen scenario of destructive interference. We explain the physics of these states in terms of multipole decomposition, and show that their appearance is accompanied by a drastic change in the far-field radiation pattern. We reveal a fundamental link between the formation of the high-quality resonances and peculiarities of the Fano parameter in the scattering cross-section spectra. Our theoretical findings are confirmed by microwave experiments for the scattering of high-index cylindrical resonators with a tunable aspect ratio. The proposed mechanism of the strong mode coupling in single subwavelength high-index resonators accompanied by resonances with high-quality factors helps to extend substantially functionalities of all-dielectric nanophotonics, which opens horizons for active and passive nanoscale metadevices.
Recently, a novel class of high-Q optical resonators based on all-dielectric subwavelength nanoparticles with high refractive index has been proposed [M. V. Rybin, et al, arXiv:1706.02099, 2017]. Here we study a complex spectrum of such nanoscale resonators by means of the resonant-state expansion, treating the problem as a nonHermitian eigenproblem. We show that the high-Q features can be described within the mechanism of external coupling of open channels via the continuum. For ceramic resonators with permittivity ε = 40, we demonstrate that the quality factor of a trapped mode with a low azimuthal index could reach the value Q = 104 .
We study the scattering of light from homogeneous cylindrical objects embedded in a transparent and homo- geneous surrounding medium that is know as the Mie problem. We analyze Mie scattering by expansion of the scattering amplitude in the series near resonant frequency and find that Lorenz-Mie coefficient can be de- scribed by Fano formula, while both waves are involved in interaction completely and intensity vanishes at the special point of switching to the invisible regime. We analyze Fano interference between resonant wave and background in general case and discuss scattering-cancellation condition. We study the influence of the aspect ratio on the mode structure and find that Mie modes shift to the long wave lengths when the cylinder aspect ratio r/h decreases. Experimentally measured spectra in microwave range are in agreement with the theoretical predictions.
We introduce a concept of phase transitions between photonic crystals and all-dielectric metamaterials suggesting a phase diagram that places two classes of such artificial structures on a common parameter plane.1 We consider photonic crystals and all-dielectric metamaterials composed of the similar structural elements and arranged in the similar geometry of a two-dimensional (2D) square lattice of dielectric cylinders of large dielectric permittivity. Such structures can display negative magnetic permeability in the TE-polarization due to the Mie resonance that occurs below the lowest Bragg resonance.2 We define a point of transition from photonic crystals to all-dielectric metamaterials as a point when the lowest Mie resonance splits from the lowest Bragg resonance creating the lowest photonic gap. Based on the numerical results, we construct the phase diagram photonic crystals - all- dielectric metamaterials for the 2D square lattice of circular rods for the TE polarization. We have verified our theoretical concept experimentally by engineering a “metacrystal” composed of glass tubes filled with water forming a 2D square lattice with a variable lattice constant.
We reveal new and remarkable manifestations of the Fano resonances in high-refractive-index all-dielectric photonic nanostructures. First, we revisit the conventional problem of light scattering by an infinite dielectric rod and observe the existence of cascades of Fano resonances in the optical cross-section, which we investigate both numerically and analytically. Our analytical study is based on the exact Mie solution of Maxwell’s equations for the light scattering by spatially homogeneous bodies of revolution. Next, we study the photonic bandgap structure and transmission spectra of two-dimensional square lattices of dielectric circular rods. We vary the refractive index of the rods from low to high values and observe a remarkable manifestation of a novel type of Fano resonances arising due to interplay between the resonant Mie scattering from individual rods and the Bragg scattering from the photonic lattice.
We report on the fabrication of inverted Yablonovite-like three-dimensional photonic crystals by nonlinear optical
nanolithography based on two-photon polymerization of a zirconium propoxide hybrid organic-inorganic material with
Irgacure 369 as photo-initiator. Advantage of this material is ultra-low shrinkage that guaranty high fabrication fidelity.
Images of the fabricated structure are obtained with a scanning electron microscope. The photonic crystal consists of
three sets of nearly cylindrical structural elements directed along the three lattice vectors of the fcc lattice and cross each
other at certain angles to produce inverted Yablonovite geometry. To investigate photonic properties of the inverted
Yablonovite structures, we calculate the photonic band structure for ten lowest-frequency electromagnetic modes. In
contrast to the direct Yablonovite structure that has a complete photonic band gap between the second and third bands,
we find no complete photonic band gaps in the inverted Yablonovite lattice. This situation is opposite to the case of fcc
lattice of close-packed dielectric spheres in air that has a complete photonic band gap only for the inverted geometry.
We report on experimental and theoretical investigations of light diffraction from opal films of different thickness.
A special attention was paid to the transformation of diffraction patterns upon building up the opal structure from two-dimensional
(2D) film structure towards bulk three-dimensional (3D) structure. In our setup the diffraction patterns are
displayed on a narrow cylindrical screen with a specimen fixed in its center. The diffraction patterns have been studied
visually and recorded in different scattering geometries with the films illuminated with white unpolarized light. With
increasing number of layers, certain regions of 2D diffraction patterns fade out and finally form diffraction spots
characteristic for 3D diffraction. We also found that stacking faults in bulk opals lead to formation of a 2D-like
diffraction pattern, i.e. such structure demonstrate 3D to quasi-2D transition in optical properties.
We report on an analytical study of the photonic band structure of 2D and 3D multi-component photonic crystals. It is found that both types of crystal demonstrate a quasiperiodic resonant behavior of (hkl) photonic stop-bands as a function of the reciprocal lattice vector, providing a selective ON/OFF switching of nonresonant (hkl) stop-bands. Our predictions are compared with the results of conventional numerical studies using the photonic Korringa-Kohn-Rostocker method. Experimental transmission spectra of a-SiO2 synthetic opals show the OFF-switching of the {111} stop-bands at the filler permittivity of ~1.82, the {200} bands at ~1.63, the {220} bands at ~1.93, and the {311} bands at ~1.75. The (222) photonic stop-band, which is due to the second order diffraction from the (111) planes, cannot be switched OFF in a wide range of filler permittivity values, thus indicating a resonant behavior. The experimental data demonstrate an excellent agreement with the theoretical predictions.
We suggest a new approach to the study of photonic crystals, based on direct visualisation of the photonic bandgap structure from Bragg diffraction patterns. Using high quality synthetic opals as photonic crystals, we have demonstrated how the Bragg diffraction of light can provide observation and analysis of the photonic band gap structure. We observed directly and photographed Bragg diffraction patterns as symmetrical sets of color spots on a screen, which appeared, displaced and disappeared, as the crystal was rotated relative to the incident laser beam. The diffraction patterns were observed under laser illumination with different wavelengths. The analysis of the experimental data can provide the number and orientation of the crystallographic planes responsible for the Bragg diffraction, as well as information about disorder in opal structure.
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