We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity being an arbitrary continuous function of the coordinate. We have shown that the problem of plane wave scattering by an inhomogeneous layer is reduced to a system of first order differential equations that contain the derivative of the refractive index or dielectric permittivity of the layer, which can be used, for example, when searching for an analytical solution. This method also makes it easy to obtain the distribution of the field strength within the layer. The reflection spectra and field distribution obtained using this method were compared with the analytical solution based on Mathieu functions.
We present an initial study of the angular spectrum of a bianisotropic refractive metasurface at an interface between two dielectric media. In this study, we report on the existence of three distinct angular regions: a)~a rotated transmission cone, b)~a modified total internal reflection region, and c)~a new total retro-reflection region.
Specially designed metal-dielectric composites can have a negative refractive index in the optical range. Specifically, it is shown that arrays of single and paired nanorods can provide such negative refraction. For pairs of metal rods, a negative refractive index has been observed at 1.5 micrometer. The inverted structure of paired voids in metal films may also exhibit a negative refractive index. A similar effect can be accomplished with metal strips in which the refractive index can reach -2. The refractive index retrieval procedure and the critical role of light phases in determining the r…
The article demonstrates uncommon manifestation of spatial dispersion in low refractive index contrast 3D periodic dielectric composites with periods of about one tenth of the wavelength. First principles simulations by the well established plane wave method reveal that spatial dispersion leads to appearance of additional optical axes and can compensate anisotropy in certain directions.
A type of 3-dimensional optical negative-refractive-index metamaterials composed of all dielectric nanospheres is proposed and demonstrated theoretically. The metamaterials are constructeded by pairing together two kinds of dielectric nanospheres as concentric shells embedded in a host medium. Mie-based extended effective theory shows that the dielectric core and the dielectric shell provide the negative permeability and the negative permittivity, respectively, both due to the strong Mie resonances. Within the coupled resonant frequency region, the negative index of refraction can be achieved.
In this work, we discuss the way in which electric and magnetic dipole resonances arising in the optical scattering spectrum of non-absorbing dielectric nanospheres can be accurately approximated by means of simple explicit expressions that depend on sphere's radius, incident wavelength and relative refractive index. We find such expressions to hold not only for high but also for moderate refractive-index values, thus complementing the results reported in previous studies.
The sensitivity of a refractive index sensor based on an optical bound state in the continuum is considered. Applying Zel'dovich perturbation theory we derived an analytic expression for bulk sensitivity of an all-dielectic sensor utilizing symmetry protected in-$Γ$ optical bound states in a dielectric grating. The upper sensitivity limit is obtained. A recipe is proposed for obtaining the upper sensitivity limit by optimizing the design of the grating. The results are confirmed through direct numerical simulations.
Conventional transparent materials at optical frequencies have refractive index values (n) greater than unity -- most commonly between about 1 and 4. This paper explores optical phenomena made possible by using materials with refractive indices less than unity. We focus primarily on fused silica (SiO2), a polar dielectric with strong phonon resonances in the mid infrared that result in a spectral region in which n < 1 with modest optical loss. Using this ubiquitous easy-to-deposit material, we demonstrate infrared-frequency external reflection, frustrated external reflection, and direct coupli…
High-refractive index dielectric nanoparticles may exhibit strong directional forward light scattering at visible and near-infrared wavelengths due to interference of simultaneously excited electric and magnetic dipole resonances. For a spherical high-index dielectric, the so-called first Kerker's condition can be realized, at which the backward scattering practically vanishes for some combination of refractive index and particle size. However, Kerker's condition for spherical particles is only possible at the tail of the scattering resonances, when the particle scatters light weakly. Here we …
We report numerical experiments of optical wave propagation in composites of high refractive index dielectric rods at frequencies where their first electric and magnetic Mie resonances are excited. The arrays of these particles have been extensively studied and proposed as non-absorbing and isotropic metamaterials. We show that negative refraction, observed in ordered particle arrays, is due to diffraction and that an effective medium theory yields constitutive parameters that do not reproduce the observations in these composites, whose transmission also depends on the sample shape. This is fu…
The use of relatively simple structures to achieve high performance refractive index sensors has always been urgently needed. In this work, we propose a lithography-free sensing platform based on metal-dielectric cavity, the sensitivity of our device can reach 1456700 nm/RIU for solution and 1596700 nm/RIU for solid material, and the FOM can be up to 1234500 /RIU for solution and 1900800 /RIU for solid material, which both are much higher than most sensing methods. This sensor has excellent sensing performance in both TE and TM light, and suitable for integrated microfluidic channels. Our sche…
High-index dielectric materials are in great demand for nanophotonic devices and applications, from ultrathin optical elements to metal-free sub-diffraction light confinement and waveguiding. Here we show that chalcogenide topological insulators are particularly apt candidates for dielectric nanophotonic architectures in the infrared spectral range by reporting metamaterial resonances in chalcogenide crystals sustained well inside the mid-infrared, choosing Bi$_2$Te$_3$ as case study within this family of materials. Strong resonant modulation of the incident electromagnetic field is achieved t…
Recently, we showed that dielectric mesoscale spheres could support so-called super-resonance effect, i.e. high-order Mie resonance modes with giant field localization and enhancement. Due to the presence of the surrounding medium leads to a significant influence in the intensity of the field in the particle, based on Mie theory we show for the first time that this effect may be use to design refractive index sensor of medium. Using the example of air as an environment, we have shown that the sensitivity of the proposed sensor concept can reach from 10-6 to 10-8, depending on the accuracy of t…
In this work, a refractive index (RI) sensor with an effective integration of colorimetric detection and optical sensing capabilities has been developed. Colorimetric detection relies on the sensitivity of the structural color of photonic crystal (PC) substrates to the changes in background RI, while the optical sensing is performed by measuring the magnification abilities of the dielectric microspheres, which depends on the position of the photonic nanojet. Based on this concept, we have successfully assembled 35 μm-diameter barium titanate glass microspheres, 4.9 μm-diameter polystyrene and …
In this paper, focal shift of a Guassian laser beam tightly focused through several planar dielectric interfaces is discussed. It is shown that the focal shift and focus point can be changed by variation of refractive index mismatch and this shift could be positive or negative, and it is proportional to refractive index mismatch between coverglass and immersion medium. It is shown also that for every immersion medium(coverglass), focal shift could be removed for a continuous range of depths by choosing a coverglass (immersion medium) with appropriate refractive index.
Dielectric tensor tomography reconstructs the three-dimensional dielectric tensors of microscopic objects and provides information about the crystalline structure orientations and principal refractive indices. Because dielectric tensor tomography is based on transmission measurement, it suffers from the missing cone problem, which causes poor axial resolution, underestimation of the refractive index, and halo artifacts. In this study, we present the generalization of total variation regularization to three-dimensional tensor distributions. In particular, demonstrate the reduction of artifacts …
We show that bulk rhenium diselenide, ReSe2 is characterized by record high value of the refractive index exceeding 5 in near-infrared frequency range. We use back focal plane reflection spectroscopy to extract the components of the ReSe2 permittivity tensor and reveal its extreme biaxial anisotropy. We also demonstrate the good agreement between the experimental data and the predictions of the density functional theory. The combination of the large refractive index and giant optical anisotropy makes ReSe2 a perspective material for all-dielectric nanophotonics in the near-infrared frequency r…
The dielectric microsphere can be directly embedded into the traditional microscope, which can significantly improve the resolution of the microscope and provide a simple and feasible way to break through the diffraction limit of optical imaging system. However, due to the lack of effective theory and formula system, the resolution limit, magnification and optimal imaging position of the microsphere microsystem cannot be determined, which hinders its application. In this paper, the microscopic theory of dielectric microspheres is studied systematically, and the ray optics is extended to the im…
In this research, we report the experimental evidence of the directional Fano resonances at the scattering of a plane, linearly polarized electromagnetic wave by a homogeneous dielectric sphere with high refractive index and low losses. We observe a typical asymmetric Fano profile for the intensity scattered in, practically, any given direction, while the overall extinction cross section remains Lorentzian. The phenomenon is originated in the interference of the selectively excited electric dipolar and quadrupolar modes. The selectivity of the excitation is achieved by the proper choice of the…
Utilizing the underlying physics of evanescent wave amplification by a negative-refractive-index slab, it is shown that evanescent waves with specific spatial frequencies can also be amplified without any reflection simply by two dielectric planar waveguides. The simple configuration allows one to take advantage of the high resolution limit of a high-refractive-index material without contact with the object.
Coordinate transformations are a versatile tool to mould the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with conformal transformations, we show how non-conformal distortions of optical space are intimately connected to the complex refractive index distribution of an isotropic non-Hermitian medium. Remarkably, this insight can be used to circumvent the material requirement of working with refractive indices below unity, which limits the applications of transformation o…
We investigate optical (transverse gradient) forces between two high-index dielectric planar waveguides immersed in low-index dielectric fluid media. Complimentary to previous studies, we extend optical forces calculations, in order to take into account a non-vacuum (and non-air) background medium, by using the Minkowski stress tensor formulation; we derived a very simple set of equations in terms of the effective refractive indexes of the waveguide eigenmodes. We also used a normalized version of the dispersion relation method to calculate the optical forces, in order to validate our results …
The mean path length invariance property is a very important property of scattering media illuminated by an isotropic and homogeneous radiation. Here we investigate the case of inhomogeneous media with refractive index mismatch between the external environment and also among their subdomains. The invariance property remains valid by the introduction of a correction, dependent on the refractive index, of the mean path length value. It is a consequence of the stationary solution of the radiative transfer equation in a medium subjected to an isotropic and homogeneous radiance. The theoretical res…
Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on the concept of geodesic lens. The requirement is a continuous refractive index profile of dielectrics, which shows almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal tra…
The refractive index of a dielectric medium comprising both passive and inverted components in its permittivity was determined using two methods: (i) in the time domain, a finite-difference algorithm to compute the frequency-domain reflectance from reflection data for a pulsed plane wave that is normally incident on a dielectric half-space, and (ii) in the frequency domain, the deflection of an obliquely incident Gaussian beam on transmission through a dielectric slab. The dielectric medium was found to be an active medium with a negative real part for its refractive index. Thereby, a recent c…
The oblique incidence of a Bessel beam on a dielectric slab with refractive index n1 surrounded by a medium of a refractive index n>n1 may be studied simply by expanding the Bessel beam into a set of plane waves forming the same angle with the axis of the beam. In the present paper we examine a Bessel beam that impinges at oblique incidence onto a layer in such a way that each plane-wave component impinges with an angle larger than the critical angle.
Diffraction gratings disperse light in a rainbow of colors with the opposite order than refractive prisms, a phenomenon known as negative dispersion. While refractive dispersion can be controlled via material refractive index, diffractive dispersion is fundamentally an interference effect dictated by geometry. Here we show that this fundamental property can be altered using dielectric metasurfaces, and we experimentally demonstrate diffractive gratings and focusing mirrors with positive, zero, and hyper negative dispersion. These optical elements are implemented using a reflective metasurface …
We investigate the prospect of achieving negative permittivity and permeability at optical frequencies in a dielectric crystal containing stoichiometric rare-earth ions. We derive the necessary transition linewidth, ion density and electric and magnetic oscillator strengths using a simplified model of non-interacting dipoles. We identify Erbium crystals in a magnetically ordered phase as the most promising material to meet these conditions, and describe initial optical measurements of two potential candidates, \ercl{} and ${}^7$\lierf{}, which display linewidths of 3~GHz and 250~MHz, respectiv…
Two choices are possible for the refractive index of a linear, homogeneous, isotropic, active, dielectric material. Either of the choices is adequate for obtaining frequency-domain solutions for (i) scattering by slabs, spheres, and other objects of bounded extent; (ii) guided-wave propagation in homogeneously filled, cross-sectionally uniform, straight waveguide sections with perfectly conducting walls; and (iii) image formation due to flat lenses. The correct choice does matter for the half-space problem, but that problem is not realistic.
We consider emitting nanoparticles in dielectric nanocomposites with varying refractive index contrast and geometry. For that we develop a simple and universal method to calculate the emission enhancement in nanocomposites that employs solely the calculation of the effective refractive index and electric field distributions from three quasistatic calculations with orthogonal polarizations. The method is exemplified for dilute nanocomposites without electromagnetic interaction between emitting particles as well as for dense nanocomposites with strong particle interaction. We show that the radia…
Optical near-fields of small dielectric particles are of particular importance and interests for nanoscale optical engineering such as field localization, fabrication, characterization, sensing and imaging. This paper represents a systematic investigation on the focusing characteristics (focal length, field enhancement, spot size) for a given refractive-index microsphere (n=1.6) with a varying size parameter across the range of pi<q0<20*pi. Conditions for super-resolution foci were analysised in details. Particularly strong super-resolution foci with spot size falling at least 50% below the di…
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…
Voigt wave propagation (VWP) was considered in a porous biaxial dielectric material which was infiltrated with a material of refractive index $n_a$. The infiltrated material was regarded as a homogenized composite material in the long-wavelength regime and its constitutive parameters were estimated using the extended Bruggeman homogenization formalism. In our numerical studies, the directions which support VWP were found to vary by as much as $300^\circ$ per RIU as the refractive index $n_a$ was varied. The sensitivities achieved were acutely dependent upon the refractive index $n_a$ and the d…
The capability of generating terajets using 3D dielectric cuboids working at terahertz (THz) frequencies (as analogues of nanojets in the infrared band) are introduced and studied numerically. The focusing performance of the terajets are evaluated in terms of the transversal full width at half maximum along x- and y- directions using different refractive indexes for a 3D dielectric cuboid with a fixed geometry, obtaining a quasi-symmetric terajet with a subwavelength resolution of ~0.46λ0 when the refractive index is n = 1.41. Moreover, the backscattering enhancement produced when metal partic…
We propose deep-subwavelength optical waveguides based on metal-dielectric multilayer indefinite metamaterials with ultrahigh effective refractive indices. Waveguide modes with different mode orders are systematically analyzed with numerical simulations based on both metal-dielectric multilayer structures and the effective medium approach. The dependences of waveguide mode indices, propagation lengths and mode areas on different mode orders, free space wavelengths and sizes of waveguide cross sections are studied. Furthermore, waveguide modes are also illustrated with iso-frequency contours in…
We consider a 4D model for photon production induced by a %superluminal refractive index perturbation in a dielectric medium. We show that, in this model, we can infer the presence of a Hawking type effect. This prediction shows up both in the analogue Hawking framework, which is implemented in the pulse frame and relies on the peculiar properties of the effective geometry in which quantum fields propagate, as well as in the laboratory frame, through standard quantum field theory calculations. Effects of optical dispersion are also taken into account, and are shown to provide a limited energy …
We investigate the role of retardation corrections to polarizability and to refractive index. We found that the classical electromagnetic theory of dielectrics requires corresponding modifications in terms of nonlocality of the dielectric constant. This nonlocality should be taken into account in the interpretation of accurate measurements of the optical refractivity.
High refractive index dielectric spheres present remarkable light-scattering properties in the spectral range dominated by dipolar modes. However, most of these properties are absent for larger spheres under plane wave illumination. Here, we propose to unravel dipolar regimes regardless of the sphere size and refractive index by illuminating with a pure dipolar field. This type of illumination ensures that the scattering response of the sphere is purely dipolar. In this scenario, we show that Kerker conditions are not only related to duality symmetry and a strong backward-to-forward asymmetric…
Circular microresonators (microdisks) are micron sized dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental equations. The behavior of such eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analysed. This analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonant modes for both TM and TE polarizations. This is especially important for TE polarization for which internal an…
We consider refractive index sensing with optical bounds states in the continuum (BICs) in dielectric gratings. Applying a perturbative approach we derived the differential sensitivity and the figure of merit of a sensor operating in the spectral vicinity of a BIC. Optimisation design approach for engineering an effective sensor is proposed. An analytic formula for the maximal sensitivity with an optical BIC is derived. The results are supplied with straightforward numerical simulations.
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…
Effective refractive index of disordered all-dielectric metasurfaces consisting of gallium phosphide (GaP) spheres is studied by means of three-dimensional finite-difference time-domain (FDTD) simulations at the wavelength of 532~nm. It is shown that a mixture of the high index nanoparticles with sizes close to the first magnetic and electric resonances randomly dispersed on metasurface may possess negative refraction. The dependence of the metasurface effective refractive index on the nanoparticle concentration and size is constructed. The feasibility of negative refraction at large concentra…
Anomalous field enhancement accompanied by resonant absorption phenomenon was originally discussed in the context of plasma physics and in applications related to radio-communications between the ground and spacecraft returning to Earth. Indeed, there is a critical period of time when all communications are lost due to the reflection/absorption of electromagnetic waves by the sheath of plasma created by a high speed vehicle re-entering the atmosphere. While detailed experimental studies of these phenomena in space are challenging, the emergence of electromagnetic metamaterials enables research…
A simple user-friendly software named PRISA has been developed to determine optical constants (refractive index and extinction co-efficient), dispersion parameters (oscillator energy and dispersion energy), absorption co-efficient, band gap and thickness of semiconductor and dielectric thin films from their measured transmission spectrum, only. The thickness, refractive index, and extinction co-efficient of the films have been derived using Envelope method proposed by Swanepoel. The absorption co-efficient in the strong absorption region is calculated using the method proposed by Connel and Le…
We show that transparent dielectrics with strong optical anisotropy support a new class of electromagnetic waves that combine the properties of propagating and evanescent fields. These "ghost waves" are created in tangent bifurcations that "annihilate" pairs of positive- and negative-index modes, and represent the optical analogue of the "ghost orbits" in the quantum theory of non-integrable dynamical systems. Similarly to the regular evanescent fields, ghost waves support high transverse wavenumbers, but in addition to the exponential decay show oscillatory behavior in the direction of propag…
The study of invisibility of an infinite dielectric rod with high refractive index is based on the two-dimensional Mie scattering problem, and it suggests strong suppression of scattering due to the Fano interference between spectrally broad nonresonant waves and narrow Mie-resonant modes. However, when the dielectric rod has a finite extension, it becomes a resonator supporting the Fabry-Perot modes which introduce additional scattering and eventually destroy the invisibility. Here we reveal that for shorter rods with modest values of the aspect ratio r/L (where r and L are the radius and len…
A simple optical lens plays an important role for exploring the microscopic world in science and technology by refracting light with tailored spatially varying refractive index. Recent advancements in nanotechnology enable novel lenses, such as, superlens, hyperlens, Luneburg lens, with sub-wavelength resolution capabilities by specially designing materials' refractive indices with meta-materials and transformation optics. However, these artificially nano/micro engineered lenses usually suffer high losses from metals and are highly demanding in fabrication. Here we experimentally demonstrate f…
The engineering of light confinement is a topic with a long history in optics and with significant implications for the control of light-matter interaction. In inhomogeneous and disordered media, however, multiple scattering prevents the application of conventional approaches for the design of light fields with desired properties. This is because any local change to such a medium typically affects these fields in a non-local and complicated fashion. Here, we present a theoretical methodology for tailoring an inhomogeneous one-dimensional (1D) Hermitian dielectric index distribution, such that …
We investigate electromagnetic propagation in uniaxial dielectrics with a transversely varying orientation of the optic axis, the latter staying orthogonal everywhere to the propagation direction. In such a geometry, the field experiences no refractive index gradients, yet it acquires a transversely-modulated Pancharatnam-Berry phase, that is, a geometric phase originating from a spin-orbit interaction. We show that the periodic evolution of the geometric phase versus propagation gives rise to a longitudinally-invariant effective potential. In certain configurations, this geometric phase can p…
An effective medium model is developed for disordered metamaterials containing a spatially random distribution of dielectric spheres. Similar to effective medium models for ordered metamaterials, this model predicts resonances in the effective permeability and permittivity arising from electric- and magnetic-dipole Mie resonances in the spheres. In addition, the model predicts a redshift of the electric resonance with increasing particle loading. Interestingly, when the particle loading exceeds the percolation threshold of 33\%, the model predicts that the electric resonance overlaps with the …
Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index, ultra-high index and chiral optical properties. Recently, metamaterials with near-zero refractive index have drawn much attention. Light inside such materials experiences no spatial phase change and extremely large phase velocity, properties that can be applied for realizing directional emission, tunneling waveguides, large area single mode devices, and electromagnetic cloaks. However, at optical frequencies previously demonstrated zero- or negative-r…
We consider meta materials made from a two-dimensional dielectric rod-type photonic crystal. The magnetic response is studied within the recently developed homogenization theory and we in particular study the effects of topology and inhomogeneous broadening. While topology itself mainly affects the Mie resonance frequency we find that the dispersion in the topological radius R of the dielectric rods may lead to significant inhomogeneous broadening and suppression of the negative-mu phenomena for dR/R0 >> epsilon''/epsilon', with epsilon=epsilon'+i*epsilon'' being the relative dielectric functi…
Evolution of resonant frequencies and resonant modes as dependent on the aspect ratio is considered in a dielectric high index spheroid. Because of rotational symmetry of the spheroid the solutions are separated by the azimuthal index $m$. By the two-fold variation of a refractive index and the aspect ratio we achieve exceptional points (EPs) at which the resonant frequencies and resonant modes are coalesced in the sectors $m=0$ for both TE and TM polarizations and $m=1$.
High-refractive-index semiconductor optical waveguides form the basis for modern photonic integrated circuits (PICs) , but the conventional methods of achieving optical confinement require a thick lower-refractive-index support layer that impedes large-scale co-integration with electronics. To address this challenge, we present a general architecture for single-mode waveguides that confine light in a high-refractive-index material on a native substrate. Our waveguide consists of a high-aspect-ratio fin of the guiding material surrounded by lower-refractive-index dielectrics and is compatible w…
