Isotropic Dielectrics Research Articles

Electrostatics in Materials Revisited: The Case of Free Charges Combined with Linear, Homogeneous, and Isotropic Dielectrics

Here we revisit the electrostatics of material systems comprising of free charges and linear, homogeneous, and isotropic (LHI) dielectrics. We focus on D(r) suggesting that this is the primary vector field of electrostatics. We show that D(r) is sufficient to conceptually describe all underlying physics and to mathematically accomplish all necessary calculations, beforehand, independently of the secondary vector fields P(r) and E(r) that, if needed, can be easily calculated from D(r). To this effect, we introduce a P-D electric susceptibility, χε, with , that couples linearly P(r) with D(r) (instead of the standard P-E electric susceptibility, χe, with , that couples linearly P(r) with E(r)). This concept restores the somehow misleading causality/feedback between P(r) and E(r) of the standard formulation, captures efficiently the underlying physics, enables electrostatics to obtain a form analogous to that of magnetostatics, and facilitates analytical/computational calculations in relevant systems. To document these claims, we provide technical means, among others, the free scalar potential, , and clarify the conditions that enable the calculation of D(r) on a standalone basis, directly from the free charge density, , and the electric susceptibility, χε, of the LHI dielectrics. Our concept sets interesting perspectives for the treatment of all dielectrics.

Characterization of Rectangular Waveguides Loaded E-Plane Dielectrics Using the Newton-Raphson Method

Homogeneous metallic waveguides have long been used to carry high powers. They are often filled with inhomogeneous, isotropic dielectrics to reduce their size and cut-off frequencies. To characterize these inhomogeneous rectangular waveguides made of homogeneous and isotropic media, the Newton-Raphson method is used in this article. Frequency of cutoff, attenuation, and power flow distribution are all properties of the EM wave that are highly dependent on the physical structure and composition within the guide. This article presents the characterization of an inhomogeneous and isotropic rectangular guide. The analysis of this type of guide is based on the Borgnis potential method for determining the components of the electric field E and the magnetic field H, to obtain the guide's dispersion equations. The modes that were found to exist in these waveguides are hybrid, meaning that they have both axial E- and H-fields. Numerical resolution of these equations using the Newton-Raphson method obtains the guide's propagation constants. A MATLAB program is used to plot these dispersion curves. The propagation constant increases as a function of frequency, and the d/a ratio influences the dispersion curves. Increasing the relative permittivity of the dielectric leads to an increase in the ratio of the propagation constant in the z direction to the wave number.

Rayleigh wave propagation in centrosymmetric materials with micro-stiffness, flexoelectric and micro-inertia effects

A theoretical investigation of Rayleigh waves propagation in polarized media has been carried out using a reformulated flexoelectric theory for isotropic dielectrics with micro-inertia effect. Within this non-classical theory, the internal energy density is the functional of the strain tensor, dilatation gradient, deviatoric part of stretch gradient and rotation gradient tensors, polarization vector, and polarization gradient. The obtained system of governing equations additionally contains three material length-scale parameters to account the micro-stiffness effect, one material constant to capture the micro-inertia effect, two flexoelectric constants to describe the flexoelectric effect and three length scale parameters related to the polarization gradient. To solve the coupled governing equations, the method of Lamé-type potentials for mechanical displacement and electric polarization vectors is used. The influences of various factors such as micro-stiffness, flexoelectricity, electric quadrupoles and micro-inertia effects on the phase velocity of the Rayleigh waves in a homogeneous isotropic half-space are studied. It is found that above effects become significant with the increase of the wavenumber. This study can be important for the investigation of high frequency surface acoustic waves in dielectric materials.

Electromagnetic wave propagation in cylindrical photonic crystals with engineered disorder effects

In this study, the manipulation of engineered disorder effects in cylindrical photonic crystals is examined, with a focus on the influence of three varied types of disorder effects on the transmission spectra near the first five photonic band gaps of CPCs. The investigation employed the basic (ABA)N model, where A and B depict two isotropic dielectrics, and N is the number of periods. The impact of the disorder on the CPCs is analyzed and discussed in detail. In addition, the disorder-induced localization and delocalization of the electromagnetic waves are measured by the inverse participation rate and disorder-to-order energy ratio. These results are analyzed numerically. Based on this, the intrinsic connection between the defined parameters and the mechanism of disorder-influenced structure switching between the localized and transmitted states is investigated. All the above phenomena and findings might lead to a new understanding of electromagnetic wave transmission and localization in micro and nano-optical devices.

Strong polarization-dependent photonic bandgap and giant photonic spin Hall effect in a one-dimensional photonic crystal entirely composed of all-dielectric metamaterials

In conventional one-dimensional (1-D) photonic crystals (PhCs) consisting of isotropic dielectrics, photonic bandgaps (PBGs) exhibit weak polarization-dependent property since the propagating phase of the isotropic dielectric film is polarization-independent. The weak polarization-dependent property of PBGs intensively impedes the potential application of 1-D PhCs in the photonic spin Hall effect (PSHE). Herein, we investigate the polarization-dependent property of PBGs in a class of 1-D PhCs entirely consisting of all-dielectric elliptical metamaterials (EMMs) called all-EMM 1-D PhCs. Driven by the combination of 1-D PhCs and all-dielectric EMMs, strong polarization-dependent PBGs can be realized. Then, we exploit the strong polarization-dependent PBG to achieve giant PSHE. The enhanced transverse shift of the PSHE reaches the order of 102 μm. Our work not only establishes a bridge between PhCs and all-dielectric metamaterials, but also paves a new route to manipulating polarization of light.

Ultra-large near-infrared omnidirectional photonic bandgaps in cascaded one-dimensional photonic crystals containing all-dielectric metamaterials.

In conventional one-dimensional (1-D) photonic crystals (PCs) consisting of isotropic dielectrics, photonic bandgaps (PBGs) substantially shift toward shorter wavelengths as incident angle increases. This strong blueshift characteristic of PBGs significantly reduces the widths of near-infrared omnidirectional photonic bandgaps (OPBGs). Recently, researchers achieved a kind of special PBG called angle-insensitive PBGs in 1-D PCs containing all-dielectric elliptical metamaterials (EMMs). The emergence of angle-insensitive PBGs provides us a possibility to achieve ultra-large near-infrared OPBGs. Herein, we design two 1-D PCs containing all-dielectric EMMs with near-infrared angle-insensitive PBGs in different wavelength ranges. By cascading two 1-D PCs containing all-dielectric EMMs together, we achieve an ultra-large near-infrared OPBG with a width up to 1.004µm (relative bandwidth of 63.9%). In addition, the width of the near-infrared OPBG demonstrates robustness against the layer thickness. Our work not only provides a feasible route to achieving ultra-large near-infrared OPBGs, but also facilitates the design of broadband omnidirectional mirrors.

Large omnidirectional mid-infrared photonic bandgap in a one-dimensional ternary photonic crystal consisting of isotropic dielectric, elliptical metamaterial and plasma

Photonic bandgaps (PBGs) in traditional one-dimensional (1-D) binary photonic crystals (PhCs) consisting of two kinds of isotropic dielectrics strongly shift towards shorter wavelengths as incident angle increases. Such blueshift property of PBGs intensively limits the widths of omnidirectional photonic bandgaps (OPBGs). Very recently, researchers achieved a special kind of PBGs called angle-insensitive PBGs in novel 1-D binary PhCs consisting of isotropic dielectric and elliptical metamaterial (EMM). The emergence of such angle-insensitive PBGs provides us an opportunity to achieve large OPBGs. Herein, we periodically introduce plasma layers into a 1-D binary PhC consisting of isotropic dielectric and EMM with an angle-insensitive PBG to achieve a large OPBG at mid-infrared wavelengths. The EMM is mimicked by an all-dielectric subwavelength multilayer. The broaden effect of the OPBG originates from the plasmonic property of plasma and the angle-insensitive property of the PBG. The width of the OPBG reaches 4.19 μm. Our work provides a feasible route to achieving large OPBGs in 1-D PhCs and would promote the development of OPBG-based devices, such as omnidirectional broadband reflectors and omnidirectional filters.

On the plane strain problem of dynamical flexoelectric effect in dielectrics subject to Sinc-shaped surface loading

Flexoelectricity is a nanoscale phenomenon in dielectric crystals, where the mechanical loads resulting from the first strain gradient shares producing electricity. In this work, we present a numerical investigation for the plane strain problem of the dynamical flexoelectric effect in isotropic dielectrics. A surface loading based on the Sinc function, that is, sincπ(x), with a temporal exponentially decay, is applied to the upper surface of a semi-infinite dielectric crystal. Two cases for the electric potential are considered: (1) Open circuit, in which there is zero charge on the terminals; and (2) Short-circuit, where there is a given value for the potential of the terminals. This type of surface loading is often used in applications such as seismic analysis and electrical engineering, especially signal processing and digital signal processing. Also, it can be used to model other types of dynamic loads, such as wind or wave loads. Furthermore, this setting generates a two-dimensional formulation, known as the plane strain problem. Laplace and Fourier transform techniques are employed for solving the field equations. Suitable numerical techniques are implemented to present the solution to the physical domain. We choose the Strontium Titanate material (SrTiO3) for the two-dimensional simulation. Discussion for the behavior of the dynamical polarization, electric field, electric potential, and stresses is provided in the two-dimensional setting. Effects of the model parameters on electricity generation and behavior are studied.

Couple stress-based flexoelectricity of frictionless contact in dielectrics

The presence of flexoelectricity in dielectric materials can affect the mechanics of contact between solid bodies, especially when viewed at the micro/nano-scale. Such an effect can also contribute significantly to contact electrification ─ a charge transfer event that takes place at the contact interface. In particular, the state of deformation and stresses in the vicinity of the contacting area can differ markedly from that anticipated from classical elastic Hertzian contact theory. In the present work, we investigate the flexoelectric effect near the contacting area of an isotropic dielectric material pressed by a frictionless rigid insulator probe, serving as a model problem to reveal the potential role of flexoelectricity in contact mechanics and electrification. The investigation is based on consistent couple stress flexoelectric theory, in which electric polarization may appear due to two-way coupling between the electric field and mean curvature vectors, even for centrosymmetric dielectric materials. To this end, we develop a new boundary element formulation to calculate the displacement, stress, electric potential, and electric displacement for two-dimensional isotropic flexoelectric contact problems. The subsequent computational mechanics investigation highlights several important characteristics of triboelectric phenomena and shows that the state of stress and polarization in contacting isotropic dielectrics is dependent on the effective length scale parameter l of couple stress elasticity and the coupling flexoelectric coefficient f.

Dual-Mode High-Q Multiphysics Sensor Based on the Evanescent Wave in the InSb Photonic Crystals

In this article, a dual-mode multiphysical quantity sensor is designed based on the indium antimonide (InSb) photonic crystals (PCs), which are using the evanescent wave principle. The sensor is mainly composed of InSb and three isotropic dielectrics, one layer of which is the dielectric to be measured. By adjusting the magnetic field strength, the operation modes of the structure can be controlled to switch between the transmittance and interference absorption cases. In a transmittance mode, the dielectric to be measured is set to the air layer, and sensing of magnetic field strength, thermodynamic temperature, and incident angle can be achieved. While for the interference absorption mode, the refractive index and the thickness of the dielectric to be measured can be obtained. It is worth mentioning that the linear range for sensing the dielectric thickness and refractive index in this mode is theoretically infinite based on the principle of interferometric light. In addition to the benefits of the introduction of the evanescent wave structure, the sensor has extremely high-quality factors ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> ) for the measurement of various physical quantities. Thus, this design is likely to reveal great potential in the field of physical measurements.

Polarization-sensitive photonic bandgaps inhybrid one-dimensional photonic crystals composed of all-dielectric elliptical metamaterials and isotropic dielectrics.

Photonic bandgaps (PBGs) in conventional one-dimensional (1-D) photonic crystals (PhCs) composed of isotropic dielectrics are polarization-insensitive since the optical length within a isotropic dielectric layer is polarization-independent. Herein, we realize polarization-sensitive PBGs in hybrid 1-D PhCs composed of all-dielectric elliptical metamaterials (EMMs) and isotropic dielectrics. Based on the Bragg scattering theory and iso-frequency curve analysis, an analytical model is established to characterize the angle dependence of PBGs under transverse magnetic and transverse electric polarizations. The polarization-dependent property of PBGs can be flexibly controlled by the filling ratio of one of the isotropic dielectrics within all-dielectric EMMs. Assisted by the polarization-sensitive PBGs, high-performance polarization selectivity can be achieved. Our work offers a loss-free platform to achieve polarization-sensitive physical phenomena and optical devices.

Gupta-Bleuler quantization of optical fibers in weak gravitational fields

The theory of gauge-fixed Maxwell equations in linear isotropic dielectrics is developed using a generalization of the standard ${R}_{\ensuremath{\xi}}$ gauge-fixing term. In static space times, the theory can be quantized using the Gupta-Bleuler method, which is worked out explicitly for optical fibers either in flat space time or at a constant gravitational potential. This yields a consistent first-principles description of gravitational fiber-optic interferometry at the single-photon level within the framework of quantum field theory in curved space times.

Full-space omnidirectional cloak by subwavelength metal channels filled with homogeneous dielectrics.

Cloaks can greatly reduce the scattering cross-section of hidden objects through various mechanisms, thereby making them invisible to outside observers. Among them, the full-space omnidirectional cloak based on transformation optic with full parameters are difficult to realize without metamaterials and often needs to be simplified before realization, while most cloaks with simplified parameters have limited working direction and cannot achieve omnidirectional cloaking effect. In this study, a full-space omnidirectional cloak is designed based on transformation optics and optic-null medium, which only needed natural materials without metamaterials. The designed omnidirectional cloak is realized by subwavelength metal channels filled with isotropic dielectrics whose refractive indices range from 1 to 2, which is homogeneous in each channel. The numerical simulation results verify good scattering suppression effect of the designed cloak for various detecting waves.

Monte Carlo Algorithms for the Extracting of Electrical Capacitance

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the Laplace equation. Unbiased and low-biased estimators for the capacitances are constructed on the trajectories of the Random Walk on Spheres or the Random Walk on Hemispheres. The calculation results show that the accuracy of these new algorithms does not exceed the statistical error of estimators, which is easily determined in the course of calculations. The algorithms are based on mean value formulas for harmonic functions in different domains and do not involve a transition to a difference problem. Hence, they do not need a lot of storage space.

Refraction of space-time wave packets: II. experiments at normal incidence.

The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In the first paper in this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105], we theoretically described the refraction of all families of ST wave packets at normal and oblique incidence at a planar interface between two nondispersive, homogeneous, isotropic dielectrics. Here, in this second paper in the sequence, we present experimental verification of the refractive phenomena predicted for baseband ST wave packets upon normal incidence on a planar interface. Specifically, we observe group velocity invariance, normal and anomalous refraction, and group velocity inversion leading to group delay cancellation. These phenomena are verified in a set of optical materials with refractive indices ranging from 1.38 to 1.76, including MgF2, fused silica, BK7 glass, and sapphire. We also provide a geometrical representation of the physics associated with anomalous refraction in terms of the dynamics of the spectral support domain for ST wave packets on the surface of the light cone.

Refraction of space-time wave packets: III. experiments at oblique incidence.

The refraction of space-time (ST) wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics exhibits fascinating phenomena, even at normal incidence. Examples of such refractive phenomena include group-velocity invariance across the interface, anomalous refraction, and group-velocity inversion. Crucial differences emerge at oblique incidence with respect to the results established at normal incidence. For example, the group velocity of the refracted ST wave packet can be tuned simply by changing the angle of incidence. In the third paper, we present experimental verification of the refractive phenomena exhibited by ST wave packets at oblique incidence that were in the first paper of this sequence [J. Opt. Soc. Am. A38, 1409 (2021)10.1364/JOSAA.430105]. We also examine a proposal for "blind synchronization," whereby identical ST wave packets arrive simultaneously at different receivers without a priori knowledge of their locations except that they are all located at the same depth beyond an interface between two media. A first proof-of-principle experimental demonstration of this effect is provided.

Refraction of space-time wave packets: I. theoretical principles.

Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, and isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we call the "spectral curvature". Because the spectral curvature vanishes in conventional optical fields where the spatial and temporal degrees of freedom are separable, these phenomena have not been observed to date. We derive the laws of refraction for baseband, X wave, and sideband ST wave packets that reveal fascinating refractive phenomena, especially for the former class of wave packets. We predict theoretically, and confirm experimentally in the accompanying papers, refractive phenomena such as group-velocity invariance (ST wave packets whose group velocity does not change across the interface), anomalous refraction (group-velocity increase in higher-index media), group-velocity inversion (change in the sign of the group velocity upon refraction but not its magnitude), and the dependence of the group velocity of the refracted ST wave packet on the angle of incidence.

Full-view imaging on dynamic closed surface by curved-to-flat conversion lens.

Conventional full-view imaging systems, which often need complicated image processing algorithms to reconstruct full-view images captured by motional/multiple cameras from different views, cannot have good real-time imaging capability. We design curved-to-flat conversion lens (CFCL) based on optic-null medium, which can directly project/image optical patterns from closed object surface onto image plane (e.g., the focal plane of microscopy), and shows good real-time full-view imaging performance. To realize the CFCL, the reduced optic-null medium is designed by subwavelength metal channels filled with homogeneous isotropic dielectrics. Numerical simulation results verify the function of the designed CFCL, which can image various dynamic optical patterns from the closed object surface to the finite-view image plane. The designed CFCL may have many applications in real-timely observing dynamic closed surfaces in full view, e.g., living tissue/cell and soft material's surface.

Highly Efficient Gradient Solid Immersion Lens with Large Numerical Aperture for Broadband Achromatic Deep Subwavelength Focusing and Magnified Far Field

AbstractAchromatic deep subwavelength lens with large numerical aperture (NA) is in urgent need in several fields, from optical imaging, photolithography, spectroscopy, nanophotonics to microwave engineering and sensing. However, the previous proposed approaches to achieve deep subwavelength lens suffer from severe chromatic aberrations, limited bandwidth, and limited efficiency. In this paper, enlightened by Maxwell's fish‐eye lens, a semicircular gradient solid immersion lens is proposed and manufactured by gradient isotropic dielectrics. Highly efficient (above 85%) achromatic (7–13 GHz) deep subwavelength focusing with full width at half maximum around 0.15λ and large NA of 2.4 as well as magnified far‐field radiation (4–12 GHz) with high recognition are achieved. Theoretical analysis reveals that electric field enhancement at the lens/air interface and magnification of high spatial frequency deep subwavelength information contribute to deep subwavelength focusing and magnified far‐field radiation, respectively. Measured results of near field and far field agree well with those of theoretical predictions, which makes the presented lens having the potential to be applied in deep subwavelength engineering systems.

Theoretical Study of Tunable Optical Resonators in Periodic and Quasiperiodic One-Dimensional Photonic Structures Incorporating a Nematic Liquid Crystal

In this work, the transfer matrix method (TMM) is employed to investigate the optical properties of one-dimensional periodic and quasiperiodic photonic crystals containing nematic liquid crystal (NLC) layers. This structure is expressed as (ABC)J(CBA)J and made of alternated layers of isotropic dielectrics SiO2 (A), BGO (B) and nematic liquid crystal (C). The simulation study shows that the proposed ternary configuration exhibits tunable defect mode within the photonic band gap (PBG) that can be manipulated by adjusting the thicknesses of NLC layers in order of the periodic lattice. In addition, the optimized structure permits for strong confinement light giving rise to an optical microcavity. The application of an applied voltage into NLC layers enables improving the sensitivity by guiding the local defect mode. It has been also shown that by applying quasiperiodic inflation according to Rudin Shapiro Sequence (RSS) scheme to main periodic structure, several tunable resonant modes appear within the PBG. The presence of such sharp resonant peaks reflects that the quasiperiodic NLC-based structure behaves like multiple microcavites with strong light-matter coupling.