High Dielectric Contrast Research Articles

Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions.

Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electromagnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fails when applied to the problem of shifted material boundaries. In this paper we developed coupled mode and perturbation theory formulations for treating generic perturbations of a waveguide cross section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate beyond the first order and rapidly converges to an exact result when used in a coupled mode theory framework even for the high-index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of such quantities as deterministic PMD and change in the GV and GVD of a mode due to generic profile distortion in a waveguide of arbitrary cross section. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary profile variations in high-index-contrast waveguides.

Optical frequencies of spectra of photonic crystals

We develop an effective method for calculating optical frequencies of two-dimensional photonic crystals (PC), i.e. a periodic arrangement of infinite dielectric cylinders. These frequencies, ω N , correspond to the Bloch vector at the center of the Brillouin zone, k=0, and are labeled by the band index N=1,2,… . Using the plane-wave expansion method, we derive two eigenvalue equations for the optical frequencies of the E- and H-polarized modes. These equations are valid for any geometry of the unit cell and arbitrary cross-sectional form of the cylinders. We show that optical frequencies of the E- and H-modes satisfy two different sum rules. We apply our method to PC with high dielectric contrast between constituents and calculate numerically the dependence of the lowest optical modes on the filling fraction. These graphs show splitting of degenerated frequencies with increase of the filling fraction and may be helpful for design of structures with photonic band gaps.

Effective dielectric constant of 2D photonic crystals with high dielectric contrast

We calculate the effective dielectric constant ( ε eff) of 2D photonic crystals (PCs) formed by rods of high dielectric constant arranged in a square lattice. One of the representations allows us to calculate the ε eff in the limiting case of perfectly conducting cylinders in air. We compare our results with those obtained by the electrostatic method.

Electrostatically induced submicron patterning of thin perfect and leaky dielectric films: A generalized linear stability analysis

Thin leaky and perfect dielectric films can be driven electrically to form well-ordered patterns typically of pillar arrays. The process, sometimes referred to as lithographically induced self-assembly, begins by spin coating a polymer onto a silicon wafer to generate an initially featureless film. A small gap, filled with air or another polymeric/organic liquid, is left between the first film and a second wafer called the mask, which may be patterned. This configuration is heated above the glass transition temperature of the polymer, upon which flow ensues in response to destabilizing electrical forces. The authors examined the initial stages of pillar formation under a pattern free mask by performing a linear stability analysis under the lubrication approximation [J. Non-Newtonian Fluid Mech. 102, 233 (2002)] and found the quest for smaller pillars to be assisted by the presence of free charge as described by the leaky dielectric. In practice, however, the lubrication approximation may not strictly apply in the situations of greatest interest. Contrasting the linear stability analysis with and without the lubrication approximation shows that the approximation fails where surface tension is small and electric fields are large, typical of experiments with a polymer/organic liquid instead of air in the gap—precisely the conditions that generate the smallest pillar arrays. This general linear stability analysis predicts conditions where pillars/holes pack more tightly, have smaller diameters, greater aspect ratios, and larger growth exponents for both perfect and leaky dielectric films, in which the smallest features reach deep into the submicron length scales. The analysis also highlights two approaches to smaller pillars by either making the polymer film conducting or choosing polymers with high dielectric contrast, with the former being more universally applicable.

Enhancement of the Faraday rotation in magnetically active periodic structures with defects

Relations that determine the field of a light wave transmitted through and reflected from a periodic structure lying on a substrate and containing a defect layer are derived for the case of an arbitrary symmetry of both the defect layer and the layers forming the structure. Exact expressions are obtained for the determination of the positions of the defect modes. The feasibility of a considerable enhancement of the Faraday rotation while retaining 100% transmission through the defect-containing magnetically active structure at a high dielectric contrast is revealed. It is shown that the angle of magnetooptical rotation of the polarization plane in a periodic structure is a bounded quantity.

Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates

Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electro-magnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fail when applied to the problem of shifted material boundaries. In this paper we developed a novel coupled mode and perturbation theory formulations for treating generic non-uniform (varying along the direction of propagation) perturbations of a waveguide cross-section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate and rapidly converges to an exact result when used in a coupled mode theory framework even for the high index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of induced PMD due to a generic distortion of a waveguide profile, analysis of mode filters, mode converters and other optical elements such as strong Bragg gratings, tapers, bends etc., and arbitrary combinations of thereof. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary non-uniform profile variations in high index-contrast waveguides.

Computation of high-resolution SAR distributions in a head due to a radiating dipole antenna representing a hand-held mobile phone

SAR distributions in a healthy female adult head as a result of a radiating vertical dipole antenna (frequency 915 MHz) representing a hand-held mobile phone have been computed for three different resolutions: 2 mm, 1 mm and 0.4 mm. The extremely high resolution of 0.4 mm was obtained with our quasistatic zooming technique, which is briefly described in this paper.For an effectively transmitted power of 0.25 W, the maximum averaged SAR values in both cubic- and arbitrary-shaped volumes are, respectively, about 1.72 and 2.55 W kg−1 for 1 g and 0.98 and 1.73 W kg−1 for 10 g of tissue. These numbers do not vary much (<8%) for the different resolutions, indicating that SAR computations at a resolution of 2 mm are sufficiently accurate to describe the large-scale distribution.However, considering the detailed SAR pattern in the head, large differences may occur if high-resolution computations are performed rather than low-resolution ones. These deviations are caused by both increased modelling accuracy and improved anatomical description in higher resolution simulations. For example, the SAR profile across a boundary between tissues with high dielectric contrast is much more accurately described at higher resolutions. Furthermore, low-resolution dielectric geometries may suffer from loss of anatomical detail, which greatly affects small-scale SAR distributions. Thus, for strongly inhomogeneous regions high-resolution SAR modelling is an absolute necessity.

A Fourier transform theory for photon localization and evanescence in photonic bandgap structures

We propose an approach to the problem of describing photon behaviour near the bandgap region of photonic crystal structures using a Fourier transform formalism defined in optical reciprocal-space. A modified Debye-Waller approximation in conjunction with the use of a resonant refractive index provides an analytic solution to the coupled-mode equations describing photon propagation in a periodic high dielectric contrast structure. Overall, this represents a new technique for solving the inverse scattering problem. We use this method to consider photon behaviour at the Brillouin zone edges of a one-dimensional photonic crystal structure: our results showing agreement with conventional theory for the standard assumption of an infinitely long grating structure. However, when a photon is located in the bandgap region of a finite (five periods used as an example) high refractive index contrast grating structure, we find that photon velocity becomes superluminal as the photon wave becomes evanescent. This is in agreement with the basic precepts of the uncertainty principle. Additionally, as the bandgap strength increases, the probability of transmission through the dielectric barrier reduces exponentially, with an associated reduction in tunnelling time.

Light emission from thin opaline photonic crystals of low and high dielectric contrast

Photoluminescence of dye molecules embedded in PMMA opaline photonic crystals and their SnS 2 replicas has been studied. The stop-band in the emission spectrum has been demonstrated. The role of a low dielectric contrast photonic crystal is to filter the emission from embedded light sources in accord with its transmission spectrum. In contrast, inverted opaline films of a higher dielectric contrast provide stronger radiation-to-emitter interaction, which feedback results in an amplification of a spontaneous emission of dye molecules at stop-band edges. The directionality diagram of the emission has been observed in both type photonic crystals. This, so-called, self-focusing effect has been tentatively assigned to the ultra-refraction of the emitted radiation at the sample boundary, which is dictated by the configuration of dispersion surfaces in the vicinity of the photonic band gap. The self-focusing has been found strongly dependent upon the frequency.

Photoluminescence of ZnS:Mn embedded in three-dimensional photonic crystals of submicron polymer spheres

ZnS:Mn has been in-filled in photonic crystals of submicron polymer spheres. The effect of the photonic band gap on the photoluminescence (PL) properties of ZnS:Mn has been investigated. Because of the overlap of the transmission dip of the photonic crystal and the photoluminescence band of ZnS:Mn, both suppression and enhancement in the PL of the phosphor have been observed. A strong dependence of the fluorescence lifetime on the emission wavelength in the range of the stop band has been found. This strong dependence is believed to arise from the very low photon density of state within the stop band of the ZnS:Mn in-filled photonic crystal as result of a high dielectric contrast between ZnS:Mn and the polystyrene spheres.

Lateral interactions of charges in thin liquid films and the Berezinskii-Kosterlitz-Thouless transition

At certain experimental conditions, foam films drawn from aqueous surfactant solutions can form highly stable Newtonian films. We show that the origin of the film stability can be attributed to specific patterning of surfactant molecules. Due to high dielectric contrast, the charges, together with their electrostatic images, interact as needlelike charged polymers. Below a critical thickness, such quasipolyelectrolytes undergo the Berezinskii-Kosterlitz-Thouless transition from a plasmalike state to a charge neutral one. In the latter, all the charges are bound into dipole pairs. Inherent only in thin films, the effect leads to the surfactant condensation into spots that cannot be observed on a single interface at the same surfactant concentration. We quantify a film resistance to rupture in terms of a pore line tension and show that the corresponding energy barrier needed for pore creation is much greater than the energy of thermal excitations.

Silicon-Oxynitride (SiON) for Photonic Integrated Circuits

AbstractWe report on the fabrication and analysis of silicon-oxynitride (SiON) as core material for silicon-based planar photonic waveguide circuits. Features of devices made of this particular SiON material are: (1) a silicon-compatible technology (low-cost perspective), (2) a waveguide structure with high dielectric index contrast, allowing a very compact device layout (approximately 10× smaller radius of curvature than conventional doped SiO2 technology), (3) a low optical loss &lt; 0.15 dB/cm, in the 1550 nm telecommunication window and (4) a negligible polarization dependence. The materials aspects and resulting analyses of the SiON layers as well as particular device properties are described.

Photonic band gaps of three-dimensional face-centred cubic lattices

We show that the photonic analogue of the Korringa-Kohn-Rostoker method is a viable alternative to the plane-wave method for analysing the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of a fcc lattice of homogeneous dielectric spheres, we reproduce the main feature of the spectrum obtained by the plane-wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eighth and ninth bands if the dielectric constant of the spheres is lower than the dielectric constant of the background medium. If , no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of a fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.

A simple formula for the L-gap width of a face-centred cubic photonic crystal

The width $\triangle_L$ of the first Bragg's scattering peak in the (111) direction of a face-centered-cubic lattice of air spheres can be well approximated by a simple formula which only involves the volume averaged $\epsilon$ and $\epsilon^2$ over the lattice unit cell, $\epsilon$ being the (position dependent) dielectric constant of the medium, and the effective dielectric constant $\epsilon_{eff}$ in the long-wavelength limit approximated by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic behaviour of the absolute gap width $\triangle_L$ for high dielectric contrast $\delta$ exactly. The standard deviation $\sigma$ steadily decreases well below 1% as $\delta$ increases. For example $\sigma< 0.1%$ for the sphere filling fraction $f=0.2$ and $\delta\geq 20$. On the interval $\delta\in(1,100)$, our formula still approximates the absolute gap width $\triangle_L$ (the relative gap width $\triangle_L^r$) with a reasonable precision, namely with a standard deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the close-packed case. Differences between the case of air spheres in a dielectric and dielectric spheres in air are briefly discussed.

Two-dimensional FDTD analysis of a pulsed microwave confocal system for breast cancer detection: fixed-focus and antenna-array sensors.

A novel focused active microwave system is investigated for detecting tumors in the breast. In contrast to X-ray and ultrasound modalities, the method reviewed here exploits the breast-tissue physical properties unique to the microwave spectrum, namely, the translucent nature of normal breast tissues and the high dielectric contrast between malignant tumors and surrounding lesion-free normal breast tissues. The system uses a pulsed confocal technique and time-gating to enhance the detection of tumors while suppressing the effects of tissue heterogeneity and absorption. Using published data for the dielectric properties of normal breast tissues and malignant tumors, we have conducted a two-dimensional (2-D) finite-difference time-domain (FDTD) computational electromagnetics analysis of the system. The FDTD simulations showed that tumors as small as 2 mm in diameter could be robustly detected in the presence of the background clutter generated by the heterogeneity of the surrounding normal tissue. Lateral spatial resolution of the tumor location was found to be about 0.5 cm.

Electromagnetic surface modes of a dielectric superlattice: the supercell method

We present a study of the reliability of the supercell method in calculations of surface electromagnetic modes. For a truncated superlattice constituted of nonabsorbing dielectric layers, we demonstrate that the numerical solutions obtained by this method for transverse-electric waves agree with those based on the Bloch theory for the semi-infinite superlattice. A slab of superlattice with at least nine unit cells yields satisfactory convergence to an analytic dispersion relation for the surface modes. In addition, we apply the supercell method to study in detail the dependence of transverse-electric and transverse-magnetic surface waves on the cut-off position in the cell next to the surface. As a specific case, we choose a TiO2/SiO2 superlattice—layers with relatively high dielectric contrast in the visible spectrum. We find the surface modes strongly dependent on the position of the surface. In fact, they appear only for certain terminations. By plotting the field amplitudes, we show that there exist different possibilities for the guidance of surface waves. The variation of the penetration depth of these modes is also discussed.

Active Microwave Sensing of Highly Contrasted Dielectric Bodies

In this work the active tomographic imaging of biological bodies which exhibits a high dielectric contrast is studied. Two approaches based on the Born approximation are presented: a differential reconstruction method which allows to visualize dielectric alterations and a matched synthesis method intended to minimize the distortion suffered by the illuminating field within the body. The presented techniques have been investigated by numerical simulations and experimentally in a cylindrical tomographic microwave system recently developed, considering the possible applications like Hyperthermia treatment monitoring in cancer.

Ground state of an electrorheological fluid.

The ground state of an electrorheological fluid is examined for high dielectric contrast (${\mathrm{\ensuremath{\epsilon}}}_{\mathit{p}}$/${\mathrm{\ensuremath{\epsilon}}}_{\mathit{f}}$\ensuremath{\rightarrow}\ensuremath{\infty}). In contrast to the result of Tao and Sun [Phys. Rev. Lett. 67, 398 (1991)] for the dipole limit, three structures are found to be degenerate: face-centered cubic, hexagonal close packed, and body-centered tetragonal. However, particle column surface energy favors the body-centered tetragonal structure, which has a lower surface energy per particle at the critical volume fraction of particles.

Iterative determination of complex permittivity and SAR distribution of two-dimensional biological body

An iterative inversion procedure is presented for noninvasive measurements of the complex permittivity and SAR distributions of two-dimensional biological bodies. The inversion procedure is tested numerically by using a two-layered circular model having high dielectric contrast.

Procedures for noninvasive electromagnetic property and dosimetry measurements

Five different formulations are presented that can be used to determine local values of the complex permittivity, electric field, polarization current density, and rate of energy deposition, within an inhomogeneous dielectric object of arbitrary shape. These formulations were obtained from the matrix equations for moment-method solutions of the electric field integral equation. Implementation of these formulations requires knowledge of the shape of the object and the incident electric field, and measurements of the scattered electric field at a number of points external to the object. The use of a new type of model, with antenna arrays for measurements, has caused a substantial improvement in matrix conditioning. Results of numerical simulations using 21-cell models with high dielectric contrast (bone/muscle) suggest that all five formulations have sufficient accuracy to warrant experimental testing using cylindrical scatterers with transverse magnetic polarization.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>