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The aim of this paper is to fill in the gaps left in the construction of the effective resonator model of 1D multilayer dielectric structure. In the previous papers [1–4] the model has been proposed and its physical background and interpretation [1, 2, 5], as well as orthonormalization of modes [3, 4] have been described. However, there remain a few aspects of the model, which require a rigorous treatment or explanation. They are discussed in this paper, which is a mathematical supplement to the previous ones. Because of its purpose, general assumptions, notation and definitions of quantities (not recalled in this paper, except of a few cases) are the same as in [2–4]. Discussion of general properties of the model is the topic of Sect. 2. In the next three sections, conclusions are drawn for radiation (Sect. 3), substrate and guided modes (Sect. 4). The last section, Sect. 5, contains a summary of the paper.

Design of directional couplers in an inhomogeneous suspended stripline dielectric structure has been comprehensively investigated. A new design procedure of coupled-line directional couplers has been proposed in which the equalization of inductive and capacitive coupling coefficients is achieved simultaneously with matching to the desired characteristic impedance and, therefore, the conditions of ideal coupler realization can be approached. To achieve that, a method of modification of the capacitive coupling coefficient in which shunt capacitances are added to coupled lines has been used. The proposed design procedure has been successfully applied to the design of a 3-dB directional coupler. Results of both calculations and measurements are presented. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 315–319, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24035

Chapter 7 highlights that most materials found in the Earth’s environment are randomly inhomogeneous in space and time. Their dielectric structure is then characterized by permittivity values that fluctuate about the local average. By using a notation analogous to ( 7.24), permittivity is written $$\displaystyle{ \epsilon (\boldsymbol{r},t) =\epsilon _{0}\left [\,\overline{\tilde{\epsilon }}(\boldsymbol{r}) +\tilde{\epsilon } ^{\,{\prime}}(\boldsymbol{r},t)\right ]\;, }$$ (9.1) where \(\overline{\tilde{\epsilon }}\) is the value of \(\tilde{\epsilon }\) averaged over the ensemble of realizations of the medium and \(\tilde{\epsilon }^{\,{\prime}}\) denotes its slowly fluctuating part. The electromagnetic field produced by a source modeled by its impressed electric current \(\boldsymbol{J}_{\!\mathrm{s}}\) satisfies the spectral Maxwell’s equations ( 2.1)–( 2.2): $$\displaystyle\begin{array}{rcl} \nabla \times \boldsymbol{E}& =& -\mathrm{j}\omega \mu _{0}\boldsymbol{H}\;;{}\end{array}$$ (9.2) $$\displaystyle\begin{array}{rcl} \nabla \times \boldsymbol{H}& =& \mathrm{j}\omega \epsilon _{0}\left [\,\overline{\tilde{\epsilon }}(\boldsymbol{r}) +\tilde{\epsilon } ^{\,{\prime}}(\boldsymbol{r},t)\right ]\boldsymbol{E} + \boldsymbol{J}_{\!\mathrm{ s}}\;,{}\end{array}$$ (9.3) which, given the presence of the fluctuations of permittivity which introduce a random parameter into (9.3), are stochastic Maxwell’s equations , even if, unlike the thermal currents in ( 8.1) and ( 8.2), now the source is deterministic. The equations yield the quasi-monochromatic field in the random medium characterized by (9.1).

Dynamics of a laser exploiting two-dimensional distributed feedback is considered. Two-dimensional distributed feedback can be realised using a dielectric structure (two-dimensional Bragg resonator) with the width having double-periodical modulation. It is shown that such a structure can provide production of spatial coherent radiation from extended active medium of planar geometry.

Opale sind selbstorganisierte, kubisch dichtest gepackte Kolloidkristalle mit Kolloid-Durchmessern im Nanometer- und Submikrometerbereich. Aufgrund der periodisch modulierten Dielektrizitatskonstante bilden sich photonische Bandlucken aus, so dass die Ausbreitung von Licht mit Wellenlangen in der Grosenordnung der Gitterkonstanten unterdruckt wird. Dies erklart u.a. den brillianten Farbeindruck. Opale konnen synthetisch aus Polymer- oder Metalloxidkolloiden in einem Bottom-up-Prozess hergestellt und auf vielfaltige Weise chemisch funktionalisiert, strukturiert oder als Template fur ihre invertierten Strukturen verwendet werden. Anwendungsgebiete reichen von optischen Chips, Farbdisplays und Effektpigmenten bis hin zu Biosensoren. Opals are self-assembled fcc-packed colloidal crystals with sphere diameters in the nanometer and submicrometer region. The periodic dielectric structure leads to the opening of photonic band gaps that suppress the propagation of light with wavelengths at the lattice constant scale. This explains e.g. the opals' brilliant color impression. Synthetic opals can be prepared from polymer or metaloxide spheres in a bottom-up approach that allows for chemical functionalization and processing. Also, they can be used as templates to fabricate inverted structures. Fields of application reach from optical chips, color displays and effect pigments to biosensors.

The spontaneous emission (SE) of Er3+ embedded in a double slot dielectric structure was studied by a quantum-electrodynamical formalism. The study shows that the slot width and the position of Er3+ in slot structure have a significant effect on the SE. The double slot waveguides were fabricated by embedding two low-index Er/Yb silicate material layers into high-index silicon. The radiative efficiency of Er3+ in the double slot waveguides is found to be higher than that of the single slot waveguide, which is consistent with the theory simulation. The 0.67 dB signal enhancement at 1.53 µm in a 4.6-mm-long slot waveguide was observed pumped by 1476 nm laser. These results show the relevance of our model to study the SE processes in multilayer structures and are important for future realization of silicon-compatible active optical devices.

Measurements of the negative optical phase shifts of Ag/TiO 2 and Ag/SiO 2 bilayer films have been carried out with the modified walk-off interferometer. Appearance and monotonic rise of the phase shift anisotropy for p- and s-polarization by increasing incidence angle has been revealed experimentally. The results of measurements have shown rather good coincidence with theoretical calculations.

The spectra of hybrid EMSOs in the composite ferrite-dielectric structure based on single crystal BaFe 12 O 19 with the MDS in initial state were experimentally investigated. As it can be seen from Fig. 2 the fact of simultaneous hybridization of both MSOs modes ω 1 and ω 2 with DR electromagnetic mode one has been revealed. It should be emphasized that as the result of ω 1 and ω 2 interaction with DR electromagnetic mode the three quasi-electromagnetic modes are observed for the first time even at low external in-plane static biasing magnetic fields.

A technique for calculating the effective dielectric constant for a square loop FSS located in a layered dielectric structure was developed using conformal mapping techniques. This was accomplished by approximating the FSS as a set of two coplanar strips, for which a conformal map already exists. This method yields results comparable to those found through simulation, while having a shorter computation time. Furthermore, this method can be used for arbitrary square loop FSS designs and layered dielectric structures.

Theory predicts that the deposition of a nanostructured dielectric film on the surface of a semiconductor quantum well will modulate its optical properties due to interactions between the quantum well exciton and the dielectric structure. We have chosen a columnar discotic triphenylene as dielectric medium since the columnar structure is able to provide spatial, and thus dielectric, modulations both on a 2 or a 0.4 nm scale, depending on the columnar orientation within the film. Film deposition on quantum well structures and model substrates by spincoating and via the vapour phase, in combination with annealing steps, gave rise to a rich spectrum of textural modifications and columnar orientations in the dielectric films. The investigations revealed significant modulations of the optical properties of the quantum well as a function of the textures and the columnar orientational order.

We present the computer code for a full-vector analysis of the fields inside a multilayer structure with an arbitrary number of layers. The code is validated by the analysis of a microwave resonator realized with thin-film technology. The periodic boundary conditions in the multilayer structure are derived for the cavity resonator. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 48–51, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20543

We investigate the longitudinal and transverse dynamics of sub-relativistic electrons during the trapping process, as facilitated by an adiabatically tapered dielectric structure. The characteristics of the trapped electrons are studied for different initial conditions and structure's parameters. A set of optimal parameters that exemplify our approach are presented. Specifically, we determine the condition where the transverse emittance is preserved during the trapping process.

Using the concept of generalized Wannier functions, adapted from the electronic theory of solids, we demonstrate for two-dimensional photonic crystals the existence of a localized state basis and we establish an efficient computational method allowing a tight-binding-like parameter free modelization of any dielectric structure deviating from periodicity. Examples of numerical simulations using this formalism, including modal analysis of microcavities and waveguides are presented to prove the ability of this approach to deal accurately with large scale systems and complex structures. A tight-binding version of the transfer matrix method is proposed to describe the transmission and reflection properties of finite samples of photonic crystals.

This work proposes a liquid-crystal lens based on a dual-frequency liquid crystal (DFLC) and a surface-relief (SR) dielectric structure on an electrode. The proposed LC lens can be controlled between a positive lens (lens power m) and a negative lens (lens power m ) by using the frequency modulation. Additionally, a dielectric effect occurs between the DFLC and the SR dielectric under the frequency modulation, enabling the LC lens to exhibit a much more uniform response-time distribution than a conventional LC lens.

We show that a purely dielectric structure made of alternating layers of deep subwavelength thicknesses exhibits novel transmission effects which completely contradict conventional effective medium theories exactly in the regime in which those theories are commonly used. We study waves incident at the vicinity of the effective medium's critical angle for total internal reflection and show that the transmission through the multilayer structure depends strongly on nanoscale variations even at layer thicknesses smaller than $\ensuremath{\lambda}/50$. In such deep subwavelength structures, we demonstrate dramatic changes in the transmission for variations in properties such as periodicity, order of the layers, and their parity. In addition to its conceptual importance, such sensitivity has important potential applications in sensing and switching.

The ability of an electro-optic system is here demonstrated for the mapping of the electric field vector over a wide bandwidth. Thanks to their dielectric structure, such sensors are intrinsically very low invasive and allow to perform near field analysis. Even in the reactive area of radiative devices, the probe allows to characterize the field vector distribution with a dynamics exceeding 120 dB. The associated spatial resolution is weaker than 500 μm and the measurement bandwidth reaches more than 10 GHz.

We study the localization of light in the disordered dielectric structures derived from periodic systems with photonic band gaps. It is directly shown by field pattern that with moderate disorder there exist strongly localized states in the original gap. The localization-delocalization-localization trilogy discovered in this paper embodies the concept ‘‘interplay between the order and disorder’’ that has been previously suggested, and it is pointed out that the complete understanding of this complex localization behavior should take into account two localization mechanisms with different ranges of coherence. The difference between the two localization mechanisms is demonstrated by the different localization behaviors of the TM and TE modes. The C number is introduced to show the localization centers are frequency dependent. The frequency distribution of localization centers is found to vary with the degree of disorder. @S0163-1829~99!00638-4#

The dielectric structure of mature pollen of the angiosperm Lilium longiflorum was studied by means of single-cell electrorotation. The use of a microstructured four-electrode chamber allowed the measurements to be performed over a wide range of medium conductivity from 3 to 500 mS m-1. The rotation spectra of hydrated pollen grains exhibited at least three well-resolved peaks in the kHz-MHz frequency range, which obviously arise due to the multilayered structure of pollen grains. The three-shell model can explain the complex rotational behavior of pollen grains in terms of conductivities, permittivities and thicknesses of the following compartments: the exine and intine of the pollen grain wall as well as the membrane and cytoplasm of the vegetative cell. However, the number of unknown parameters (more than 8) was too large to allow unambiguous values to be assigned to any of them. Therefore, to facilitate the evaluation of the pollen grain parameters, additional rotational measurements were made on isolated vegetative and generative cells. The rotation spectra of these cells could be fitted very accurately on the basis of the single-shell model by assuming a dispersion of the cytoplasm. The data on the membrane and cytoplasmic properties of isolated vegetative cells were then used for modeling the rotation spectra of pollen grains. This greatly facilitated the fitting of the theoretical model to the experimental data and allowed the dielectric properties of the major structural units to be determined. The dielectric characterization of pollen is of enormous interest for plant biotechnology, where pollen and isolated germ cells are successfully used for production of transgenic crop and drug plants of economic importance by means of electromanipulation techniques.

Multi-layer dielectric devices used for isolated power transfer and suitable for high frequency power applications (>100kHz) are proposed. Such devices were realized based on a four terminal multi-layer ceramic structure with barium strontium titanate and alumina layers. Some key advantages of these devices are a reduction in losses over conventional decoupling techniques and ease of manufacturing due to the planar design. The paper focuses on the design details, characterization and performance of the Multi-Layer Capacitive Isolation Devices (MLCIDs).

We present analysis and design optimization of passive UHF RFID (Radio Frequency Identification) tags for tracking automotive tires. The RFID tags are mounted on or embedded into tires to monitor their conditions, verify their history and track inventory. In this paper, we evaluated the performance of existing RFID tags designed specifically for tires. It is found that the current RFID tags do not operate well in the vicinity of adjacent tires. This is due to the tire's dielectric structure and metallic radial plies inside the sidewalls. These factors were also verified in simulation models. Recommendations for new tag designs will be provided at the meeting.

The topographical and physico-chemical complexity of protein-water interfaces scales down to the sub-nanoscale range. At this level of confinement, we demonstrate that the dielectric structure of interfacial water entails a breakdown of the Debye ansatzthat postulates the alignment of polarization with the protein electrostatic field. The tendencies to promote anomalous polarization are determined for each residue type and a particular kind of structural defect is shown to provide the predominant causal context Fil: Fernandez, Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina

We here illustrate the ability of electro-optic sensors to perform electric field vectorial measurements. Thanks to their frequency response that remains flat over nine decades and to their measurement dynamics reaching 120 dB, these sensors are of key interest for many applications. Furthermore, due to their fully dielectric structure and to their millimetric size, almost no perturbation is induced on the electric field to be measured, even in the near field region. This paper is focused on high intensity pulsed electric field characterization in different environments such as water (bioelectromagnetism applications) or plasma (in-situ assessment of the electric-field associated to an electric discharge). The use of such technology for electrical equipments and energy lines monitoring is also investigated.

The tunnelling of optical beams through chirped Bragg grating is considered. Lateral shifts of transmitted and reflected beams were calculated. The saturation of Goos-Hanchen shift of transmitted light beams is shown.

A radome is a dielectric structure that is used to protect an antenna from its environment (wind, rain, ice, salt spray, dust, insects), and it may be used to reduce aerodynamic drag. Radomes serve as feed covers, covers attached to the antenna, or covers within which an antenna moves. Therefore, they have a wide variety of shapes and wall structures (Huddleston and Bassett 1993).

We study the spatial modulation instability (MI) in a system of coupled surface plasmon polaritons propagating at a dielectric–metal–dielectric interface. One of the dielectric media considered is nonlinear and active, which provides enough gain to compensate for the losses in the metal. It is found that the system is unstable for both focusing or defocusing nonlinearity, with more instability in the focusing case. It is noted that nonlinearity is one of the key parameters for instability, with the real part controlling the maximum MI gain and the imaginary part controlling the MI gain saturation. Gain provided by the active medium is also an important parameter for the development of MI in the system. The generated sidebands are amplified as they propagate along the interfaces. We have noted that the defocusing case requires a large gain threshold to exhibit modulation instability for a symmetric solution.

New reflowable organic spin-on glass (SOG) was developed to form planarized multilevel interconnections for ULSIs. This SOG had superior gap-filling and plan-arizing characteristics compared to those of conventional organic SOGs. For example, using this SOG, a 0.025-μm wide trench with an aspect ratio of over 10 could be perfectly filled without void. The surface of a three-layered interlevel dielectric structure with this SOG was four times smoother than that with a conventional organic SOG. It was found that the excellent gap-filling planar-izing property of this SOG was due to the low temperature reflow (100 to 200°C). The film quality was almost the same as that of an organic SOG which has been widely used and has exhibited sufficient reliability. That is, this organic SOG gives a sufficient reliability with far improved gap-filling and planarization. Since the relative dielectric constant of this SOG is as low as 3.0, this SOG is promising to improve the operation speed of ULSI.

A novel technique for backscattering reduction for both TE and TM polarisations, employing a metallo-dielectric structure based on Sierpinski carpet fractal geometry, is reported. A reduction in backscattered power of ∼30 dB is obtained for normal incidence in the X-band for the structure using the third iterated stage of the fractal geometry. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 246–248, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11342

An efficient approach to design the structure of diffractive optical elements is presented. We have developed a novel vectorial diffraction method that the amount of memory consumption is almost free from the entire size of dielectric structure. In the process of the device design, we update the diffracted wave by adding groove patterns on the surface one by one so that the updated wave approaches to the desired one. The necessary memory for two-dimensional structure is only around 20 MB, and our method is sufficient with a desktop computer to perform an accurate designing even including the polarization characteristics.

In this paper, we analyzed the distribution of energy flow for dielectric waveguide introduced as defect layers composed of dielectric circular cylinder array with de formed rhombic dielectric structure along a middle layer and investigated the influence of rhombic dielectric structure compared with deformed rhombic dielectric structure by using the propagation constants at the guided area for both TE0 and TM0 modes.

The base dielectrics of commercial low temperature cofired ceramics (LTCC) systems have a temperature coefficient of resonant frequency ({tau}{sub f}) in the range -50 {approx} -80 ppm/C. In this research we explored a method to realize zero or near zero {tau}{sub f} resonators by incorporating {tau}{sub f} compensating materials locally into a multilayer LTCC structure. To select composition for {tau}{sub f} adjustment, {tau}{sub f} compensating materials with different amount of titanates were formulated, synthesized, and characterized. Chemical interactions and physical compatibility between the {tau}{sub f} modifiers and the host LTCC dielectrics were investigated. Studies on stripline (SL) resonator panels with multiple compensating dielectrics revealed that: 1) compositions using SrTiO{sub 3} provide the largest {tau}{sub f} adjustment among titanates, 2) the {tau}{sub f} compensation is proportional to the amount of SrTiO{sub 3} in compensating materials, as well as the thickness of the compensating layer, and 3) the most effective {tau}{sub f} compensation is achieved when the compensating dielectric is integrated next to the SL. Using the effective dielectric constant of a heterogeneous layered dielectric structure, results from Method of Momentum (MoM) electromagnetic simulations are consistent with the experimental observations.

We propose an experiment involving a gaussian laser tunneling through a twin barrier dielectric structure. Of particular interest are the conditions upon the incident angle for resonance to occur. We provide some numerical calculations for a particular choice of laser wave length and dielectric refractive index which confirm our expectations., 15 pages, 6 figures

A multiple scattering formulation of two-dimensional (2D) acoustic metamaterials is presented. This approach is comprehensive and can lead to frequency-dependent effective parameters (scalar bulk modulus and tensorial mass density), as it is possible to have not only positive or negative ellipsoidal refractive index, but also positive or negative hyperbolic refractive index. The correction due to multiple scattering interactions is included in the theory and it is demonstrated that its contribution is important only for lattices with high filling fractions. Since the surface fields on the scatterers are mainly responsible for the anomalous behavior of the resulting effective medium, complex scatterers can be used to engineer the frequency response. Anisotropic effects are also discussed within this formulation and some numerical examples are reported. A homogenization theory is also extended to electromagnetic wave propagation in 2D lattices of dielectric structures, where Mie resonances are found to be responsible for the metamaterial behavior. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft., This work was partially supported by the US Office of Naval Research under grant number N000140910554 and the Spanish Ministry of Science and Innovation under contract numbers TEC2010-19751 and CSD2008-66 (the CONSOLIDER program). Daniel Torrent also acknowledges support from the contract provided by the program 'Campus de Excelencia Internacional' 2010 UPV.

We consider the finite-difference counterpart, i.e., the true lattice analog, of Maxwell's equations and equations that govern the propagation of acoustic waves in a medium with a periodic dielectric structure. In particular, the vector nature of electromagnetic waves is fully taken into account. The existence of true gaps for these lattice models is proved for a two-component medium for which the dielectric constant is everywhere real and positive, and the dielectric constant of the background is essentially larger than the one corresponding to the embedded component.

The formation of vertical contact openings through planarized dielectric layers requires either very high etch selectivity between SiO 2 and silicon substrates or modification of the dielectric film structure to offset the need for extreme etch selectivity

In this paper, accuracy of equivalent models for composite materials based on a multilayer lossy dielectric structure is discussed. Three different models are described. These models are based on scalar or incomplete vector measurements of coefficients S11, S22 and S21. Agreement between simulated values of the magnitude of the reflection and the transmission coefficient and the coefficients predicted by the models is investigated within range of frequencies 100 MHz to 20000 MHz. Magnitude errors of coefficients predicted by the best of the models is 2 dB for transmission and 6 dB for the reflection coefficient. These errors are valid for both polarizations (TE and TM) and range of angles of incidences from 0 to 60 deg.

The paper describes some kinds of Photonic Crystal Fibers and their features. The problems of attenuation of the PCF in connection with their properties and design are discussed. An analytical method for calculating the attenuation and dispersion of the spreading modes of Bragg fibers, represented as a multilayer dielectric structure, is proposed. An example for illustration of the opportunity of the method is included.

In this paper, we give a complete analytical solution for wakefields generated by an azimuthally symmetric ring beam propagating in a coaxial two-channel dielectric structure. This wakefield can be used to accelerate a witness beam in the central channel. The ratio of the peak accelerating field in the center channel to the decelerating field in the ring channel (defined as transformer ratio $R$) is also derived. We find that, by appropriate choice of parameters, $R$ can be much greater than 2, the limiting value for collinear wakefield accelerators.

The passage of a free-electron beam through a nanohole in a periodically layered metal-dielectric structure creates a new type of tunable, nanoscale radiation source-a >light well>. In the reported demonstration, tunable light is generated at an intensity of ∼200W/cm2 as electrons with energies in the 20-40keV range are injected into gold-silica well structures with a lateral size of just a few hundred nanometers. © 2009 The American Physical Society., The authors from the University of Southampton acknowledge the support of the UK Engineering and Physical Sciences Research Council (EPSRC, Projects No. EP/C511786/1 and No. EP/F012810/1) and the European Union (FP6 Project No. NMP4-2006-016881, ‘‘SPANS’’); Those from the National Taiwan University thank the National Science Council of Taiwan (NSC-97- 2120-M-002-013, NSC-97-2112-M-002-023-MY2, and NSC-97-2915-I-002-001) and the EPSRC (EP/F012810/ 1); Professor Garcı´a de Abajo acknowledges the European Union (NMP4-2006-016881) and the Spanish MEC (MAT2007-66050 and Consolider ‘NanoLight.es’).

An improved SIAD structure for planar microstrip circuits' miniaturization has been presented in this paper. This structure provides enhancement of both the permittivity and the permeability, and therefore achieves guided wavelength compression, leading to circuit size miniaturization. By proper design of the SIAD, power divider can exhibit an area reduction of 74%. By change the SIAD geometrical parameters, one may achieve more area reduction. The improved SIAD structure has the potential to miniaturize many planar component and antenna applications at low cost.

Simplified equations for calculating the total reflection and transmission from a multilayer infinite and finite dielectric structure are presented. These formulas are based on examining the reflected rays within such a structure and working out an explicit form where possible. The purpose of this study is to build a simplified simulator for ground penetrating radar.

Comparison of coherent and noise probing is described in order to formulate the criteria for characterization of materials on mm-wave and microwave frequencies. Double-layers dielectric structure having Fabry-Perot resonator properties is employed to develop accurate mathematical model and to predict transmittances for both coherent and noise illuminations. Experiments have proved the basic modeling predictions as well as the role of noise bandwidth in averaging process used in material characterizations.

The scattering behaviour of Sierpinski gasket based metallo-dielectric structure loaded over metallic targets is reported. RCS reduction is obtained for the structure with frequency about 9-11 GHz. Furthermore, we have presented a fitted linear equation to describe the relationship between reduction peak frequency vs permittivity. This may has application in stealth of aircrafts or ships and the design of frequency selective surfaces.