Dielectric Waveguide Theory Research Articles

Transforming terahertz plasmonics within subwavelength hole arrays into enhanced terahertz mission via Smith-Purcell effect.

We illustrate the transformation of terahertz plasmonics within an array of rectangular sub-wavelength holes (RSHs) into coherent and enhanced terahertz emission via Smith-Purcell effect. The radiative plasmonic modes within each RSH of the array are successively excited by an free-electron beam, which then generate coherent radiation by constructive interference. Compared with the case without taking plasmonics into consideration, the radiation field intensity is enhanced by more than an order of magnitude, affording a promising way of developing high-power terahertz radiation. We perform detailed analysis of the plasmonic modes within the RSH by using the dielectric waveguide theory, and the results are verified by numerical simulations. The influences of the RSH parameters on the radiation properties are revealed and discussed.

Error estimates for a Galerkin method with perturbations for spectral problems of the theory of dielectric waveguides

We obtain error estimates for a Galerkin method with perturbations for approximating eigenvalues and eigenfunctions of one class of abstract spectral problems. Using these results, we get the justification of applying the method for spectral problems of the theory of dielectric waveguides.

Introduction to the Issue on Optical Waveguide Technology and Applications

The papers in this special section focus on optical waveguide technology and applications for its use. It seems a long time ago since Hondros and Debye in the year 1910 published the Cylindrical Dielectric Waveguide Theory and since Charles Kao in the 1960s developed the first breakthroughs of fiber optic technology. Huge steps, however, have been made since then to develop optical fibers into components, systems, and optical fiber networks. Groundbreaking research has allowed access to THz bandwidth from optical fibers carrying today’s huge Internet traffic. Advances in lasers, optical fiber amplifiers, and numerous optical fiber types, components, and devices have been developed promising even further strides in pushing performance barriers and the optical fiber as the core medium for the future of human communications and a necessary part of infrastructure for improving quality of human life.

Ultrafast self-action of surface-plasmon polaritons at an air/metal interface

We investigate both theoretically and experimentally the nonlinear propagation of surface-plasmon polaritons (SPP) on a single air/metal interface. Inspired by nonlinear dielectric waveguide theory, we analytically derive a model that describes the nonlinear propagation of SPPs, thus bridging the description of plasmonic and dielectric waveguides. The model, the numerical simulations, and the experiments, which are carried out in the 100 fs regime, reveal that the SPP undergoes strong ultrafast self-action which manifests itself through self-induced absorption. Our observations are consistent with a large, bulk, third-order nonlinear susceptibility $({\ensuremath{\chi}}^{(3)})$ of gold and provide a self-consistent theory of self-action of SPPs at an air/metal interface. Experimentally, we find $\mathrm{Im}{{\ensuremath{\chi}}^{\ensuremath{-}(3)}}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{2}/{\mathrm{V}}^{2}$. These findings have important implications in the nonlinear physics of plasmonics and metamaterials as they provide evidence that nonlinear absorption has a significant effect on the propagation of SPPs excited by intense optical pulses. This self-action is also expected to affect the anomalous absorption of light near subwavelength structures as well as the strength of desirable nonlinear processes such as third-harmonic generation and four-wave mixing, which will inevitably compete with nonlinear absorption.

Multi-port admittance model for quantifying the scattering response of loaded plasmonic nanorod antennas.

In this paper we demonstrate the feasibility of using multiport network theory to describe the admittance properties of a longitudinally loaded plasmonic nanorod antenna. Our analysis reveals that if the appropriate terminal ports are defined across the nanorod geometry then the corresponding voltage and current quantities can be probed and thus it becomes feasible to extract the admittance matrix of the structure. Furthermore, it is demonstrated that by utilizing cylindrical dielectric waveguide theory, closed form expressions can be derived that uniquely characterize the loading material in terms of its admittance. The combination of the admittance matrix information along with the load admittance expressions provides an effective methodology for computing the nanorod's input admittance/impedance for arbitrary loading scenarios. This is important because the admittance resonances are associated with the structure's scattering peaks which are excited by a plane wave polarized parallel to its long dimension. Subsequently, the proposed approach provides a fast and computationally efficient circuit-based methodology to predict and custom engineer the scattering properties of a loaded plasmonic nanorod without having to rely on repetitive lengthy full wave simulations.

Theoretical analysis of surface plasmon resonance in capillary sensors

Surface plasmon resonance (SPR) sensors are tending toward miniaturization, and easy-to-use, low-cost sensors are in demand. Here, to meet this demand, we propose a capillary SPR sensor consisting of a capillary with a gold film plated onto the inner wall. A simple ideal model is constructed, cylindrical metal–dielectric waveguide theory is discussed, analytic equations are established, and the SPR curve of the capillary containing water was obtained by calculating the reflectivity. Optical simulations were also carried out in TracePro, and the simulation results are shown to be consistent with the theoretical calculations. Both ideal and Gaussian light sources are studied and small differences in the spectra are compared. Sensor performances and the CCD placement were also discussed. A method of s-polarized light as reference light to eliminating aberration was introduced. The results demonstrate the feasibility of the proposed capillary SPR sensor.

Characteristics of Electromagnetic Waves Propagation in Corridor for High-Rise Buildings

With the popularity of wireless communication systems, the question of radio signal coverage is getting more and more attentions in corridor for high-rise buildings. Using loss rectangular dielectric waveguide theory, the attenuation of electromagnetic wave transmission rate is calculated in theory. Because of the complexity of electromagnetic waves propagation conditions, site measurement of transmission loss is done in band 210MHz, 460MHz, 1.2GHz and 2.0GHz. Measurement results show that the wireless signal transmission loss rate is similar with the calculation of loss rectangular dielectric waveguide theory on the trend

INEXPENSIVE AND EASY FABRICATION OF MULTI-MODE TAPERED DIELECTRIC CIRCULAR PROBES AT MILLIMETER WAVE FREQUENCIES

Tapered dielectric flbers are widely used in the near fleld microscopy to focus the incident beam or collect near fleld signal. Single mode is always required so that the geometrical dimension of the waveguide is smaller than the wavelength. This paper proposes an inexpensive and easy fabrication of multimode tapered Te∞on probe which has bigger dimensions than the wavelength. The fleld distribution in and outside the probe is analyzed by the total internal re∞ection theorem and solid core circular dielectric waveguide theory. Simulations are carried out in Microwave Studio CST. Novel applications based on focal points in and outside the probe are discussed, especially dielectric permittivity sensing of biomolecules using a capillary tube is emphasized by the simulations and experiments.

Exact Nonlocal Boundary Conditions in the Theory of Dielectric Waveguides

The original problem in an unbounded domain is reduced to a linear parametric eigenvalue problem in a circle, which is convenient for numerical solution. The examination of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. The existence of surface guided waves is proved, and properties of the dispersion curves are investigated. An algorithm for the numerical solution of the problem based on the flnite element method is proposed. The convergence of the numerical method is proved. Numerical results are discussed. 1. INTRODUCTION Optical waveguides are dielectric cylindrical structures that can conduct electromagnetic energy in the visible and infrared parts of the spectrum. The waveguides used in optical communication are ∞exible flbers made of transparent dielectrics. The cross section of a waveguide usually consists of three regions: the central region (core) is surrounded by a cladding which, in turn, is surrounded by a protective coating. The dielectric permittivity of the core can be constant or can vary over the cross section; the dielectric permittivity of the cladding is usually positive constant (denote it by 1). The coating is optically isolated from the core; for this reason, it is usually neglected in mathematical models, and it is assumed that the cladding is unbounded from the outside. We use the classical model (see (1)), in which the waveguide is assumed to be unbounded and linearly isotropic. A mathematical analysis of surface waves based on the theory of unbounded self- adjoint operators can be found in (2). In that paper, the original problem is considered as a problem of the form A(fl)H = k 2 H with respect to the spectral parameter k 2 , and the dependence k = k(fl) is studied (H is the magnetic vector amplitude, k is the wavenumber, fl is the propagation constant). In (3), a similar technique is used to extend the results obtained in (2) to the case of waveguides with a variable magnetic permeability. The results obtained in (2,3) give a complete understanding of the qualitative properties of the spectrum of surface guided waves; however, in order to calculate the spectral characteristics of waveguides, numerical methods are needed (see survey (4)). The formulations of the problems used in (2,3) are not quite convenient for obtaining numerical solutions. This is due to two speciflc features of those statements. 1. The problems are formulated for the entire plane R 2 . For a numerical solution, special measures must be taken to restrict the integration domain and to formulate additional boundary conditions. 2. Spectral problems (except for a point spectrum) have a continuous part of the spectrum. Although the location of this part is known exactly, a numerical solution requires that false ap- proximate solutions be detected and discarded. Statements of problems suggested in (5,6) are free of those drawbacks. In those papers, exact nonlocal boundary conditions (see (7,8)) are used to reduce the problems that were originally formulated for the entire planeR 2 to equivalent problems in a circle. In (5,6) the spectral problems are formulated in a circle › which includes waveguide's cross-section domain ›i (see Fig. 1); these problems have no continuous spectrum. Moreover, their spectrum is identical to the point part of the spectrum of the original problem. These statements are convenient for the flnite element method. The cost of this advantage is that the spectral parameter appears in the equation in a nonlinear fashion; more precisely, the problems have the form A(fl;‚)H = ‚H, where A is a compact self-adjoint operator. The solution of such problems requires the use of special iterative methods. In this paper, we use a new formulation of the problem proposed in (9). The original problem by exact nonlocal boundary conditions method is reduced to an equivalent linear self-adjoint eigenvalue problem A(p)H = fl 2 B(p)H in the circle ›. Here, the parameter p is the transverse wave number p =

Leaky and bound modes of surface plasmon waveguides

While theoretical studies of finite width plasmonic waveguides have focused on the bound modal solutions of metallic structures in homogeneous or near-homogeneous dielectric matrices, experimental studies have mainly probed the leaky surface plasmon modes along the air-exposed surfaces of metallic stripes on glass substrates. Combining a full-vectorial, magnetic field finite-difference method with complex coordinate stretching perfectly matched layer boundary conditions, we have solved for both the leaky and bound modes of metallic slab and stripe waveguides. Solutions for the leaky modes excited via attenuated total reflection in the Kretschmann configuration provide added insight into the results of recent near and far-field experimental studies. For these cases, an analytical approximation for the number of allowed modes as a function of waveguide width is derived based upon the guidance condition of dielectric waveguide theory. Then, consistent with a ray optics interpretation for surface plasmon-polariton propagation, a direct comparison is made between our simulations and published results with regard to field profiles and propagation lengths.

Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function

Motivated by problems in scanning near-field optical microscopy, we discuss light propagation in circular dielectric waveguides with finite aluminum cladding. In order to understand the origin of the different solutions, optical modes are first investigated for the dielectric waveguide with infinite aluminum cladding and for the aluminum cylinder. For aluminum a plasma dispersion law is assumed, leading to complex dielectric constants with negative real parts and to generally complex propagation constants. The dependence of the dispersion on the geometry and on the frequency is discussed for the various kinds of modes. We find that the existence of most of the modes is limited to certain frequencies and geometries, i.e., the solutions have a cutoff in the complex propagation constant plane. Contrary to dielectric waveguide theory, where cutoff describes the abrupt transition from propagating to evanescent modes, no other solution is generated when cutoff of a mode is reached. Surface modes and other kinds of modes, such as guided or bulk modes, can either couple between each other or transform into each other.

An electromagnetic theory of dielectric waveguides with multiple embedded cylinders

We consider a dielectric waveguide or optical fiber having a real isotropic ambient refractive index. In addition, several isotropic and uniform embedded cylindrical regions of differing refractive index are considered. The radii, refractive indexes, and positions of the cylindrical subregions are arbitrary. We establish a rigorous method of determining the fields and propagation constants for the vector electromagnetic modes supported by this structure. We verify the accuracy of the method by comparing its results with those of other authors in particular cases, and exhibit direct demonstrations of convergence.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A remark about mode coupling in guided wave optics

An alternate derivation of a well-known coupled-mode theory of dielectric waveguides is presented to discuss the roles of slowly varying amplitude approximation and phase matching condition. The approach is based on two vector wave equations for electric and magnetic fields and no approximations are needed. The resulting coupled-mode equations for ideal modes are shown to be the same as those coming directly from Maxwell’s equations.

Theory of superpotentials in a graded-index dielectric waveguide

This paper deals with the theory of dielectric waveguides in a graded-index media. The theory is first developed in terms of electrical and magnetic potentials and a gauge condition which is a generalization of the Lorentz gauge used in classical electromagnetic theory for the isotropic, homogeneous medium. The existence of these potentials under the generalized Lorentz gauge in the context of a generalized Helmholtz theorem are then proven. Even though this generalized gauge uncouples the governing equations, it does not lead to partial differential equations in the normal form. To alleviate this problem, superpotentials of the Hertzian variety are introduced and it is shown how equations governing the vector superpotential can be reduced to a form which is amenable to standard analysis. Then several uniqueness theorems associated with this superpotential are proven. As an illustration of the use of the superpotential and its relative merits, it is applied to certain waveguide problems in an inhomogeneous medium with variable permittivity.

A Waveguide Model for the Evening Type Transequatorial VHF Propagation: Comparison with Experiment for the Euro-African Sector

ABSTRACT A waveguide model is proposed for the evening type transequatorial propagation mode. Field aligned irregularities observed in equatorial ionosphere are assumed to form dielectric waveguides. A local Champan type layer electron density distribution is taken inside the guide. The transequatorial wave propagation is treated by using this model and the propagation theory of dielectric waveguides. The total attenuation is computed between two points located in opposite hemispheres. The analytic form of the results permits easy interpretation of the propagation characteristics. A good agreement is observed between the experimental results and the theoretical calculations for the total attenuation. Comparisons have also been done for the propagation delay and the incoming elevation angle at the reception point.

Coupled wave propagation in closely spaced dielectric rod waveguides

In this paper the coupling between two parallel dielectric rod waveguides is investigated analytically. An intergal equation approach is employed in conjuction with Green~ function theory of dielectric waveguides. Cylindrical vector wave functions are used to expand the guided waves inside and outside of the dielectric rod wav~guides. The case of dissimilar guides is examined in detail. Furthermore several coupling geometries are investigated and simplifications are introduced to develop a design procedure for millimeter wave directional couplers.

Analysis of propagation characteristics of radio waves in tunnels using a surface impedance approximation

A simple approximate method to analyze the propagation of radio waves in tunnels is proposed, based on a surface impedance assumption. This method is used, as a basic application, to determine the propagation constants of normal modes in circular tunnels bounded by a uniform lossy dielectric or bounded by two lossy dielectric layers. From the comparison of numerical results it is shown that our approximate solutions agree with the exact ones obtained from the general dielectric waveguide theory, with enough precision for practical purpose.

Additivity of the Stiles-Crawford effect for a Fraunhofer image

Additivity of the Stiles-Crawford effect over pupil area was examined for a Fraunhofer image focused on the retina. Two hypotheses were compared: (1) the Stiles-Crawford effect is absent under these conditions because the wavefronts are flat near focus: and (2) the Stiles-Crawford effect is additive for all positions of focus. Consideration of wave-superposition principles along with dielectric waveguide theory leads to the prediction of additivity. Additivity was tested indirectly by comparing increment thresholds for focused and defocused test flashes viewed through an annular pupil, and directly by comparing thresholds for focused test flashes viewed through the annulus to those viewed through (1) a small, centered, circular pupil and (2) a small section of the annulus. Additivity was found to hold precisely for all conditions: the nonadditivity hypothesis was rejected.

Insect antennae with special reference to the mechanism of scent detection and the evolution of the sensilla

A review of insect antennae sensilla is given and the dimensions and forms of the sensilla are related to dielectric waveguide theory. The design criteria for antennae include dielectric constant measurements, shapes, molecular emitters (molecules), length/wavelength, thin layer outer covering of sensilla, and the electret properties of antennae. Sensilla are described in terms of open resonator-waveguide theory, and the length and diameter of various species of insects are fitted to the 2 wavelength criteria of open resonator design. The importance of tapering the open resonator sensilla for good frequency “fit” is emphasized. Characteristics of molecules of insect attractants are described in terms of their luminescent and fluorescent properties. The surface textures of various types of insect sensilla are related to the form characteristics of efficient open resonator systems. Surface textures found on insect sensilla include smooth, corrugated, helical, equiangular, terraced, and furrowed. The attraction of molecules to sensilla pores is demonstrated and explained in terms of the electret properties of the outer wax layer of the epicuticle. The various shapes of the sensilla are classified into 15 categories, all of which except No. 15 (corn ear configuration) can be found described and utilized by man-made communication systems in the microwave region. A table is given of the vibration frequency range of various orders of insects, and the frequencies are related to the modulation content of infrared emissions from host plant and pheromone attractants. The Johnston's organ is considered by the author as a piezoelectric feedback (pressure) transducer utilized by the insect to set and hold the proper modulation frequency. Insect grooming is related to the electret properties of the sensilla and the rubbing of sensilla to the maserlike emissions from insect host plant and pheromone attractants. Based on the 7 criteria of length and diameter of sensilla, dielectric constant, sensilla electret properties, apertures in sensilla, surface sculpturing, form, and (array) arrangements of sensilla, and also on the vibration frequency and grooming of the cabbage looper moth, log-periodic infrared emissions were predicted from the pheromone. As predicted, log-periodic maserlike frequencies were detected in the 17 and 26-μm infrared regions. They emit log-periodic with time over a half-hour period. At a wind speed of 0·5 M per minute the pheromone emits long wavelengths close to the female and short wavelengths further from the female. This is termed “concentration tuning” and operates as a proximity frequency indicator to the male flying the maserlike beam of scent. In the opinion of the author, the evolutionary selection of species has involved divergent drift in the form of the antenna sensilla concurrent with the selective pressure of gradually changing molecular emissions. The emission shifts conceivably were due to the changing infrared environment over the eons.

Optical modulation in thin films

Thin-film optical modulators may find widespread application in communications and information processing systems because of their high bandwidth, low electrical power requirements, and compatibility with other thin-film components. A thin-film modulator consists of a dielectric waveguide and an appropriate electrode structure. An applied electric or magnetic field or a traveling acoustic wave alters the dielectric tensor of the film and/or substrate in such a manner as to change the amplitude, phase, or frequency of the guided light wave. Materials have included semiconducting III–V and II–VI compounds, LiNbO3, and nitrobenzine liquid for electro-optic devices, garnets for magneto-optic devices, and glass films on quartz and LiNbO3 substrates for acousto-optic devices. This paper will review the theory of dielectric waveguides and input-output coupling as well materials, fabrication techniques, and performance characteristics for the various types of thin-film modulators.