Efficient analysis of periodic dielectric waveguides using Dirichlet-to-Neumann maps

We present a numerical scheme for the analysis of periodic dielectric waveguides using Floquet-Bloch theory. The problem of finding the fundamental propagation modes is reduced to a nonlinear eigenvalue problem involving Dirichlet-to-Neumann maps. This approach leads to much smaller matrix problems than the ones that have appeared previously. By an increase of the discretization fineness, any desired precision of the method can be achieved. We discuss an eigensolver and extend the conventional rule to choose the branches of the transverse wave numbers. This ensures analytic dependence on the Floquet multiplier and convergence of the nonlinear solver. We demonstrate that even for a complicated multilayer waveguide structure the propagation factors can be calculated within seconds to several digits of accuracy.     

Lossy multilayer channel optical waveguides analyzed by the transmission line matrix method

We demonstrate that the three-dimensional vectorial transmission line matrix (TLM) method is applicable to the analysis of lossy multilayer optical waveguiding structures. Any lossy multilayer waveguide geometry, including sharp discontinuities in the transverse plane, can be treated taking into account the coupling between all optical field components. The complex propagation constants (propagation constants and the attenuation coefficients) for the fundamental TE-like and TM-like modes can be determined. These parameters of the fundamental TM-like mode of a typical lossy multilayer rib dielectric waveguide are obtained as functions of free-space wavelength. Calculation of the electric-field pattern is also included. Numerical comparisons with the argument principle method (for the case of lossy multilayer slab waveguides) and the spectral-index technique (for the case of lossy multilayer rib waveguides) are also included, and it is shown that the application of the TLM method to lossy multilayer optical waveguides is accurate.     

Matrix method for two-dimensional waveguide mode solution

In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a ‘folded’ plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.     

Propagation properties of an elliptical anisotropic metamaterial cylinder

The propagation characteristics were investigated of an open elliptical cylinder comprising a uniaxial anisotropic metamaterial. The dispersion relation for hybrid modes in this cylinder was examined theoretically. It is shown that forward and backward waves can be supported by such a metamaterial cylinder. Even and odd modes have different losses in a realistic anisotropic elliptical cylinder. The forward wave can propagate longer distances than the backward wave because of its lower loss. The light can propagate backward on the cylinder without the limit of structure size. The odd modes have higher operating wavelengths than the even modes. The extraordinary properties in this structure are identified as multilayer plasmons. The validity of the effective medium approximation of this structure is examined.     

Reflection and transmission in pre-stressed stratified multilayers

Summary Time-harmonic wave propagation is investigated in multilayers whose slabs are pre-stressed anisotropic, dissipative solids. The material properties vary continuously within each slab and suffer jump discontinuities at the interfaces. The multilayer is sandwiched between homogeneous half-spaces. The constitutive equations due to the motion are taken to be linear, and hence the governing equations are shown to allow for a Stroh-like form. The solution is determined for any slab, and hence for the multilayer, through an integral-equation formulation, in terms of a propagation matrix which incorporates the jumps at the interfaces. Next the reflection and transmission problem for the multilayer, with an oblique incident wave, is solved by determining the reflection and transmission matrices in terms of the propagation matrix, the parameters of the incident wave and the eigenmode polarization vectors in the halfspaces. By way of application, results are derived in detail for horizontally-polarized waves.     

Modal behavior in single-mode slab waveguides consisting of inhomogeneous cores

We present an analytical method for TE and TM modes in weakly guiding inhomogeneous single-mode slab waveguides. Based on our results, the modal behavior or propagation constants depend on index profiles of the waveguides. It is important to know how the modal behavior depends on the index profile in single-mode waveguides, because it determines wave-front characteristics of propagating modes.     

A variational finite element formulation for dielectric waveguides in terms of transverse magnetic fields

A spurious-mode-free variational formulation for the finite-element analysis of anisotropic, inhomogeneous dielectric waveguides is derived and demonstrated with examples. Apart from avoiding the occurrence of spurious modes, this formulation has numerous advantages, including the ability to treat problems including significant amount of loss, the direct solution for the propagation constant at a given frequency, and the use of the most efficient representation of the problem, needing only two vector components. This is achieved without losing the sparsity of the resultant (canonical) matrix eigenvalue problem, which depends on the topology of the mesh used.<>     

Stable and accurate method for modal analysis of multilayer waveguides using a graph approach

A method for calculating the propagation constants of allowed guided and leaky modes in multilayer planar waveguides is presented. We develop a two-way graph model to describe the tangential fields propagating in the waveguides. According to the special structure of the graph model, it is convenient to employ a topology scheme to derive analytical and closed-form dispersion equations for TE and TM modes. By comparing the dispersion equations formulated by series-expansion methods, approximation methods, and transfer-matrix methods, we find that the use of these equations for finding the eigenmodes has some benefits. First, this method can be easily employed to solve eigenmodes accurately in numerical computation without using series truncation. Second, the dispersion equations are exact. Moreover, all the eigenmodes can be determined according to the formulas without losing roots or causing numerical instability even for a waveguide with thick layers.     

Finite element analysis of helicoidal waveguides

The purpose of the paper is to propose an efficient method to compute propagation modes in helicoidal waveguides. An helicoidal system of co-ordinates is introduced to define the structure and to set up the problem. These co-ordinates, albeit non-orthogonal, preserve the translational invariance in a way that allows a two-dimensional finite element model similar to that of classical straight waveguides     

The exact finite difference method: A new approach to the calculation of leak modes in multilayer waveguide structures

A new approach to the calculation of electromagnetic modes in optical waveguides (OWGs), which is based on the exact finite difference method (EFDM) representing a combination of the finite difference method and the transmission matrix technique, is described. The efficacy of the EFDM is demonstrated in application to the calculation of leak modes in multilayer planar OWGs of the ARROW type, featuring antiresonance reflection from a multilayer shell (rather than the total internal reflection from the shell-core interface as in the usual OWGs). The proposed method can be used for calculations of both the electromagnetic modes in dielectric OWGs and the quantum states of electrons in multibarrier semiconductor heterostructures. The parameters of a nine-layer OWG calculated using the EFDM are compared to the published data obtained by solving a dispersion equation within the framework of the transmission matrix technique. The results of calculations of the spectrum of radiative losses for the first (leak) TE mode in planar OWGs with various numbers of layers are presented.     

Characteristic analysis of absorptive multiple-quantum-well optical waveguides

Abstract

By extending the transfer matrix technique from the real domain to the complex, the complex eigenvalue equation is presented for both transverse electric and transverse magnetic modes of absorptive multiple-quantumwell optical waveguides, and a computer program is developed to solve the eigenvalue equation in the complex plane. On the basis of the computed results, the effects of the structural parameters and the refractive index profile on the mode propagation and loss properties are analysed and discussed for In^x Ga^1?xAs/Al^yGa^1?yAs absorptive multiple-quantum-well optical waveguides. The results indicate that, if approximate guided structural parameters and an appropriate refractive index profile are selected, higher-order modes can be controlled and single-mode propagation can be realized in the multiple-quantum-well optical waveguide with lower mode loss.     

Simple recurrence matrix relations for multilayer anisotropic thin films

Generalized Abelès relations for one anisotropic thin film [E. Cojocaru, Appl. Opt. 36, 2825-2829 (1997)] are developed for light propagation from an isotropic medium of incidence (with refractive index n(0)) within a multilayer anisotropic thin film coated onto an anisotropic substrate. An immersion model is used for which it is assumed that each layer is imaginatively embedded between isotropic gaps of zero thickness and refractive index n(0). This model leads to simple expressions for the resultant transmitted and reflected electric field amplitudes at interfaces. They parallel the Abelès recurrence relations for layered isotropic media. These matrix relations include multiple reflections while they deal with total fields. They can be applied directly to complex stacks of isotropic and anisotropic thin films.     

Analysis of the left-handed corrugated circular waveguide

Infinite circular corrugated waveguide is analysed to investigate its ability to support modes with backward wave behaviour. Such waveguides provide an alternative structure, easier to manufacture than those already reported based on rectangular symmetry with corrugated walls or filled with frequency selective surfaces. The corrugations if sufficiently deep provide a guiding structure with the required series capacitance and shunt inductance to allow left-handed propagation within some frequency bands. These backward waves are analysed using the surface impedance model of propagation in corrugated waveguides to predict their properties. Interpreting the physical meaning of the analysis, the authors discuss how backward waves are related to resonances in corrugated structures. The relationship between power flows in the guide and the behaviour of the group velocity for such guides is shown. A full wave simulator is also applied to validate these results and the case of a dielectric filled waveguide is considered showing the improved ability to support left-handed modes. The authors present the results of a parametric study of how left-handed propagation depends on the corrugation depth. Potential applications of backward waves in corrugated circular waveguides are proposed.     

A New Fuzzy Controlled Antenna Network Proposal for Small Satellite Applications

This research contributes to small satellite system development based on electromagnetic modeling and an integrated meta-materials antenna networks design for multimedia transmission contents. It includes an adaptive nonsingular mode tracking control design for small satellites systems using fuzzy waveless antenna networks. By analyzing and modeling based on electromagnetic methods, propagation properties of guided waves from metallic structures with simple or complex forms charge partially or entirely by anisotropic materials such as metamaterials. We propose a system control rule to omit uncertainties, including the inevitable approximation errors resulting from the finite number of fuzzy signal power value basis functions in antenna networks. Moreover, both the stability and the tracking performance of the closed-loop robotic system are experimentally validated. The research lies within the scope of the improvement of speed, effectiveness, and precision of numerical methods applied to electro-magnetic modeling with complex structures, essentially rectangular metallic waveguides filled with isotropic or anisotropic metamaterials. Three axes of our research are presented: waveguides, filters, and antennas. The proposed controller does not require prior knowledge about the dynamics of the fuzzy system controller for antenna networks or the offline learning phase. In addition, this work contributes to solving the problem of non-visibility stations to ensure data transmission in wireless networks. The proposed solution maximizes inter-connection by using a fuzzy controlled antenna network, and the novelty guarantees non-limited interconnection in wireless networks compared to traditional methods.     

Unidirectional wavelength filtering characteristics of the two-dimensional triangular-lattice photonic crystal structures with elliptical defects

The unidirectional wavelength filtering characters of the two-dimensional triangular-lattice photonic crystal structures consisting of two waveguides and an elliptic defect are theoretically studied by the finite-difference time-domain method. Through designing the coupling regions between the elliptical defect and the adjacent waveguides, the unidirectional wavelength filtering is achieved owing to the modes’ match and mismatch between the elliptical defect and waveguides, which converts the incident fundamental even-symmetric modes to the higher order odd modes. Based on the abundant defective modes with different symmetries supported by the elliptical defect, this kind of wavelength filters can allow the unidirectional light propagation with inverse forward directions, and the bidirectional propagation through the same structure at different wavelengths.     

On the propagation of waves in layered anisotropic media in generalized thermoelasticity

In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting N-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.     

Beam propagation in parabolically tapered graded-index waveguides

To a good approximation, the electromagnetic-propagation characteristics of graded-index waveguides can be written in terms of polynomial-Gaussian modes. For uniform quadratic-index waveguides the behavior of these modes is well known. However, there are sometimes practical reasons for using tapered waveguides, but detailed propagation solutions are known for only a few specific taper functions. The parabolic taper is perhaps the most important special case, and the solution-generating techniques that we generalize are used to obtain analytic solutions for this case.     

Calculation of radiation modes by the Lanczos-Fourier expansion

For construction of the TE radiation modes of planar waveguides several methods are employed that are based on collocation techniques. The field representation in the core is based on the Lanczos-Fourier sinusoidal series. The numerical codes are very simple and give accurate results. The validity of these methods is checked for constant refractive-index profiles, while numerical results are also given for parabolic profiles. Furthermore, the validity of the orthogonality condition between the guided and the radiation modes is checked. These methods are demonstrated to be effective and can also be employed to study the TM case and waveguides of lossy media, as well as anisotropic and chiral structures.     

Long-range surface plasmon polariton waveguides embedded in fluorinated polymer

Low-attenuation waveguides based on the propagation of long-range surface plasmon polaritons (LRSPPs) along thin Au stripes embedded in low absorption perfluorocyclobutane (PFCB) polymer are presented. A new low in propagation loss of <2.0 dB/cm was achieved for a 4 microm wide waveguide by optimizing the cladding material and fabrication process. The coupling efficiency between the LRSPP waveguide and the optical fiber is studied theoretically and experimentally for different widths of Au stripes and various cladding thicknesses. Lower coupling loss is found when the cladding thickness is close to the mode diameter of the butt-coupled fiber. Based on the 2D distribution of SPP modes calculated by a finite-difference mode solver, a symmetric structure of multilayer claddings with different refractive indices is proposed to optimize device insertion loss.     

Swift and heavy ion implanted chalcogenide laser glass waveguides and their different refractive index distributions

Planar waveguides have been fabricated in Nd- or Ho-doped gallium lanthanum sulfide laser glasses by 60?MeV Ar or 20?MeV N ion implantation. The refractive index profiles were reconstructed based on the results of prism coupling. The Ar implanted waveguides exhibit an approximate steplike distribution, while the N implanted ones show a "well + barrier" type. This difference can be attributed to the much lower dose of Ar ions. After annealing, the N implanted waveguides can support two modes at 1539?nm and have low propagation loss, which makes them candidates for novel waveguide lasers.