Modes In Dielectric Waveguides Research Articles

Fast calculation of the propagation constants of leaky and Berenger modes of planar and circular dielectric waveguides terminated by a perfectly matched layer

AbstractA fast technique is proposed to determine the complex propagation constants of the leaky and Berenger modes of circular dielectric waveguides terminated by a perfectly matched layer (PML). The method relies on a coordinate transformation in the complex plane and uses the approximate analytical solutions of the dispersion relations as a first estimate. The efficiency of the technique is shown for a microstrip substrate and a VCSEL configuration, both terminated by a perfectly matched layer. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 167–171, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10857

On the propagation characteristics of metal clad waveguides with a quantum well

The electromagnetic modes of planar metal clad dielectric waveguides containing an n-doped quantum well (QW) are studied theoretically. Special attention is paid on the coupling between metal surface plasmons and intersubband plasmons and the manifestation of this coupling in the propagation characteristics of metal/QW/dielectric and multimode metal/QW/dielectric/metal waveguide structures. The results obtained indicate that the modification of the propagation characteristic induced by the above-mentioned coupling is substantial only in the case of metal/QW/dielectric waveguide structures.

Numerical and Theoretical Study of Photonic Crystal Fibers

In this work, we study a novel type of optical waveguide, whose properties derive from a periodic arrangement of fibers (not necessarily circular), and from a central structural defect along which the light is guided. We first look for propagating modes in photonic crystal fibers of high indexcore region which can be single mode at any wavelength (1-4). Unlike the first type of photonic crystal fibers, whose properties derive from a high effective index, there exists some fundamentally different type of novel optical waveguides which consist in localizing the guided modes in air regions (4-5). These propagating modes are localized in a low-indexstructural defect thanks to a photonic bandgap guidance for the resonant frequencies (coming from the photonic crystal cladding). We achieve numerical computations with the help of a new finite element formulation for spectral problems arising in the determination of propagating modes in dielectric waveguides and particularly in optical fibers (7). The originality of the paper lies in the fact that we take into account both the boundness of the crystal (no Bloch wave expansion or periodicity boundary conditions) and the unboundness of the problem (no artificial boundary conditions at finite distance). We are thus led to an unbounded operator (open guide operator) and we must pay a special attention to its theoretical study before its numerical treatment. For this, we choose the magnetic field as the variable. It involves both a transverse field in the section of the guide and a longitudinal field along its axis. The section of the guide is meshed with triangles and Whitney finite elements are used, i.e., edge elements for the transverse field and node elements for the longitudinal field. To deal with the open problem, a judicious choice of coordinate transformation allows the finite element modeling of the infinite exterior domain. It is to be noticed that the discretization of the open guide operator leads to a generalized eigenvalue problem, solved thanks to the Lanczos algorithm. The code is validated by a numerical study of the classical

Analysis of leaky modes in circular dielectric rod waveguides

The leaky modes of dielectric rod waveguides are analysed based on the normalised phase and attenuation constants obtained using Davidenko's method. It was found that for several lower-order transverse magnetic (TM) modes, the nonphysical leaky mode, antenna mode, reactive mode, and spectral gap all existed below the cutoff frequency of the guided mode.

Highly efficient full-vectorial integral equation solution for the bound, leaky, and complex modes of dielectric waveguides

A full-vectorial contour integral equation analysis of the natural modes of dielectric waveguides (DW) of arbitrary cross section is presented. The Galerkin method, together with the Analytical Regularization procedure, is applied to discretizing and solving the eigenvalue problem. This ensures the fast convergence and superior accuracy of the numerical algorithms. The waveguide cross section is characterized by a parametrical curve defining its contour, with a limited curvature at each point. This avoids the singularity points at corner regions and provides accurate results, even for waveguides with virtually sharp corners. Both fundamental and higher order mode propagation characteristics are studied in the bound, leaky, and complex regimes. Numerical results consistent with other theories and experimental data are presented for a wide range of practical dielectric waveguides that demonstrate the efficiency, accuracy, and versatility of the method developed. Finally, the technique is applied to model a fused fiber coupler.

Full vectorial finite-element solution of nonlinear bistable optical waveguides

The accurate computation of the propagation constants and field distributions of different modes in nonlinear optical dielectric waveguides is addressed in this paper. Using the vector finite-element formulation of the beam propagation method, combined with the imaginary distance propagation technique, both linear and nonlinear modes can be accurately calculated. The proposed technique is applied to obtain the fundamental TE nonlinear mode of a strip-loaded waveguide, and the excellent agreement seen with published results shows its high numerical precision.

Modeling of photonic crystal optical fibers with finite elements

The photonic crystal structures have given rise to innovative techniques to build optical fibers. This paper presents finite element magnetic and electric field models for determining the propagation modes in dielectric waveguides. A combination of edge elements for the transverse field and nodal elements for the longitudinal field is used together with a geometric transformation to cope with the open domain. The model is applied to the study of photonic crystal fiber structure. The case of leaky modes is also discussed.

A finite element formulation for spectral problems in optical fibers

This paper is devoted to the presentation of a new finite element formulation for spectral problems arising in the determination of propagating modes in dielectric waveguides and particularly in optical fibers. As an example, we compute the coupling between two parallel optical wave guides. The originality of the paper lies in the fact that we take into account both the vector character of the problem (no weak coupling assumption) and the unboundness of the domain.

Resonant scattering of electromagnetic waves by a lossy periodic dielectric waveguide

The problem of the excitation of guided modes in planar dielectric waveguides with periodically modulated surfaces is considered. In particular, the form of the radiation pattern of a lossy waveguide, the width and the position of the central angle of the radiation pattern as a function of the surface modulation depth are studied. A special numerical-analytical method for the calculation of the intensities of guided modes has been developed. In the case of a small modulation depth, this method makes use the expansion of the solutions of Maxwell equations into the Laurent series near the scattering matrix pole.

Two-dimensional vector-coupled-mode theory for textured planar waveguides

We develop a model to treat coupling between guided modes in planar dielectric waveguides that have been textured in two dimensions with a thin surface grating. The formulation is based on a general Green's-function technique that self-consistently determines the field in the surface grating due to the polarization there. With simplifying approximations, this formalism is cast into a two-dimensional (2D) vector-coupled-mode theory that is more computationally efficient, and that gives considerable insight into the nature of mode coupling in 2D textured structures. These models are applied, by way of example, to illustrate some interesting properties of leaky and bound modes that are coupled together by 2D periodic texture. In particular we discuss the complex photonic band structure describing the dispersion, lifetimes, and polarization properties of the resonant states associated with the textured waveguide. In our analysis we emphasize the fundamental differences between coupling in 2D textured waveguides and infinite 2D photonic crystals. We also show that the vector-coupled-mode theory agrees well with the self-consistent formulation.

Efficient β-formulation for the FEM analysis of leaky modes in general anisotropic channel waveguides

An efficient method to model guided and leaky modes of anisotropic dielectric waveguides with arbitratry dielectric tensor e¯¯ is presented. This method takes advantage of a particular β-formulation approach of the finite element method (FEM), leading to an optimized use of the computational resources.

Vectorial electromagnetic modes in V-shaped dielectric waveguides with application to quantum wire devices

The properties of V-shaped optical dielectric waveguides are investigated in detail using a vectorial finite element method. The fundamental modes exhibit extremely tight, heart shaped near field patterns. The maximum intensity of the fundamental mode is found to be vertically shifted with respect to the geometrical center of the waveguide. Fundamental and higher order mode properties are extensively studied, including mode patterns, dispersion curves and polarization properties. The local mode polarization of the two fundamental modes varies from a horizontal (vertical) orientation at the groove center to TM (or TE respectively) far in the side wings. The optimal design of waveguides for GaAs/AlGaAs quantum wire diode lasers and Quantum Confined Stark Effect modulators grown on V-grooved substrates is discussed.

Analysis of a cylindrical dielectric waveguide with three regions by use of an invariant mode-definition parameter

Boundary conditions at a dielectric interface are expressed in terms of electrodynamic vector and scalar potentials that are expressed in terms of two-dimensional scalar solutions to the wave equation. Possible field configurations are expressed in terms of linear combinations of the scalar solutions. Their behavior at a dielectric interface and within a region of constant permittivity is investigated, and a parameter that is used to define propagation modes in cylindrical dielectric waveguides is shown to have the same value in regions with different permittivities. Scalar expressions that include this parameter are used to calculate exact expressions for fields and propagation constants in a cylindrical dielectric waveguide with three coaxial regions. The characteristics of propagation modes in these waveguides are discussed.

A general transform for regularizing planar open waveguide dispersion relation

Recently, conformal mapping technique has been introduced to unfold the characteristic equation of multilayered dielectric waveguides. The previous transformations have various deficiencies, i.e., the corresponding transformed functions are either multivalued, or have a singular point. Also one of them is not generally applicable. We introduce a new mapping that has none of the above deficiencies. Furthermore, in the new plane, the modal zones are rectangular strips which facilitate the implementation of the corresponding numerical routines. By this transformation, various modes of general planar dielectric waveguides can be traced easily.

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.

Computer-aided design and optimization of NRD-guide mode suppressors

A novel class of optimized nonradiative dielectric waveguide (NRD-guide) mode suppressors are proposed for wideband applications in passive and active NRD integrated circuits. A rigorous field-theoretical analysis is made by using the frequency-domain TLM technique. The optimum design is based on a filter-like scheme with a low-pass filter simulation technique and its performance-prediction algorithm. Compared to the existing choke metallic pattern, the proposed mode suppressor demonstrates excellent capabilities of effectively suppressing unwanted modes while offering a more compact geometry. Using the geometry proposed in this work for a three-section low-pass filter, for example, it is found that the transmission loss of the mode suppressor is better than -30 dB over the frequency band of interest which is well confirmed theoretically and experimentally. In addition, the length of the resulting mode suppressor becomes shorter than its counterpart using the choke metallic pattern by 20%. The theoretical prediction of electrical performance is well confirmed by our measurements.

Analysis of the effective-index method for the vector modes of rectangular-core dielectric waveguides

The approximations involved in the effective-index method for analyzing the vector modes of rectangular-core dielectric waveguides are examined in detail. It is shown that the effective-index method does not solve the full vector-wave equation that governs the modes. Instead, it solves the reduced vector-wave equation, which is accurate only for approximately linearly polarized waves. Furthermore, in solving the reduced vector-wave equation, the method of separation of variables is used, which leads to additional errors as the waveguide being analyzed is a mathematically nonseparable structure. To characterize the performance of the effective-index method, asymptotic expressions are derived for the errors in the calculation of propagation constants. Apart from separating the effects of different approximations involved, these expressions show explicitly how the accuracy of the method depends on the mode type, the normalized frequency, the mode orders, the dimensions of the waveguide, and the relative refractive-index differences between the core and the surrounding media. With the help of these expressions, it is demonstrated that more accurate results can be obtained by combining various effective-index solutions.

Guided and defect modes in periodic dielectric waveguides

The nature of guided modes and defect modes in periodic dielectric waveguides is investigated computationally for model systems in two dimensions. It is shown that defect states that exist within the band gap of guided modes can be excited to form tightly localized high-Q resonances.

Nonlinear resonant conversion of modes in optical waveguides

A new class of resonant exchange of power among three co-propagating modes in dielectric optical waveguides exhibiting Kerr-like nonlinearity is reported. Unlike the coupling of modes travelling in different, spatially separated channels as in the directional coupler (Jensen, IEEE J. Quantum Electron. QE-18 (1982) 1580; Chen, Snyder and Mitchell, Electron. Lett. 26 (1990) 77; Schmidt-Hattenberger, Trutschel and Lederer, Optics Lett. 16 (1991) 294) this paper points out the possibility of obtaining an efficient coupling of modes travelling in one single channel. The key point here is the imposition of a geometrical resonance between modes, to improve the coupling process. Due to this resonance condition, which is related with the wavelength through the propagation constants, the power exchange process is very sensitive to the wavelength.

Application of the transmission line matrix method to the analysis of slab and channel optical waveguides

The applicability of the three-dimensional vectorial transmission line matrix (TLM) method to the analysis of optical waveguiding structures is demonstrated. Any waveguide geometry, even incorporating anisotropic materials, can be treated by taking into account the coupling between all optical field components. The application of the TLM method to optical waveguides is shown to be both efficient and accurate. The dispersion curve for the fundamental TE-like mode of a typical rib dielectric waveguide as well as its electric-field pattern is obtained by the use of the TLM method. Numerical comparisons with the integral-formulation technique, the effective-index method, the finite-difference analysis, the spectral-index method, and the beam-propagation technique are also included.