Boundary Residual Method Research Articles

The Analysis of the Biconical Antenna by the Least-Squares Boundary Residual Method

Abstract The paper offers another approach to the radiation of the biconical antenna. This is one of the possible applications of the more general theory of the radiation problem that is based on the use of the Least-squares boundary residual method. The theory appeared to be equally efficient both for symmetric and asymmetric bicone antenna, and also for small and large cone angles.

Least Squares Boundary Residual Method for the Analysis of Step Discontinuities in Open Chiral Waveguides

Summary We analyse the reflection, transmission and radiation characteristics of a step discontinuity in a grounded chiral slab and we show that the step radiation can be enhanced due to the effect of the chirality. The analysis is performed using a mode matching technique. The fields are expressed in terms of the discrete modes and the continuous spectrum using two subsets of hybrid radiation modes: incident transverse electric (ITE) and incident transverse magnetic (ITM) modes. The scattering matrix of the step is determined by minimizing the boundary residual error in the sense of the least squares. The influence of chirality on the characterization of the step is demonstrated and we show that control of the radiation pattern is achieved, including angle and width of the radiation beam.

Design of compact optical bends with a trench by use of finite-element and beam-propagation methods

We address various approaches to the reduction of optical bending loss in photonic integrated circuits. Different methods, such as offsetting of waveguides and incorporation of the effect of an isolation trench on reduction of radiation loss, are demonstrated. A combination of the vectorial finite-element and the least-squares boundary residual methods is used to calculate transition losses and the required offset for their minimization. The semivectorial finite-element-based beam-propagation method is employed to calculate radiation loss. These vectorial approaches are also used to investigate several important properties, such as effects that are due to the sidewall slopes, rib heights, rib widths, and trench location, to optimize bend designs.

Characterisation of low-loss waveguide bends with offset-optimisation for compact photonic integrated circuits

Use of a semivectorial finite element-based beam propagation method is benchmarked with the results available by using alternative numerical methods to analyse compact optical bends in photonic integrated circuits. It is also shown that the incorporation of the perfectly matched layers boundary condition is a superior approach for the treatment of high radiation loss from compact bends to the more common use of the absorbing boundary conditions. The least squares boundary residual method is employed to calculate the lateral offset necessary to maximise the transmission and simultaneously to minimise the reflection coefficients at the straight-to-bend waveguide interfaces. Using these efficient numerical techniques, the radiation loss, transition loss and the required waveguide offset to maximise the transmission and reduce the reflection are calculated.

Design considerations for an electrooptic directional coupler modulator

A rigorous numerical model is presented for an electrooptic directional coupler (DC) modulator. It was observed that it is possible for such a device to be optimized by the variation of a number of fabrication parameters. The applied field, the induced refractive index changes, and hence the change in the waveguide optical field due to the antisymmetric refractive index change are calculated for an elected structure. Finally, the product of switching voltage and coupling length, the power transfer efficiency, obtained using the least squares boundary residual (LSBR) method, and the optical loss due to the metal electrodes are also given.

A rigorous comparison of the performance of directional couplers with multimode interference devices

The authors report, for the first time, a direct comparison between a directional coupler and a multimode interference-based device, in relation to their performance characteristics such as crosstalk, polarization dependence and the effect of fabrication tolerances. The coupling efficiency for a nonidentical coupler, produced inadvertently due to problems with fabrication tolerances, is also demonstrated. The vector finite element (FE) and the least squares boundary residual (LSBR) methods are employed as the numerical tools used in this simulation study.

E-plane symmetrical five-port waveguide junction with oversized central cavity

The mathematically rigorous least-squares boundary residual method is used to develop a reliable model of a symmetrical five-port waveguide junction that has an oversized central cavity loaded with metallic rod and dielectric sleeve. Tests on a prototype junction yield measured scattering-coefficient results that are in excellent agreement with the predicted values over the entire WR90 bandwidth.

Accurate numerical analysis of multimode-interference-based 3-dB couplers

The power coupling characteristics of a multimode-interference-based 3-dB coupler have been analyzed by using the vector finite-element and least-squares boundary residual methods. The numerical results obtained have been compared with published experimental data to show the accuracy and the versatility of these numerical schemes. The results predict that a full treatment of the two-dimensional cross section is of particular importance for the design and the simulation of effective waveguide devices to enable a study of their important optical properties such as polarization and fabrication tolerances.

Numerical study of spot-size expanders for an efficient OEIC to SMF coupling

Different types of spot-size converters are studied numerically, and their coupling loss and reflection properties are discussed in detail. The rigorous vector finite-element method is used to calculate the modal propagation properties and the least-squares boundary residual method is employed to calculate the coupling loss, reflection coefficient, and the alignment tolerances of the devices. It has also been observed that the reflection coefficient reaches a minimum when the mode confinement is at its maximum.

Spot size expansion for improved OEIC-to-fibre coupling using directional couplers with 2D confinement

In optical fibre applications, by using an intermediate multiguide directional coupler section, this work has shown that the field profile of the source laser used can be expanded to match that of the receiving optical fibre. The vector H-field finite element method has been employed to determine the modal propagation constants and vector field profiles. An accurate calculation of the excited modal coefficients was achieved by using the least squares boundary residual method, which satisfies the continuity of the transverse field components more rigorously than through the use of the simple overlap integral approach.

Thick eccentric circular iris in circular waveguide

Other researchers have observed that eccentric irises possess certain advantageous features that may lead designers to prefer them over the conventional concentric irises. The least-squares boundary residual method (LSBRM) is utilized in this paper to analyze the behavior of such an eccentric-iris structure (of nonzero thickness). Tests have confirmed that the computer model thus obtained is capable of yielding numerical results that are accurate to within /spl perp/1%.

The analysis of Bragg-reflector pairs using transfer matrix, overlap and least-squares boundary residual methods

Three different methods have been used to analyse periodic three-dimensional Bragg-reflector structures and a comparison of the results obtained is drawn. The work has shown that the least-squares boundary residual (LSBR) method, when combined with the finite-element method (FEM), both being vectorial approaches, offers an accurate model of the Bragg-reflecting pair, taking into account both the variation in indices and the structural dimensions at the waveguide junctions. This work demonstrates that the rigorous LSBR method is both accurate and versatile in its application and is thus more appropriate for the characterization of practical photonic devices incorporating a distributed Bragg-reflector (DBR) section, in spite of the slightly increased computational cost associated with it.

E-plane cross junction loaded with central metallic post

The Least-Squares Boundary Residual Method is utilized in the present paper for the analysis of the E-plane cross junction that has a centrally located metallic post. The computer model thus developed (which is able to yield numerical accuracies of ±0.5%) has thereafter been used to design a prototype that has the same electrical characteristics over the 26–40 GHz bandwidth as the H-plane cross junction reported earlier by Suet al in [1].

Accurate analysis of multimode interference devices

The accurate analysis of multimode interference devices is demonstrated by using the least-squares boundary residual (LSBR) method. Accurate modal propagation constants and spatial field profiles in the multimode interference (MMI) section can be obtained by using the finite-element method. The accurate calculation of the excited modal coefficients is achieved by using the LSBR, which satisfies the continuity of the transverse field components more rigorously than the simple overlap integrals.

Application of least-squares boundary residual method to the analysis of a thin circular iris in a TE11-mode circular waveguide

The mathematically rigorous least squares boundary residual method is used in the present article to develop a computer model that is able to predict the characteristics of the TE11-mode circular waveguide loaded with a thin circular iris. Test results demonstrate that the software package thus developed (which runs on a DEC workstation or its equivalent) is able to yield scattering-coefficient data that are accurate to within ±0.5%. © 1996 John Wiley & Sons, Inc.

Accurate analysis of MMI devices with two-dimensional confinement

The accurate analysis of multimode interference (MMI) devices with two-dimensional (2-D) confinement has been demonstrated by using the least squares boundary residual (LSBR) method. Accurate modal propagation constants and spatial field profiles in the MMI section are obtained by using the vector H-field based finite element method. The accurate calculation of the excited modal coefficients is achieved by using the LSBR, which satisfies the continuity of the transverse field components more rigorously than using simple overlap integrals.

Performance of the LSBRM using efficient weighting functions for planar structures

A new variant of the least squares boundary residual method (LSBRM) is presented, which takes into account electromagnetic field singularities at metal-dielectric edge due to the existence of the Gibbs phenomenon. Systematic weighting functions are used in this method allowing one to obtain accurate and efficient numerical results with accelerated convergence. The structure to be analysed is enclosed in a resonant cavity and the resonant frequency is calculated using the least squares criterion.

Analysis of Mode Conversion at Discontinuities between K+–Na+ and Ag+–Na+ Ion-Exchanged Waveguides in Glass

The analysis of mode conversion caused by discontinuity between K+–Na+ and Ag+–Na+ ion-exchanged waveguides in glass is carried out. The experimentally obtained refractive index profiles of the waveguide regions are considered. Structures consisting of single-mode potassium and 2-, 5-, or 11-mode silver waveguides are studied using the least squares boundary residual method. The power coefficients of light propagation through the interface between the two waveguide regions are evaluated. In the case of structure consisting of a single-mode potassium waveguide and 11-mode silver one, the power transmittance coefficient for the lowest-order transverse electric mode reaches a value of 98.9%.

Propagation characteristics of circular chirowaveguides periodically loaded with metal gratings

A new type of periodical chirowaveguide is proposed in the paper. A numerical approach for solving the problem, which is a combination of the mode expansion method and the least-squares boundary residual method, is developed. Canonical examples are presented to show the validity and usefulness of the method. The novel features of the new type of waveguide are also shown. To help design band-reject filters and leaky-wave antennas, some theoretical curves and useful conclusions are presented.

Rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide

Using a discretizing procedure for the continuous spectral amplitude of the radiation modes and the least-squares boundary residual method a rigorous analysis of a step discontinuity in a dielectric planar anisotropic waveguide is presented. The numerical examples clearly show the effect of the medium anisotropy on the scattering characteristics—namely on the radiation pattern—of a uniaxial dielectric step. © 1992 John Wiley & Sons, Inc.