Least-squares Boundary Residual Method Research Articles

Compact and fabrication-tolerant polarization splitter based on horizontal triple-slot waveguide.

A compact and fabrication-tolerant polarization beam splitter (PBS) based on the horizontal triple-slot waveguides is proposed and optimized by using the rigorous H-field-based full-vectorial finite element method and the least-squares boundary residual method. It can be noted from the simulation results that a fabrication-tolerant PBS with a compact length of 33 μm can be yielded based on the horizontal triple-slot waveguides. The polarization extinction ratios are -21.8 and -20.3 dB at 1.55 μm wavelength for the quasi-TE and quasi-TM modes, respectively. The 1 dB bandwidth is 100 nm for both the polarizations. The fabrication tolerances are also thoroughly calculated for the proposed PBS.

Design of compact polarization rotator using simple silicon nanowires.

In this paper, an ultracompact design of a polarization rotator (PR) based on a silicon-on-insulator (SOI) platform is presented. The design contains two simple silicon nanowires but with unequal width, which will be easier to fabricate. It is shown here that a low-loss, wide-bandwidth, and 52.8-μm-long compact PR with polarization cross talk of -20 dB can be achieved. A full-vectorial finite element method and the least-squares boundary residual method are used to study the effects of the fabrication tolerances. This design shows reasonably stable performances.

SYMMETRICAL SIX-PORT WAVEGUIDE JUNCTION WITH METALLIC POST AND DIELECTRIC SLEEVE IN OVER-SIZED CAVITY

The Least-Squares Boundary Residual Method is em- ployed in the present paper to develop a computer model of the sym- metrical six-port waveguide junction. The analytical formulation is di-cult because of the insertion of a metallic post together with a di- electric sleeve into the over-sized cavity of the junction. Computational and experimental tests conflrm that the resultant model is able to com- pute the scattering parameters of such a structurally-complicated com- ponent with numerical accuracies of §0:001 and §0:1 - for magnitude and phase respectively.

Field Analysis of the Archimedean Spiral Antenna

This article offers an alternative to investigating the radiation of the Archimedean spiral 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 field potentials are expressed through the general wave equation basis functions in a spherical coordinate system. For highly accurate fulfillment of the boundary condition, only 20 modes were required. All field components in both the near and far zones are derived from the radial component of magnetic and electric vector potentials.

A NUMERICAL ANALYSIS OF STOP BAND CHARACTERISTICS BY MULTILAYERED DIELECTRIC GRATINGS WITH SINUSOIDAL PROFILE

An effective computational method based on a conven- tional modal expansion approach is presented for handling a multilay- ered dielectric grating whose profiles are multilayered and sinusoidally modulated. This structure fabricated by dielectric material is one of the useful photonic crystals. The method is based on Yasuura's modal expansion, which is known as a least-squares boundary residual method or a modified Rayleigh method. In the extended method, each layer is divided into shallow horizontal layers. The Floquet modal func- tions and approximate solutions are defined in each shallow layer, and the latter are matched with boundary conditions in the least-squares sense. A huge-sized least-squares problem that appears in finding the modal coefficients is solved by the QR decomposition accompanied by sequential accumulation. This procedure makes it possible to treat the case where the groove depths are the same as or a little more than the grating period. As numerical example, we calculate a diffractive char- acteristic by a multilayered deep dielectric grating and confirm that a common band gap occurs for both polarizations.

A COMBINATION OF UP- AND DOWN-GOING FLOQUET MODAL FUNCTIONS USED TO DESCRIBE THE FIELD INSIDE GROOVES OF A DEEP GRATING

An effective computational method based on a conven- tional modal-expansion approach is presented for solving the problem of diffraction by a deep grating. The groove depth can be the same as or a little more than the grating period. The material can be a perfect conductor, a dielectric, or a metal. The method is based on Yasuura's modal expansion, which is known as a least-squares boundary residual method or a modified Rayleigh method. The feature of the present method is that: (1) The semi-infinite region U over the grating sur- face is divided into an upper half plane U0 and a groove region UG by a fictitious boundary (a horizontal line); (2) The latter is further di- vided into shallow horizontal layers U1 ,U 2, ··· ,U Q again by fictitious boundaries; (3) An approximate solution in U0 is defined in a usual manner, i.e., a finite summation of up-going Floquet modal functions with unknown coefficients, while the solutions in Uq (q =1 , 2, ··· ,Q ) include not only the up-going but also the down-going modal functions; (4) If the grating is made of a dielectric or a metal, the semi-infinite region L below the surface is partitioned similarly into L0 ,L 1, ··· ,L Q, and approximate solutions are defined in each region; (5) A huge-sized least squares problem that appears in finding the modal coefficients is solved by the QR decomposition accompanied by sequential accu- mulation. The method of solution for a grating made of a perfect conductor is described in the text. The method for dielectric gratings can be found in an appendix. Numerical examples include the results for perfectly conducting and dielectric gratings.

Review of finite-element characterization of photonic devices

We report the development and applications of finite-element-based numerical approaches for the characterization of a wide range of photonic devices. The full-vectorial finite-element method is considered for the modal solutions of uniform guided-wave sections and the least-squares boundary residual method is used to calculate the scattering coefficients for butt-coupled uniform waveguide sections. Several guided-wave components are discussed and their operating characteristics are illustrated. Particular emphasis is given to key photonic components such as the spot-size converters, Bragg gratings, polarization splitters, polarization rotators, multimode interference-based devices and modulators. Valuable results relating to the design and characterization of these important photonic components are presented.

Review of finite-element characterization of photonic devices

Abstract We report the development and applications of finite-element-based numerical approaches for the characterization of a wide range of photonic devices. The full-vectorial finite-element method is considered for the modal solutions of uniform guided-wave sections and the least-squares boundary residual method is used to calculate the scattering coefficients for butt-coupled uniform waveguide sections. Several guided-wave components are discussed and their operating characteristics are illustrated. Particular emphasis is given to key photonic components such as the spot-size converters, Bragg gratings, polarization splitters, polarization rotators, multimode interference-based devices and modulators. Valuable results relating to the design and characterization of these important photonic components are presented.

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.

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.

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.

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.

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.

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.

Dielectric-loaded elliptical waveguide

The least-squares boundary residual method is used to develop an electromagnetic model for predicting the propagation characteristics and modal-field distributions of an elliptical waveguide loaded with a dielectric rod. Tests indicate that the model, when implemented as a selfcontained software package for running on the NEC SX-1A supercomputer, is capable of yielding numerical accuracies of better than ±1%.