Split-step finite difference analysis of rib waveguides

Presents a new rapid approach to the analysis of strongly guiding and longitudinally varying semiconductor rib waveguide structures. The technique, which is a synthesis of the beam propagation and finite difference methods is Hermitian, second-order accurate and intrinsically stable.<>     

Scalar BPM analyses of TE and TM polarized fields in bent waveguides

We have applied the effective index method to reduce the two-dimensional (2-D) refractive index profile into the 1-D refractive index structure and modified the wave equations to obtain the paraxial wave equations. Then, transverse electric (TE) and transverse magnetic (TM) polarized fields in the curved single-mode planar waveguides are analyzed by using the scalar beam-propagation method (BPM) employing the finite-difference method with a slab structure. The bending loss in bent waveguides is analyzed for optical fields obtained from the BPM and comparisons are made between the loss for the waveguides with various radius of curvature and refractive index difference. The outward shift of the optical field, which is generated at the connection between a straight and a bent waveguide, is obtained from the results of calculation of location of the maximum optical intensity. The transition loss can be reduced by introducing an optimized inward offset at a straight-to-bend junction. The birefringence for TE and TM polarized fields in bent waveguides is calculated from the phase difference of the optical fields. The wavelength shift due to the birefringence of TE and TM polarized fields in bent waveguides is also calculated.     

Local field analysis of bent graded-index planar waveguides

A local field analysis is proposed for bent planar waveguides with arbitrary refractive index profiles. Exact vector wave equations that include the gradient index, or polarization correction, term are derived for both transverse electric and transverse magnetic modes from Maxwell's equations in a local bent coordinate system. The approximate local field and correction to the propagation constants are obtained by perturbation analysis. As an example of the method, an infinitely extended parabolic index profile is studied     

A new approach for analysis of closed dielectric waveguides

The dispersion characteristics of a class of closed dielectric waveguides are investigated by the method which combines the building-block approach of mul timode network theory with rigorous mode matching procedure. Several numerical examples for different guiding structures have been given by the approach. The same structures are also analyzed with the finite element method and the EDC method for comparison. The calculations show that the present approach yields as highly accurate results as the finite element method while almost retaining the simplicity of the EDC method, and justify the utility of the present method     

Radiation from bent optical waveguides

A simple method is presented for determining the radiation losses due to the bending of an optical waveguide. This method circumvents the use of continuous modes and reduces the problem to elementary antenna theory in which radiation is found from a known surface-current distribution. Practical results are given for the bent fibre of circular cross-section. i.e. a toroidal geometry, both for the HE11 mode and for rays in an overmoded fibre.     

A conformal finite difference time domain technique for modelingcurved dielectric surfaces

In this paper, we present a simple yet accurate conformal Finite Difference Time Domain (FDTD) technique, which can be used to analyze curved dielectric surfaces. Unlike the existing conformal techniques for handling dielectrics, the present approach utilizes the individual electric field component along the edges of the cell, rather than requiring the calculation of its area or volume, which is partially filled with a dielectric material. The new technique shows good agreement with the results derived by mode matching and analytical methods     

Finite element analysis of lossy dielectric waveguides

This paper presents a full-wave analysis of lossy dielectric waveguides using a hybrid vector finite element method. To avoid the occurrences of spurious modes in the formulation, edge elements and first-order nodal finite element basis functions are used to span the transverse and the z components of the electric field, respectively. Furthermore, the direct matrix solution technique with minimum degree of reordering has been combined with the modified Lanczos algorithm to solve for the resultant sparse generalized eigenmatrix equation efficiently     

Experimental analysis of metal coated dielectric waveguides

This paper concerns the experimental characteristics of metal coated dielectric waveguides with a rectangular surface corrugation. Waveguide are designed to operate at a second Bragg frequency of 90 GHz. The period, height and the duty cycle of a rectangular grating were calculated using the chosen frequency. A metallic layer of aluminum is sputtered on one side of the slab waveguide. The purpose of the metallic layer is to simulate a layer of high density plasma on the surface of the waveguide similar to that obtained by optical excitation of semiconductor structures. Experiments were performed to examine the far field radiation pattern, attenuation constant and the dispersion relation. Due to the presence of the plasma layer there will be an angular shift in the far field radiation pattern. We have observed angular shifts of about 20? in the radiation pattern of the waveguide before and after coating. Measurements are made in the frequency range of 88–95 GHz. This waveguide structure can be used to design an electronically steerable antenna and an electronic phase shifter operating in the millimeter-wave frequency band.     

Sparse matrix eigenvalue solver for finite element solution of dielectric waveguides

A method is presented to find a selected set of eigenvalues and the respective eigenvectors of the generalised eigenvalue problem Ax= lambda Bx for large, sparse, real or complex, nonHermitian matrices. Although the method is clearly applicable to other problems, results are given of application to the vectorial finite element analysis of dielectric waveguides.<>     

Coupled-mode analysis of anisotropic dielectric planar branching waveguides

We present a theoretical study of mode propagation in anisotropic planar branching waveguides consisting of isotropic and anisotropic layers. The characteristic equation of anisotropic five-layered structure is introduced to calculate the propagation constants and field patterns of the branching-waveguide modes. Coupled-mode analysis shows that the normalized parameter is effective for the evaluation of mode-coupling effects in the anisotropie branching waveguides as well as in the isotropic branching waveguides.     

Coupled mode analysis of dielectric planar branching waveguides

The mode conversion behavior of planar dielectric branching waveguides is studied as a function of branching angle, propagation direction of modes, and thickness ratio of branches. The multimode coupled equation and new step approximation method of branch taper are introduced, which give the accurate analysis of mode behavior in the branching waveguide of a large taper angle.     

A variational vector finite difference analysis for dielectricwaveguides

A numerical technique based on the finite difference method is developed for the analysis of lossless dielectric waveguides. This method is a variational approach which uses all three components of the magnetic field vector, allowing for the enforcement of the divergence condition. The dispersion characteristics and field distributions for dielectric waveguides are accurately computed. Comparisons are made between the magnetic vectorial finite difference method and a finite element method incorporating the same functional     

Method of lines for the analysis of dielectric waveguides

This paper is concerned with the application of the method of lines (MoL) to the analysis of general dielectric waveguides that are uniform along the direction of propagation, lossfree, and passive. Hybrid-mode dispersion curves, field and intensity distributions for integrated optical waveguides are presented     

Full-wave analysis of dielectric waveguides using tangential vectorfinite elements

A novel method is presented for the analysis of dielectric waveguides. This method provides four major new contributions: (1) a transformation of variables is introduced that allows propagation constants to be computed directly; (2) H₁ (curl) tangential vector finite elements are applied to dielectric waveguides to obtain reliable approximate electromagnetic fields; (3) the Lanczos algorithm is modified to solve the required eigenmatrix equation efficiently; and (4) the reaction principle is used to provide a posteriori error estimates for use in adaptive mesh refinement. The method produces reliable solutions and applies to structures that contain both electric and magnetic inhomogeneities. The answers are refined adaptively to generate waveguide eigenmodes to a specified accuracy. Numerical results of an image guide, a microstrip transmission line, and a pedestal-supported stripline are shown. Computed solutions agree very well with previously published results     

Low transition losses in bent rib waveguides

We reduce the transition losses that occur between curved and straight rib waveguides, by offsetting the guides and placing isolation trenches. Using a three-dimensional (3-D) semivectorial beam propagation program, we also can investigate more novel effects such as rib heights and sidewall slopes. Our consideration of all these effects results in an optimized design     

Comparative analysis of the method-of-lines for three-dimensionalcurved dielectric waveguides

We discuss the effects of waveguide geometry on the radiation loss of tightly curved multimode dielectric waveguides. Three waveguide geometries are investigated: a ridge waveguide, a buried waveguide, and an interdiffused waveguide. We compare the effective index method with both semi- and full-vectorial method-of-lines analyses for these waveguide geometries. This comparison shows that the effective index method is accurate for curved waveguides except where the outer confinement region is in cut-off or, in the case of TM-polarization, for the ridge waveguide. In the latter case, the full-vectorial method-of-lines predicts a resonant feature of the TM-mode radiation loss of curved ridge waveguides; this is not predicted by either the semivectorial method-of-lines or the effective index method     

Infinite elements for the analysis of open dielectric waveguides

The finite-element method is applied to the modal analysis of unbounded, arbitrarily shaped, and arbitrarily inhomogeneous dielectric waveguides with the use of new infinite elements incorporating several radially decaying exponential trial functions. The outer optimization loop required by methods that use a single decaying trial function is eliminated, and all modes corresponding to a given phase constant are calculated in one pass of the solver. The method is tested for examples involving slab, circular, and square dielectric waveguides     

Graded-index planar dielectric waveguides

Properties of planar dielectric waveguides having a diffusion-induced index of refraction distribution are investigated. It is found that the spatial distribution of modes, group velocity, and mode spectrum of these guides differed qualitatively from the corresponding properties found in a slab waveguide. These results were experimentally verified by measuring the mode spectrum of a dielectric waveguide having an assumed complimentary error-function distribution of refractive index.     

A spectral technique for the analysis of time and space-transientsin planar dielectric waveguides

A novel method is proposed for the analysis of transients in dielectric guide, e.g., when excited by a Gaussian beam pulsed in time and modulated by a cosine waveform. This approach, utilizing the full modal spectrum of the guide, results more reliable than existing numerical techniques, while, by virtue of its analytical nature, greatly reducing the computational complexity of the problem