Analysis of geodesic lenses by beam propagation method

It is shown that geodesic lenses can be analysed by means of the propagating beam method. This method allows one to take diffraction effects and anisotropy into account, while requiring only a moderate amount of computer time. To illustrate the method, a few geodesic lenses are analysed.     

A modified transverse resonance method for the analysis ofmultilayered, multiconductor quasiplanar structures with finiteconductor thickness and mounting grooves

A modified transverse resonance method is presented for analyzing generalized multilayered, multiconductor quasiplanar structures with practical parameters such as finite conductor thickness and mounting grooves. Recurrence relations are obtained by using network theory for obtaining the overall transverse equivalent network. while the discontinuity involving the finite-thickness metal sheet and mounting groove is carried out by a field-theory-based multimodal variational formulation. The frequency behaviors of propagating, evanescent, and complex modes are obtained for several commonly used quasiplanar lines, showing good agreement with published results. Furthermore, a leaky-wave study is carried out for open structures, since the open condition can be included in this formulation without difficulties     

A finite-difference vector beam propagation method forthree-dimensional waveguide structures

A finite-difference vector beam propagation method (FD-VBPM) for three-dimensional waveguide structures is developed. The polarization dependence and coupling of the optical guided-waves in the 3-D structures can be modeled and simulated     

Finite element beam propagation method for three-dimensionaloptical waveguide structures

A beam propagation method (BPM) based on the finite element method (FEM) is described for longitudinally varying three-dimensional (3-D) optical waveguides. In order to avoid nonphysical reflections from the computational window edges, the transparent boundary condition is introduced. The present algorithm using the Pade approximation is, to our knowledge, the first wide-angle finite element beam propagation method for 3-D waveguide structures. To show the validity and usefulness of this approach, numerical results are shown for Gaussian-beam excitation of a straight rib waveguide and guided-mode propagation in a Y-branching rib waveguide     

Analysis of dielectric guides by transverse magnetic field finiteelement penalty method

The main purpose of this paper is to use the finite element method using a penalty function formulation to solve the vector wave equation with transverse H-field formulation together with the boundary operator. We impose continuity conditions on the boundary interfaces for both E _z and H_z components. We apply this technique to obtain the propagation constant for a three-layer ridge structure and a multiple quantum well ridge guide as examples, and a comparison with previously published results shows excellent agreement     

Analysis of lossy dielectric guides by transverse magnetic fieldfinite elements method

Recently a transverse magnetic field formulation of the finite element method for solving lightwave propagation in lossless optical waveguides was demonstrated using only two components of the magnetic field. We extend this formulation to include loss in the waveguides, and compare the results from this formulation with those of other formulations for three different types of waveguides. Our results from the new approach show good agreement with those from previously published data. No perturbation technique is needed to arrive at these results     

Accurate finite difference beam propagation method for complexintegrated optical structures

A simple and effective finite-difference beam propagation method in a z-varying nonuniform mesh is developed. The accuracy and computation time for this method are compared with a standard finite-difference method for both the 3-D and 2-D versions     

Application of the method of lines to cylindrical inhomogeneous propagation structures

The method of lines is applied to the Helmholtz equation in cylindrical co-ordinates to analyse cylindrical inhomogeneous propagation structures such as finlines in circular waveguide housings. The numerical results for the frequency dependent propagation characteristics and the dominant mode characteristic impedance for the finline structures are presented.<>     

A versatile method for analyzing paraxial optical propagation in dielectric structures

This paper presents a fast and accurate quasi-analytic model for studying optical field propagation in weakly guiding dielectric structures. The proposed efficient and versatile computational scheme is obtained by merging the Hermite-Gauss (HG) total field expansion with the numerical collocation method and is particularly suited for longitudinally nonuniform structures. By means of a quasilinearization scheme, the same procedure has also been successfully applied to the analysis of field propagation in Kerr-nonlinear media. The latter achievement gives an indication of the great potentialities offered by this straight forward method. Several examples are discussed in the paper and in all cases the results computed by the proposed method favorably compare with those from alternative methods.     

Network representation and transverse resonance for layeredchirowaveguides

This paper presents an equivalent network method for dispersion analysis of general chirowaveguides. First, wave propagation in each homogeneous layer is represented by two pairs of transmission lines, the matrix wave impedance is defined. Next, the transformation properties of the input impedance are established. It is then demonstrated that the transverse resonance condition involving the previously obtained matrix impedance leads to the dispersion equation for the waveguides. The numerical results show that this network approach is feasible and practicable     

Study of microstrip step discontinuities on bianisotropicsubstrates using the method of lines and transverse resonance technique

A hybrid approach, combining the method of lines (MoL) and transverse resonance technique (TRT), is presented for the analysis of microstrip step discontinuities that are printed on uniaxial or biaxial bi-anisotropic substrates. The method of lines, formulated in terms of Kronecker products, is used to determine the characteristic equation for the resonant length. The transverse resonance technique is applied to obtain the S-parameters of the junction by casting the discontinuity problem as a microwave equivalent network. Good agreement is found between results of the MoL/TRT approach and those obtained by other methods. Effects of individual tensor elements of the substrate on the scattering parameters of the discontinuity are investigated at selected frequencies. The proposed MoL/TRT approach is found to converge very fast and does not require excessive computer memory, with all computations performed on a 486DX-50 MHz PC     

Simulation of waveguide birefringence by beam propagation method

It is demonstrated that, by modifying the waveguide geometry, the beam-propagation method (BPM) can be extended to determine the mode indexes of both polarizations. Such an approach has been implemented into BPM routines. It can be used to determine the birefringence in waveguide structures. The same approach is also applicable in other waveguide simulation programs based on the scalar field approximation. The operational principle and numerical results for planar waveguides are presented, and the extension of this technique to channel waveguides is discussed.<>     

Admittance of transverse waveguide slots in cylindrical structures

The self and mutual admittances of transverse slots in arbitrary conducting cylindrical structures are computed. The analysis is performed in the spectral domain, where all fields and currents have been Fourier transformed along the structure. There are, however, no transformations in the transverse directions. A system of integral equations for cylindrical structures are formulated and solved with the moment method. The induced currents on the structure can thus be determined and used to compute the spectral self and mutual admittance of the slots. The spectral admittance is inverse transformed and included in the overall slot antenna analysis. The analysis is rigorous with trigonometric basis function expansions at the inner and outer slot apertures. Computed results on scattering parameters in the waveguide show good agreement with measured data     

Analysis of abrupt bent waveguides by the beam propagation methodand the conformal mapping method

In this study, we propose a simple and applicable approach to analyze the large angle (larger than 100) abrupt bent waveguides. By using the conformal mapping technique, the abrupt bent waveguide is transformed into an equivalent straight one which the conventional (paraxial) beam propagation method (BPM) can be applied to analyze it directly. The field distribution in a 20° microprism type abrupt bent waveguide is also demonstrated by our method     

Computation of frequency-dependent propagation characteristics ofmicrostriplike propagation structures with discontinuous layers

A general procedure based on the method of lines is presented for the full-wave analysis of propagation structures having layered substrates with step inhomogeneities in each layer. Examples of such structures include microslab lines and microstrip near a substrate edge. It is shown that with this extended method of lines technique the frequency-dependent characteristics, including the modal impedance, current distribution, and other properties of these structures, can be calculated. To illustrate the technique, typical structures such as microstrips on a finite-width dielectric slab and microstrips near a substrate edge are considered, and the effect of the proximity of the edge on the propagation characteristics of the microstrip is computed. For the case of a microstrip near a substrate edge, the numerical results obtained are compared with measured values of propagation constants, showing that the proximity effect is predicted to within 1%     

Analysis of the dispersion characteristics of slow-wave structures with two microwave propagation channels

Models of rectangular and axially symmetric resonator slow-wave structures, which are built using transmission matrix for determining the characteristics of the slow-wave structures in different operation modes, are investigated. Elements of the transmission matrix are determined from the results of 3D simulation with the use of the HFSS software. In the analysis of the dispersion characteristics, slow-wave structures with two microwave propagation channels are studied and simulated using a 4×4 transmission matrix.     

Rotary propagation characteristics of light in multimode- single mode-multimode fiber structures using ray tracing method

The mode theory is the main way to study the propagation characteristics of light in fiber so far, but it is not suitable for analysis of light in duct. By using ray-tracing method, the rotary propagation characteristics of light in multimode-single mode-multimode (MSM) fiber structures are analyzed in this paper. Firstly, the light ray in fiber can propagate around an inscribed circle, and the central axis of this fiber is the propagation axis. Secondly, the radius of the inscribed circle is decided by both incident angle and incident position, and its variation is between 0 and RM, where RM is the radius of the multimode fiber. Lastly, the bigger the ratio of core and cladding diameter is, the higher the propagation efficiency is.     

Structural complexity effects on transverse propagation in atwo-dimensional model of myocardium

A thin sheet of cardiac tissue was modeled as a set of resistively coupled excitable cables with membrane dynamics described by the modified Beeler Reuter model. Transverse connections have a resistance Rn and are regularly distributed with a spacing delta on any given cable, to provide alternating input and output junctions. Flat wave longitudinal propagation corresponds to propagation along a single continuous cable since all units of the network are functionally isolated due to the absence of transverse current flow. Events on a given cable during flat transverse propagation include electrotonic spread of potential from input to output junctions, action potential initiation at input junctions, and collision at output junctions. The propagating two-dimensional transverse wavefront is an undulating transmembrane potential surface with highs at the input junctions and lows at the output junctions. The action potential upstroke is also modulated in a periodic manner with minimum and maximum Vmax at the input and output junctions respectively. Thus, the network is capable of a diversity of dynamic behavior spatially distributed in relation to the specific pattern of transverse connections chosen. Overall, the behavior of the network model is in good agreement with available structural and electrophysiological data on myocardium. In addition, this network topology allows to handle more easily parameters governing propagation and to avoid very large matrices which are costly in computational effort and overall computer time.