On weakly guiding single-mode optical waveguides

This paper presents a powerful technique to treat the problem of wave propagation along weakly guiding single-mode optical waveguides. The shape as well as the 3-D index variation of the guide may be quite arbitrary as along as the weakly guiding character is preserved. The technique is based on the solution of a scalar-wave equation by the forward-marching fast Fourier transform (FFT) method. Excellent agreements were obtained, with known solutions, for various optical guiding structures. We have also demonstrated the capability of this technique to treat other exotic single-mode structures.     

A partial variational approach for arbitrary discontinuities inplanar dielectric waveguides

A novel approach for analyzing arbitrary discontinuities in planar dielectric waveguides is proposed that uses the finite-element method along with the frontal solution technique. On the basis of the partial variational principle (PVP), the fields interior and exterior to the discontinuity finite-element region can be treated independently and eventually can be coupled. The interior fields are expanded by the finite-element nodal values and the corresponding local bases, while the exterior ones are handled by an approach combining modal expansion and Green's function. In numerical computation, the continuous spectra of the waveguide modes are discretized by the Laguerre expansion method. To check the correctness of the present analysis, two numerical results are compared to those of other methods. The scattering characteristics of several linearly tapered discontinuities, such as transformers and feed structures, are analyzed and compared to those having step junctions     

Study by conformal mapping of TE and TM waves in open dielectric waveguides

We show by suitable conformal mapping and appropriate boundary conditions that theHguide permits study on the Goubau line, theOguide, and the dielectric rod. By this method, we confirm a well-known result [10] and generalize about some new waveguides.     

A scalar variational analysis of rectangular dielectric waveguidesusing Hermite-Gaussian modal approximations

A scalar variational analysis of rectangular dielectric waveguides using Hermite-Gaussian modal approximations is presented. The technique analyzes waveguides by finding a closed-form, approximate solution to the given problem. We begin with an assumed, closed-form field solution, with unknown parameters which can be chosen to best match the assumed field to the actual field solution using variational principles. The values of the unknown parameters of the assumed field are determined by solving a set of simultaneous equations, not by a search method. As a result, this analysis method is computationally fast. Another benefit is that this method gives best-fit, closed-form modal approximations     

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     

A variational coupled-mode theory for periodic waveguides

A simple variational theorem for the dispersion relations and propagation constants of periodic waveguides is derived. The trial fields used in the variational formula incorporate all the Floquet components correct to first order. This yields a propagation constant in which errors enter only to fourth order in the trial field. The analysis yields a new coupled mode formulation which is shown to yield excellent agreement with exact analytic solutions (in l-D), and numerical simulations (in 2-D), for high-index contrast structures     

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     

Full-wave analysis of coplanar waveguides by variational conformalmapping technique

A new full-wave analysis of coplanar waveguides is presented. The modified mapping technique of C.P. Wen (1969) is used to map the original infinite domain into a finite image domain and also to account for the singularity of fields near the conductor edges. The finite thickness of the dielectric substrate is considered together with the assumptions of lossless guides and negligible metallization thickness. The current distributions on the center signal strip as well as the tangential electric fields over the slot along the air-dielectric interface are examined. Numerical results for the frequency-dependent effective dielectric constants and characteristic impedances of coplanar waveguides are presented. Particular attention is given to the electric field distributions over the air-dielectric interface of slots and the current distributions of the signal strip     

Failure of scalar analyses in dielectric optical waveguides with perturbed refractive-index profile

It is theoretically shown that scalar analyses cannot properly predict the propagation constant of a particular mode in circular dielectric optical waveguides when the angular order of the mode satisfies some condition with respect to the order of the Fourier spectrum of the perturbed refractive-index profile.     

Fast frequency sweep technique for the efficient analysis of dielectric waveguides

This paper describes a new approach to spectral response computations of an arbitrary two-dimensional (2-D) waveguide. This technique is based on the tangential-vector finite-element method (TVFEM) in conjunction with the asymptotic waveform evaluation (AWE) technique. The former is used to obtain modes characteristics for a central frequency, whereas the latter employs an efficient algorithm to compute frequency moments for each mode. These moments are then matched via Pade approximation to a reduced-order rational polynomial, which can be used to interpolate each mode over a frequency band with a high degree of accuracy. Furthermore, the moments computations and subsequent interpolation for a given set of frequency points can be done much more rapidly than just simple simulations for each frequency point.     

A modified ray-optic method for arbitrary dielectric waveguides

A modified ray-optic method (MRO) is proposed for evaluating the propagation characteristics of dielectric waveguides with arbitrary refractive index profile. The authors correct the error caused by assuming a constant phase shift for any mode at the turning point on the substrate side. Very simple formulas are given for calculating the dispersion characteristics including those for planar optical waveguides and single-mode fibers. The results are more accurate than those of the ordinary ray-optic method, especially in the near cutoff regions, and agree well with those of the exact numerical methods. A comparison with other analytical and the exact numerical methods shows that the proposed method is simpler than other methods. This method can be extended to other more complicated cases     

Microbending losses for noncircular weakly guiding single-modefibers

The relations between the microbending losses and the mode field halfwidth (MFHW) W_x1, W_y1 based on the nearfield second moment (NFSM) for arbitrary symmetric noncircular weakly guiding single-mode fibers are derived. which can be reduced to the known result for circular-symmetric single-mode fibers     

Analysis of closed arbitrary dielectric waveguides using a modifiedRayleigh-Ritz technique

To avoid the meshing difficulties of the finite-element method, the classical Rayleigh-Ritz method is combined with an additional optimization to analyze closed arbitrary dielectric waveguides. The method is easily implemented in compact code and is user-friendly. The method and its rationale are developed, and numerical examples are presented to demonstrate its accuracy in propagation constant and nonperturbational loss calculations. The method is shown to be rapidly convergent and extremely stable     

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     

A MATRIX METHOD FOR SOLVING PLANAR DIELECTRIC OPTICAL WAVEGUIDES

A matrix method used in multilayer stack of dielectric films is applied-to planar dielectric optical waveguides. A simple and applicable method for obtaining characteristic equation is presented.     

A simple variational approach to optical rib waveguides

A simple method for the calculation of the mode properties of optical rib waveguides is presented. The method is based on a scalar variational principle combined with a vector perturbation analysis for the polarization correction. It is demonstrated that, with the proper trial functions, the approach can predict very accurately the dispersion characteristics with much less effort (in terms of formulation and computation) than the existing numerical techniques. The field patterns of the modes can be computed from the scalar analysis. The vector property of the mode can be taken into account by a perturbation formula. The computation is carried out on an IBM PC. The user-friendly computer program is written in Fortran     

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     

About coupled-mode theories for dielectric waveguides

A critical examination is made of recent works on coupled-mode theory for dielectric waveguides with strongly overlapping fields. It is shown that there is no best formulation. In each case, explicit or implicit approximations lead to errors that are difficult to estimate. An investigation is made of the accuracy of coupled-mode formulas, in the case of strong guidance, for TM waves along coupled slabs or for HE11 modes along circular rods. Contrary to a previous prediction, there is no breakdown of coupled-mode formulas when the guidance is increased. The coupled-mode equations are applied to the problem of nonparallel waveguides in optical directional couplers. Comparison between coupled-mode predictions and beam-propagation-method simulations shows that bending effects in converging and diverging sections affect the accuracy. An improved coupled-mode theory is proposed in order to take these effects into account     

Analysis of dielectric waveguides by a modified Fourierdecomposition method with adaptive mapping parameters

The adaptive modified Fourier decomposition method (A-MFDM), a recently proposed technique to perform the modal analysis of linear and nonlinear two-dimensional dielectric waveguides, is now extended to three-dimensional scalar structures for the first time. The method includes a strategy to automatically find quasioptimum numerical parameters of the technique, which, on the one hand, improves the accuracy in relation to the known Fourier decomposition method (FDM) and, on the other, makes the method self-adaptive. To validate the performance of the method, two linear dielectric waveguides with exact solutions have been defined and analyzed. Finally, the modal analysis of an asymmetrical rib waveguide directional coupler is carried out and the obtained results confirm the clear superiority of the A-MFDM in realistic situations     

FDTD (2, 4)-compatible conformal technique for treatment of dielectric surfaces

A modified conformal technique implemented in the high-order finitedifference time-domain (FDTD) (2, 4) is proposed to investigate the interaction of electromagnetic waves with three-dimensional electrically large curved dielectric objects. The proposed conformal technique uses an average dielectric constant related to the area of different dielectric regions in nine spatial discrete cells. It is numerically demonstrated that the results obtained by this new technique show good agreement with the results obtained by the analytical method and some references, even with coarse meshes adopted for handling electrically large objects effectively.