Impedance boundary method of moments for accurate and efficientanalysis of planar graded-index optical waveguides

An impedance boundary method of moments (IBMOM) is proposed to accurately and efficiently compute the propagation characteristics including the number of guided modes of general graded-index dielectric slab waveguide structures. The method is based on Galerkin's procedure in the method of moments and employs the exact impedance boundary condition at the interfaces between the graded-index region and constant-index cladding. Legendre polynomials are utilized in the field expansion. Computational results are shown for waveguides with various inhomogeneous refractive index profiles. The results indicate that typically five Legendre polynomials are sufficient for accurate solutions of the dominant TE and TM modes in optical waveguides having a finite region of inhomogeneous refractive index. Diffused optical waveguides with untruncated index profiles as well as coupled dielectric waveguides can be accurately analyzed using ten Legendre polynomials     

Rigorously modeling short bent, graded-index dielectric slabwaveguides

Circularly short bent, graded-index dielectric slab waveguides are mathematically modeled using both a direct integration method and a source-type integral equation method. The former method is easy to implement, requiring only small amounts of computer time. The latter method has the potential to be extended to a rigorous model for bent channel waveguides. Both homogeneous and inhomogeneous slab waveguide layers are considered. The mathematical models are validated through comparison of the numerical results with results obtained by the analytical resonance conditions. Numerous numerical examples are given     

Comparison of Absorption Loss in Metal-Clad Optical Waveguides (Short Paper)

A comparison of the absorption loss performance of three types of metal-clad slab waveguides is made with the material and waveguide properties standardized. The basic three-layer configuration of the step-index waveguide and two graded-index waveguides is considered the latter two are also considered as two-layer structures. The comparative loss behavior is discussed from the point of view of application in mode and polarization filtering.     

A Semianalytical Technique for Leaky-Mode Loss Calculation in Hollow Dielectric Waveguides With Arbitrary Cross Sections

We present an approximate semianalytical technique for the calculation of the loss coefficient of leaky modes in 3-D hollow dielectric waveguides having an arbitrary cross section. The hollow waveguides are assumed to have an axis of symmetry and to have a cladding with a higher refractive index than the core. An expression for the modal loss coefficient is derived using a ray-optics approach with paraxial approximation. For the special cases of specific cross sections with known solutions, our technique gives results that are identical to the available analytical solutions. The technique is then applied on practical waveguide geometries, allowing the calculation of polarization- and wavelength-dependent losses. Full numerical alternatives to the technique involve time-consuming simulations and, sometimes, difficulty in incorporating a suitable boundary condition to obtain leaky-mode solutions.     

Utilization of Anisotropic Metamaterial Layers in Waveguide Miniaturization and Transitions

We introduce a new approach which enables a waveguide to support propagation of electromagnetic waves below the cutoff frequency, as well as which avoids undesirable reflections in a waveguide. These are achieved through the usage of an anisotropic metamaterial layer by employing the concept of coordinate transformation. The proposed method can be utilized for the fabrication of miniaturized waveguides, and for the elimination of discontinuities in abrupt waveguide transitions. We demonstrate some numerical experiments for finite element simulations of parallel-plate and dielectric slab waveguides.     

Loss reduction in curved dielectric optical slab waveguide

Formulas of the pure bending loss and the transition loss valid for TM modes in dielectric optical slab waveguides are presented. The characteristic of the total transmission loss of a step-index slab waveguide containing a circular bend having an asymmetric waveguide structure are analysed numerically by applying derived loss formulas. It is found that the features of the total transmission loss of TM modes are closely analogous to those of TE modes except for small discrepancies in the numerical values.     

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     

Uniform Asymptotic Technique for Analyzing Wave Propagation in Inhomogeneous Slab Waveguides

The guided modes of inhomogeneous dielectric slab waveguides are analyzed by a uniform asymptotic technique based on the related equation method. This technique gives highly accurate solutions in the sense of asymptotic expansion. The algorithm for calculating the guided modes of slab waveguides with an even polynomial refractive-index medium is presented. As an example, we calculate the third-order approximate solutions for the guided modes in an analytic form. The results show that the WKB solutions for higher order modes are more accurate than for the lower order modes and the correction to the WKB solutions is significant for the lower order modes. The numerical result for eigenvalues and modal fields confirms that the third-order asymptotic solution is accurate for all the guided modes of the near-parabolic profile waveguides and for higher order modes in the case of the quasi-Gaussian profile.     

High-silica multimode channel waveguide structure for minimizing fiber-waveguide-fiber coupling loss

The optimum structure for high-silica channel waveguides which are connected to input and output graded-index fibers having a 50-μm core diameter and a 1.0-percent refractive-index difference is studied theoretically and experimentally. Theoretical optimum waveguide structure is obtained on the basis of ray optic analysis. For the step-index waveguide with 1.0-percent refractive-index difference, the theoretical minimum coupling loss (input coupling loss + output coupling loss) is 1.7 dB for an optimum core of 38 μm both in depth and width. For the graded-index waveguide with parabolic-index profile in the depth direction and step-index profile in the width direction, the theoretical coupling loss is 1.1 dB for an optimum core of 38 μm in width and 50 μm in depth. These estimations were in good agreement with the experimental results, which were 1.8 dB for the step-index waveguide and 1.3 dB for the graded-index waveguide.     

Twin Symmetric E-plane Slab Loaded Waveguide Structure for Point Beam Acceleration

Renewed interest regarding the exploitation of dielectric loaded waveguides in high gradient accelerator structures requires a closed form field formulation as cut-off frequencies and optimisation are problematic for numerical methods. In this paper we will present efficient closed form solution for generic slab loaded waveguide boundary value problems. This solution offers flexibility in a sense that it can be further exploited to derive a Green’s function linking transverse field expressions for planar structures. The developed solution is demonstrated for a twin slab E-plane slab loaded structure coupled to a Point source emitter assembly. The emission characteristics of the point source emitter assembly are optimized to generate a high intensity and focused beam to be fed to this E-plane slab loaded waveguide structure for beam acceleration. The field analysis, mode nomenclature, modal hierarchy, modal bandwidth, cut-off plane, impedance plane and dispersion relations for this accelerating structure is included for sake the of completeness.     

A novel design and analysis of low loss abrupt bends of dielectricslab waveguides

On the basis of the well-known laws of reflection and refraction of the plane electromagnetic waves, a concept for designing very low loss nonadiabatic junctions between tilted straight sections of dielectric waveguides is investigated. Combining the ray representation of the propagating modes with the equivalent source formulation of the dielectric waveguide excitation problem, a simple and accurate 2-D theory for treating such bends in slab waveguides is developed. Numerical results for typical cases are explained along with some new junctions for achieving large angle redirection of guided waves with very low bending loss     

Properties of the slab modes in photonic crystal optical waveguides

We show that by placing a slab of semiconductor material between two photonic bandgap (PBG) mirrors, waveguide modes at frequencies out of the PBG can be obtained. These modes are similar to the modes of a conventional dielectric slab waveguide. Using these modes, we can obtain very good coupling between a PBG waveguide and a dielectric slab waveguide with similar slab properties. We discuss the properties of these slab modes and outline the guideline for the optimization of the PBG waveguides based on these properties     

A nonuniform FDTD technique for efficient analysis of propagationcharacteristics of optical-fiber waveguides

In this paper, we present a highly efficient one-dimensional cylindrical nonuniform finite-difference time-domain (1-D CNUFDTD) method, which utilizes the unsplit anisotropic perfectly matched layer (APML) for mesh truncation along the radial direction to analyze axisymmetric optical-fiber waveguides. As a first step, we validate the proposed FDTD algorithm by analyzing a uniform dielectric waveguide of circular cross section and show that the results are in excellent agreement with the conventional mode theory solutions. Next, we apply the algorithm to analyze propagation characteristics of a number of commonly used optical-fiber waveguides, i.e., step-index multimode, graded-index multimode, and single-mode step-index configurations     

A dielectric rod waveguide coupled with metal rectangular waveguide

Measurements have been done in the millimeter wave region on a composite waveguide which comprises a dielectric rod waveguide connecting two metal rectangular waveguides. Such a waveguide has been used by us in a Josephson harmonic mixer installed in a small metal cryostat, to prevent the thermal invasion from outside environment and to transmit both signal and LO waves with small losses. The measured transmission loss, that is caused mainly by the coupling loss between metal rectangular waveguides (TE₁₀ mode) and a dielectric rod waveguide (HE₁₁ mode), has been less than 2dB in the frequency range of 52–104 GHz.     

Confinement factors and gain in optical amplifiers

A new identity is derived which relates the gain and the field distribution (or confinement factor) in a dielectric waveguide with complex refractive indices. This identity is valid for any guided mode of waveguides with an arbitrary cross section. It provides a new check of the accuracy of mode solvers. Also, it can be used in a variational approach to predict the gain or loss of a guided mode based on knowledge of confinement factors. It is shown that a previous analysis that is often used, is not correct. In addition, approximate expressions for the gain in slab waveguides are presented     

Phase constants and scattering electromagnetic properties of circular dielectric waveguides

A variational method, based on the telegraphist's equations, is used to calculate the dispersion and scattering characteristics of circular dielectric waveguides which arc enclosed by perfectly conducting walls of rectangular cross-section. Our propagation solutions are compared with those obtained by other authors and the convergence of the method is evaluated. A procedure which combines this variational method with the modal matching technique was implemented in order to analyse multiple discontinuities in cyclindrical dielectric waveguides. To verify the usefulness and accuracy of the procedure, theoretical and experimental results were obtained for different dielectric guiding structures, connected by means of abrupt and gradual transitions. The experimental values show a good agreement with the theoretical ones.     

Mode structure and lateral confinement in strip-loaded opticalwaveguides: Effects of asymmetric cladding

Strip-loaded waveguides formed from three dielectric layers are used in integrated optics to confine and channel light in two dimensions. The numerical analysis reported shows that modal characteristics of such systems can be strongly affected by any differences between the refractive indexes of the upper and lower cladding. Asymmetries that tend to shift intensity toward the upper cladding generally act to tighten lateral confinement, introduce additional lateral modes, and displace the modes up into the strip. These effects are explained by noting the interplay of vertical and lateral confinement in a strip-loaded waveguide, and by analogy to one-dimensional slab waveguides     

非均匀介质填充波导本征值问题的有限元分析

本文讨论了用有限元法求解非均匀介质填充波导本征值问题的具体过程。给出了有关的计算公式和程序。作为例子,对条形介质填充矩形波导主模场结构的分析和色散特性的计算,获得了与解析解十分一致的结果,从而证实了所述程序的可靠性。     

Losses in optical waveguide formed by silver-sodium ion exchange

Propagation losses of optical waveguides formed by ion exchange from molten salts of silver nitrate are discussed. The refractive index in pyrex glass substrates is shown to obey an exponential profile and the resultant mode functions are also examined for the graded-index surface waveguide in order to understand the mechanism of a scattering loss. The attenuation of the sample waveguides is found to range from 2.0 to 2.5 dB/cm for TE0mode excitation and to be decreasing with increasing both the mode number of the guided beam and the waveguide thickness that is proportional to a square root of diffusion time. These results indicate that the predominant loss origin is silver ion concentration diffused in the glass.