New full-vectorial numerically efficient propagation algorithmbased on the finite element method

A new full-vectorial beam propagation algorithm based on the versatile finite element method, in order to accurately characterize three-dimensional (3-D) optical guided-wave devices, is presented. The computationally efficient formulation is based on the two transverse components of the magnetic field without destroying the sparsity of the matrix equation. The robust perfectly matched layer (PML) boundary condition is incorporated into the formulation so as to effectively absorb the unwanted radiation out of the computational domain. The efficiency and precision of the proposed full-vectorial propagation approach is demonstrated through the analysis of single optical waveguide, directional couplers, and electrooptic modulator     

Full-vectorial finite-element beam propagation method for nonlineardirectional coupler devices

A new full-vectorial beam propagation algorithm based on the computationally-efficient finite element method is presented which can accurately model nonlinear directional couplers. The robust perfectly matched layer boundary condition is incorporated into the formulation so as to effectively absorb the unwanted radiation out of the computational domain. The accuracy of the proposed vectorial propagation approach is demonstrated through comparison with other semivectorial approaches and the weaknesses of the commonly-used scalar approaches are highlighted. The proposed full-vectorial approach considers only two transverse components of the magnetic field without destroying the sparsity of the matrix equation, so it is numerically very efficient     

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     

3-D Full-Vectorial Analysis of Strong Optical Waveguide Discontinuities Using Pade Approximants

A full-vectorial 3-D numerical method applicable to high-index contrast optical waveguide discontinuities is presented. Rigorous treatment of the longitudinal boundary condition is incorporated in the formulation. The square root of the characteristic matrix is approximated using Padeacute approximants which results in an efficient implementation. The biconjugate gradient stabilized method is utilized to iteratively calculate the reflected and transmitted fields. A preconditioner is proposed which results in reduced number of iterations. The proposed method is applied to various optical waveguide facets exhibiting strong transverse and longitudinal refractive index discontinuities. In all cases, the modal reflectivities of the fundamental TE-Like and TM-Like modes are calculated for both the full-vectorial and the semi-vectorial formulations. Significant difference in the calculated modal reflectivity is seen between the full and semi-vectorial models. The error in the power balance remains low in the full-vectorial case irrespective of the waveguide dimensions. However, in the semi-vectorial case, the error in the power balance is found to increase when the waveguide width is reduced     

Explicit finite difference vectorial beam propagation method

A vectorial beam propagation method (VBPM) is formulated and implemented using the explicit finite difference (EFD) scheme. The accuracy of semivectorial EFD-BPM, where the polarisation coupling is ignored but polarisation dependence is included, is found to be as good as that of full-vectorial EFD-BPM.<>     

Full-Vectorial Mode Solver for Bending Waveguides Using Multidomain Pseudospectral Method in a Cylindrical Coordinate System

A full-vectorial mode solver for bending waveguides using a spectral collocation method in a local cylindrical coordinate system is described. The perfectly matched layers' absorption boundary conditions are incorporated into the present method for effectively demonstrating the leaky nature of the bending waveguides. The domain decomposition technique is utilized for improving the computational accuracy and stability. A bending rib waveguide with high index contrast is considered as a numerical example to validate the established method.      

Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide

The full-vectorial beam-propagation method with the improved finite-difference formula is applied to the analysis of a TE/TM mode converter based on an asymmetric periodic loaded waveguide. The polarization conversion behavior is measured at a microwave frequency. It is demonstrated that the calculated complete conversion length is in agreement with the experimental result.     

A full-vectorial beam propagation method for anisotropic waveguides

An extension of the full-vectorial beam propagation method to anisotropic media is presented. Optical waveguides made of anisotropic materials can be modeled and simulated. The polarization dependence and coupling due to both the material and the geometric effects are considered     

Optimization of the optical properties of a deeply etched semiconductor electrooptic modulator

A rigorous numerical study of a deeply etched semiconductor electrooptic modulator is presented. A Laplace equation solver followed by a full-vectorial modal solution technique for general anisotropic optical waveguides, all based on the versatile finite-element method, is used to find the potential distribution, the modulating electric fields, the changes in the permittivity tensor associated with the electrooptic effect, and the different modes of propagation. In particular, the optimization of the optical properties of the modulator structure such as the half-wave voltage length product V/sub /spl pi//L and the optical losses due to the imperfectly conducting electrodes has been carefully carried out and results reported. In addition, the effect of the waveguide parameters on the microwave properties such as the microwave index n/sub m/ and characteristic impedance Z/sub c/ is explained.     

Improved full-vectorial beam propagation method with high accuracy for arbitrary optical waveguides

An improved finite-difference (FD) full-vectorial beam propagation method is introduced for arbitrary optical waveguides with a dramatic improvement in accuracy. This method is developed based on the generalized Douglas scheme and a novel FD formula for the cross-coupling terms which, expressed in explicit form, is independent of specific types of waveguides. The present method is demonstrated for a strongly guiding rib waveguide.     

Novel finite-element formulation for vectorial beam propagationanalysis in anisotropic medium

A novel full-vectorial finite-element beam propagation method for dielectric anisotropic media is presented. This computationally efficient approach uses only the transverse magnetic field components and is free of spurious solutions. Comparisons with other numerical and experimental results validate the method     

Imaging of biomedical data using a multiplicative regularizedcontrast source inversion method

In this paper, the recently developed multiplicative regularized contrast source inversion method is applied to microwave biomedical applications. The inversion method is fully iterative and avoids solving any forward problem in each iterative step. In this way, the inverse scattering problem can efficiently be solved. Moreover, the recently developed multiplicative regularizer allows us to apply the method blindly to experimental data. We demonstrate inversion from experimental data collected by a 2.33-GHz circular microwave scanner using a two-dimensional (2-D) TM polarization measurement setup. Further some results of a feasibility study of the present inversion method to the 2-D TE polarization and the full-vectorial three-dimensional measurement will be presented as well     

Generalized Finite-Difference Time-Domain Method Utilizing Auxiliary Differential Equations for the Full-Vectorial Analysis of Photonic Crystal Fibers

We present the generalized finite-difference time-domain full-vectorial method by reformulating the time-dependent Maxwell's curl equations with electric flux density and magnetic field intensity, with auxiliary differential equations using complex-conjugate pole-residue pairs. The model is generic and robust to treat general frequency-dependent material and nonlinear material. The Sellmeier equation is implicitly incorporated as a special case of the general formulation to account for material dispersion of fused silica. The results are in good agreement with the results from the multipole method. Kerr nonlinearity is also incorporated in the model and demonstrated. Nonlinear solutions are provided for a one ring photonic crystal fiber as an example.     

Two-dimensional Kagome photonic bandgap waveguide

The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes is investigated with respect to the width of the 2D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out     

Implicit Yee-mesh-based finite-difference full-vectorial beam-propagation method

A novel Yee-mesh-based finite-difference full-vectorial beam-propagation method is proposed with the aid of an implicit scheme. The efficient algorithm is developed by splitting the propagation axis into two steps. The eigenmode analysis of a rib waveguide is performed using the imaginary-distance procedure. The results show that the present method offers reduction in computational time and memory, while maintaining the same accuracy as the conventional explicit Yee-mesh-based imaginary-distance beam-propagation method. It is demonstrated by the analysis of a polarization converter that the present method can be used for not only the eigenmode analysis but also the propagating beam analysis.     

Rigorous numerical analysis of mode beating in tapered semiconductor amplifiers

The evolution of the optical beam profile along a high-power tapered semiconductor amplifier has been demonstrated by using rigorous and full-vectorial numerical approaches, based on the finite-element method. Numerically simulated results indicate the generation of many higher order modes, and their interference with the fundamental mode causes a variation of the optical beam, both along the transverse and the axial directions, which could significantly modify the output beam quality.     

Metal-Coated Defect-Core Photonic Crystal Fiber for THz Propagation

Modal solutions for metal-coated defect-core photonic crystal fiber (PCF) with a central air-hole have been obtained by using a full-vectorial finite element method to model the guidance of THz waves. It has been shown that the surface plasmon modes can couple with the defect-core PCF mode to form supermodes, with potential for sensing applications.      

Finite-element formulation for full-vectorial propagation analysis in three-dimensional optical waveguides

A three-dimensional (3-D) full-vectorial beam propagation method based on finite elements is presented. A new formulation suitable for the numerical discretization through the finite elements and able to take into account both polarization dependence and field component coupling has been derived. Advantages and potentialities of the finite elements usage are discussed. The precision of the proposed approach is demonstrated through numerical examples.     

An efficient full-vectorial finite-element modal analysis ofdielectric waveguides incorporating inhomogeneous elements acrossdielectric discontinuities

A new vectorial finite-element method (FEM) free of spurious modes is proposed for analyzing optical waveguides with sharp corners in the cross section. The method is formulated in terms of the transverse field components H_x and H_y or E_x and E_y , and it explicitly shows the relationships between the semivectorial and the full-vectorial wave equations. In this method, we introduce the distribution concept and an inhomogeneous element to describe the field across the dielectric interface, and the error in the numerical solution caused by the dielectric discontinuity is reduced. We show how the width of such inhomogeneous elements and the number of nodes would affect the numerical result and its convergent rate using the dielectric-loaded rectangular waveguide, the channel waveguide, and the rib waveguide as analysis examples. For the dielectric-loaded rectangular waveguide, we compare our results with the exact solutions. For the rib waveguide, we compare our results with previously published data based on other methods. Also, field convergence near the corners is discussed     

Bragg光纤色散和损耗特性的全矢量有限差分分析

利用全矢量有限差分方法分析了空气纤芯Bragg光纤中模式的色散和泄漏损耗特性,并结合光子带隙图,讨论了其中TE01模和HE11模泄漏损耗的变化趋势.当色散曲线由光子禁带进入光子导带,模式的泄漏损耗将相应地明显增大;此外,当λ1.49μm时,HE11模的截止引起了泄漏损耗的急剧上升.这表明,Bragg光纤中,模式泄漏损耗的增加至少可以归结于两种不同的机制:模式失去光子带隙的约束和模式截止.同时,通过分析发现,其中高阶模的截止条件类似于金属波导;这是Bragg光纤与金属波导特性具有一定相似性的又一例证.