Optical Waveguides: Numerical Modeling
 

An asterisk next to a package name (e.g. FemSIM*) indicates the software that can only be used for mode solving; all other software described in this page can be used as both, mode solvers and wave propagators.

FEM Software developed and used for optical waveguides

COMSOL Multiphysics

Commercial software sold by COMSOL Multiphysics (formerly FEMLAB).

FEMLAB is a simulation package that solves systems of coupled nonlinear partial differential equations through the finite element method in one, two and three dimensions.

Simulation Technology and Capabilities:

  • Interactive modeling and simulation using finite element analysis
  • Predefined physics and user defined equations in the GUI
  • Unlimited physics combinations
  • High-performance numerical algorithms
  • Powerful postprocessing capabilities
  • Extensive model libraries
  • Optional application-specific add-ons
  • Bidirectional interface to Matlab® & Simulink®
  • RF Module developed for RF, microwave and optical structures engineering that can be easily combined with other modules

Waveguides-related applications:

  • Optical fibers and waveguides
  • Photonic crystal waveguides
  • Microwave and optical components
  • Plasmonics
  • Surface plasmon resonance

Waveguides-related publications:

  • S.-K. Kim et al., "Metal-slotted polymer optical waveguide device, " Appl. Phys. Lett. 90, 243507 (2007).
  • J. S. Petrovic et al., "Multiple Period Resonances in Long Period Gratings in Photonic Crystal Fibres, " Opt. and Quantum Electron. 38, 209 (2006).
  • P. Dardano et al., "Investigation of a tunable T-shaped waveguide based on a silicon 2D photonic crystal, " J. Opt. A: Pure Appl. Opt. 8, S554 (2006).
  • F.M. De Paola et al., "Novel optoelectronic simulation strategy of an ultra-fast InP/InGaAsP modulator," Opt. Commun. 256, 326 (2005).
  • J. Brown et al., "Nano dispersion amplified waveguide structures," Opt. Express 12, 1228 (2004), www.opticsinfobase.org/abstract.cfm?id=79444.
  • T. Schwartz and R. Piestun, "Waveguiding in air by total external reflection from ultralow index metamaterials, " Appl. Phys. Lett. 85, 1 (2004).

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EMFlex

Commercial software sold by Weidlinger Associates.

EMFlex is a time domain finite-element solver for Maxwell's electromagnetics equations for optical modeling.

Simulation Technology and Capabilities:

  • Wide range of modeling capabilities in two and three dimensions
  • The materials are assumed to be isotropic or anisotropic dielectrics
  • Drude model is included for modeling metals or dielectrics
  • Perfectly conducting material is supported as a useful approximation for metals
  • Time-domain analyses are performed using an explicit time-integration technique that avoids the difficulties of manipulating large assembled matrices for the model. This approach restricts the computational time-step to satisfy the Courant stability criteria
  • EMFlex uses cartesian isoparametric finite elements to model a continuum
  • 2-D models use 4-noded quadrilateral elements, 3-D models use 8-noded hexahedron elements
  • Robust and accurate boundary conditions
  • Output includes time histories and/or snapshots of field variables
  • Although frequency domain results are typically of interest, large advantages in speed and problem-size are obtained by integrating to steady state in the time domain, then extracting amplitude and phase quantities via a discrete Fourier transform

Waveguides-related applications:

  • Integrated optics
  • Waveguides
  • Grating couplers
  • Resonators

Waveguides-related publications:

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FemSIM*

Commercial software sold by RSoft.

FemSIM is a generalized mode solver based on the finite element method that can calculate any number of transverse or cavity modes of an arbitrary structure on a non-uniform mesh.

Simulation Technology and Capabilities:

  • FemSIM is based on a full-vector implementation of the finite element method on a non-uniform mesh
  • Full-vectorial analysis for both Cartesian and cylindrical (azimuthally symmetric) structures
  • Accommodates complex index for lossy materials and high index contrast profiles
  • Intelligent meshing scheme which conforms to the index profile using hybrid triangular and rectangular mesh elements
  • First and second order elements used to avoid spurious modes
  • PML and symmetric/anti-symmetric boundary conditions
  • Determination of propagating, leaky, and cavity modes
  • Higher order modes can be found with minimal additional computational expense

Waveguides-related applications:

  • Structures with arbitrary profiles, including those with curved or uncommon shapes
  • Structures with high index contrast and/or small feature sizes
  • Highly hybrid devices
  • Lossy structures
  • Silicon-based devices
  • Polarization rotators
  • Air or solid core photonic fibers
  • Laser and PBG defect cavities

Waveguides-related publications:

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FIMMWAVE-FEM-Solver*

Commercial software sold by Photon Design.

FIMMWAVE-FEM-Solver is a finite element method based solver that locates and analyzes the eigenmodes of almost any waveguide supported by FIMMWAVE.

Simulation Technology and Capabilities:

  • Real index and lossy materials
  • Fast
  • Fully automatic mode finder
  • Finds many modes simultaneously
  • First and second order elements
  • Anisotropic materials
  • High quality, fast fully automatic mesh generator optimised for electro-magnetic problems
  • Ideal for structures with curved interfaces or unusual shapes
  • All features of FIMMWAVE available, including:
    • Calculation of confinement factor, group index and dispersion
    • Plot all fields of mode profiles in many forms – contour plot, colour maps, Gouraud
      (surface) plots
    • Export all mode data to ASCII file.
    • General Scanner to generate plots of mode properties versus any waveguide parameter – e.g. group index versus core refractive-index, confinement factor versus core thickness etc.
  • Fully integrated with the FIMMPROP (propagation tool), so that it may be used to generate the basis-set modes of a FIMMPROP simulation.

Waveguides-related applications:

  • Holey fibers
  • Elliptical fibers
  • Odd-shaped waveguide with curved and/or slanting interfaces
  • Diffused waveguides and other structures with smoothly varying refractive index

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JCMwave

Commercial software sold by JCMwave.

JCMwave is a finite element software for the computation of electromagnetic wave propagation and more specifically, modern nano-optical devices.

Simulation Technology and Capabilities:

  • The rigorous physical model for all three main modules JCMharmony , JCMmode and JCMresonance are the time-harmonic fully vectorial Maxwell's equations
  • Nedelec's Edge Elements of higher order used
  • TBC implemented with the Pole Condition Concept which allows to deal with inhomogeneous exterior domains
  • Based on an error estimator the solver automatically refines the finite element mesh to reach a prescribed accuracy
  • Predefined Calculation Accuracy
  • Automatic Mesh Refinement
  • Fast and Robust Multi-Grid Algorithms
  • New Implementation of the PML method based on the Pole Condition
  • Smooth and Abrupt Changes in the Permittivity and Permeability Tensor Fields
  • Multiscale Structures in 1D, 2D and 3D
  • High Refractive Index-Contrast Structures
  • Polarization Effects, Gain and Loss
  • Anisotropic Materials
  • Inhomogeneous Exterior Domains

Waveguides-related applications:

  • Integrated Optics
  • Gratings, Coatings
  • Fiber-to-Chip Coupling
  • Transmission and Reflection of Waveguides,
  • Microlenses, Micromirrors
  • Meta Materials, Nano-Optics
  • Optical Fibers, Photonic Crystal Fibers
  • Integrated Optical Waveguides
  • Plasmonic Waveguides
  • Microcavities, Microlaser Modes, VCSEL
  • Photonic Bandgap Structures

Waveguides-related publications:

  • L. Zschiedrich et al., "Goal oriented adaptive finite element method for precise simulations of optical components," Proc. of SPIE Vol. 6475, 64750H (2007)
  • J. Pomplun et al., "FEM investigation of leaky modes in hollow core photonic crystal fibers," Proc. of SPIE Vol. 6480, 64800M (2007)
  • R. Holzlöhner et al., "Efficient optimization of hollow-core photonic crystal fiber design using the finite element method," JEOS-Rapid Publications 1, 0611 (2006)
  • S. Burger et al., Adaptive FEM Solver for the Computation of Electromagnetic Eigenmodes in 3D Photonic Crystal Structures, Springer (2007).

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PDE2D

Commercial software sold by Visual Numerics. Earlier IMSL versions: TWODEPEP and PDE/PROTRAN.

PDE2D solves general nonlinear, time-dependent, steady-state and eigenvalue systems of partial differential equations, in 1D intervals, general 2D regions and a wide range of simple 3D regions.

Simulation Technology and Capabilities:

  • Galerkin finite element method with isoparametric triangular elements of up to 4th degree used for the 2D problems
  • Collocation finite element method with cubic Hermite basis functions used for 3D problems.
  • Both Galerkin and collocation algorithms are available for 1D and 2D problems
  • Adaptive refinement and grading of the triangular mesh are available for 2D problems.
  • Interactive user interface
  • Extensive graphical output capabilities
  • Easy to use, user does not need to be a programmer
  • Eliminates the need to write code from scratch
  • All the speed and flexibility of FORTRAN
  • Display results with built-in graphics, a MATLAB m-file, or other graphics programs

Waveguides-related applications:

  • Birefringent optical fibers
  • Nonlinear optical fibers and waveguides
  • Strongly guiding structures
  • Gain/loss effects in photonic devices
  • Integrated optical resonators

Waveguides-related publications:

  • D. Chowdhury and D. Wilcox, "Comparison Between Optical Fiber Birefringence Induced by Stress Anisotropy and Geometric Deformation," IEEE J. Sel. Top. Quantum Electron. 6, 227 (2000).
  • M. Fontaine, "Cross-phase Modulation Phenomena in Strongly Guiding Waveguides: A Theoretical Approach Revisited," J. Opt. Soc. Am. B15, 964 (1998).
  • M. Fontaine, "Theoretical Approach to Investigating Cross-phase Modulation Phenomena in Waveguides with Arbitrary Cross Sections," J. Opt. Soc. Am. B14, 1444 (1997).
  • V. Tzolov et al., "Full Vectorial Simulation for Characterizing Loss or Gain in Optical Devices with an Accurate and Automated Finite-Element Method," Appl. Opt. 36, 622 (1997).
  • M. Fontaine et al., "Theoretical and Experimental Analysis of Thermal Stress Effects on Modal Polarization Properties of Highly Birefringent Optical Fibers," J. of Lightwave Technol. 14, 585 (1996).
  • P. Heimala et al., "Thermally Tunable Integrated Optical Ring Resonator with Poly-Si Thermistor," J. Lightwave Technol. 14, 2260 (1996).
  • V. Tzolov et al., "Nonlinear Modal Parameters of Optical Fibers: A Full-Vectorial Approach," J. Opt. Soc. Am B12, 1933 (1995).
  • V. Tzolov and M. Fontaine, "Theoretical Analysis of Birefringence and Form-Induced Polarization Mode Dispersion in Birefringent Optical Fibers: a Full-Vectorial Approach," J. Appl. Phys. 77, 1, (1995).
  • S. Cvetkovic et al., "Comparison of Two Interactive Finite Element Programs for Analysis of Optical and Microwave Waveguides," J. Lightwave Technol. 12, 1112 (1994).
  • S. Cvetkovic et al., "Automated Finite Element Solution of Non-Linear Optical Waveguide Problems in Two Dimensions," Microwave and Optical Technol. Lett. 7 293 (1994).

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FE Solvers that could be useful for optical waveguide modeling

EMAP

EMAP (ElectroMagnetic Analysis Program - free software) is a family of three-dimensional finite element modeling codes that can be used to analyze simple 3-dimensional geometries. The EMAP codes are relatively easy to learn to use and are distributed in source code form. The EMAP codes are not intended to compete with commercial finite element modeling codes. They do not have a sophisticated mesh generator, graphical output, or unlimited technical support. Their primary strengths are ease-of-use, modest resource requirements, and accurate modeling of simple three-dimensional configurations over a wide range of frequencies.

Simulation Technology and Capabilities:

  • EMAP1 is based on a variational formulation
  • EMAP-2 uses the Galerkin finite element formulation
  • Both EMAP1 and EMAP2 are scalar (node-based) codes
  • EMAP3 is a vector (edge element) code
  • EMAP4 is an improved version of EMAP3, more efficient and can model lossy materials
  • EMAP5 is a hybrid FEM/MOM code
  • EMAP1 is a good choice of codes for instructors that wish to illustrate "spurious modes", which are often a problem with scalar full-wave finite element codes
  • Non spurious modes in EMAP2
  • All of the EMAP codes are written in the C programming language and can be compiled and run on PCs, workstations, or mainframes
  • The EMAP1, EMAP2, and EMAP3 codes are no longer supported, but they may be useful to educators or researchers who are looking for basic scalar or non-complex-element vector FEM codes

Waveguides-related publications:

  • G. L. Maile, "Three-dimensional analysis of electromagnetic problems by finite element methods," Ph.D. Dissertation, University of Cambridge, U.K. (1979); http://www.emclab.umr.edu/emap4/.
  • D. R. Lynch and K. D. Paulsen, "Origin of vector parasites in numerical Maxwell solutions," IEEE Trans. on Microwave Theory and Techniques 39, 383 (1991).
  • D. R. Lynch and K. D. Paulsen, "Elimination of vector parasites in finite element Maxwell solutions," IEEE Trans. on Microwave Theory and Techniques 39, 395 (1991).
  • T. H. Hubing et al., "EMAP: a 3-D, finite element modeling code for analyzing time-varying electromagnetic fields," Journal of the Applied Computational Electromagnetics Society 8 (1993).
  • T. H. Hubing and M. W. Ali, "EMC Applications of EMAP-2: A 3D Finite Element Modeling Code," Proc. of the 1993 IEEE International EMC Symposium, 279 (1993).
  • Y. Ji and T. Hubing, "EMAP5: a 3D hybrid FEM/MOM code," Journal of the Applied Computational Electromagnetics Society 15, 1 (2000).

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EMSolve

Free software developed by Lawrence Livermore National Laboratory.

Simulation Technology and Capabilities:

  • Galerkin discretization of Maxwell's equations using Nedelec's H(curl) and H(div) finite element basis functions
  • Stable, charge conserving, and energy conserving solution of Maxwell's equations
  • Several different types of finite element basis functions are supported
  • Several different differential operators are supported
  • EMSolve can be used to solve a variety of PDEs such as Poisson's equation, div-curl systems, diffusion problems, Helmholtz equations, wave equations, etc.
  • Designed primarily for MPI-based distributed memory supercomputers
  • EMSolve code suite can be made available to external users

Waveguides-related applications:

  • Optical fibers, bent fibers
  • Photonic crystal waveguides

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FlexPDE

Commercial software sold by PDE Solutions.

FlexPDE is a scripted finite element model builder and numerical solver.

Simulation Technology and Capabilities:

  • From a script written by the user, FlexPDE performs the operations necessary to turn a description of a partial differential equations system into a finite element model, solve the system, and present graphical and tabular output of the results.
  • FlexPDE is also a problem solving environment. It performs the entire range of functions necessary to solve partial differential equation systems: an editor for preparing scripts, a mesh generator for building finite element meshes, a finite element solver to find solutions, and a graphics system to plot results. The user can edit the script, run the problem and observe the output, then re-edit and re-run repeatedly without leaving the FlexPDE application environment.
  • FlexPDE has no pre-defined problem domain or equation list. The choice of partial differential equations is totally up to the user. FlexPDE can solve systems of first or second order partial differential equations in one, two or three-dimensional Cartesian geometry, or in axi-symmetric two-dimensional geometry.
  • The system may be steady-state or time-dependent, or alternatively FlexPDE can solve eigenvalue problems. Steady-state and time-dependent equations can be mixed in a single problem.
  • Any number of simultaneous equations can be solved, subject to the limitations of the computer on which FlexPDE is run.
  • The equations can be linear or nonlinear. FlexPDE automatically applies a modified Newton-Raphson iteration process in nonlinear systems.
  • Any number of regions of different material properties may be defined.
  • Modeled variables are assumed to be continuous across material interfaces. Jump conditions on derivatives follow from the statement of the PDE system. CONTACT boundary conditions can handle discontinuous variables.
  • FlexPDE can be extremely easy to use, and this feature recommends it for use in education as well as in research

Waveguides-related publications:

  • D. V. Batrak and S. A. Plisyuk, "Applicability of the effective index method for simulating ridge optical waveguides," Quantum Electron. 36, 349 (2006).
  • C. D. Watson et al., "Acoustooptic Resonance in Deep-Etched GaAs–AlGaAs Electrooptic Modulators," J. Lightwave Technol. 22, 1598 (2004).

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FreeFem++

Free software developed by O. Pironneau, F. Hecht, and A. Le Hyaric at Université Pierre et Marie Curie Laboratoire Jacques-Louis Lions.

FreeFem++ is a software to solve partial differential equations numerically using finite element method.

Simulation Technology and Capabilities:

  • Highly adaptive program can handle multiple finite element meshes within one application with automatic interpolation of data on different meshes and possible storage of the interpolation matrices
  • Can quickly calculate multi-variables, multi-equations, bi-dimensional (or 3D axisymmetric), static or time dependent, linear or nonlinear coupled systems
  • Problem description (real or complex valued) by their variational formulations, with access to the internal vectors and matrices if needed
  • Automatic mesh generator
  • High level user friendly typed input language with an algebra of analytic and finite element functions
  • A large variety of linear direct and iterative solvers and eigenvalue and eigenvector solvers
  • Includes a fast quadtree-based interpolation algorithm and a language for the manipulation of data on multiple meshes
  • Older versions freefem and freefem+

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pdnMesh*

Free software.

pdnMesh is an automatic mesh generator and solver for finite element problems. It will also do post-processing to generate contour plots and Postscript printouts. GUI support using GTK or MFC (Win32) is available. The problem definition can be done in any form and given to pdnMesh as an input data file. Drawing Exchange Format (DXF) files can be directly imported to pdnmesh. The quality and the coarseness of the mesh can be controlled by giving input parameters.

pdnMesh is a program that can solve 2D potential problems (Poisson Equation) and eigenvalue problems (Helmholtz Equation) using the finite element method. Common applications occur in electromagnetics, heat flow and fluid dynamics. It can solve problems using both Nodal Based Formulation and Edge Based (Vector) Formulation.

Simulation Technology and Capabilities:

  • Automatic mesh generation according to given boundaries
  • Adaptive and Interactive mesh refinement
  • Problem solution using Cholesky Decomposition or Conjugate Gradient Method with sparse storage
  • Eigenvalue solution using LAPACK
  • (Optionally) Eigenvalue solution using QR iteration with shifts
  • (Optionally) Eigenvalue solution using ARPACK for very large eigenvalue problems using very little memory
  • Generating plots of contours, mesh and gradient on screen
  • Generating Encapsulated Postscript plots of contours and mesh
  • Generating a data file of the mesh to be used by other solvers
  • Can import DXF files generated by CAD programs
  • GUI is avaibale with GTK/GTKGLExt for Unix like systems or MFC for MS Windows, needs OpenGL

Waveguides-related applications:

  • Inhomogeneous Waveguides

Waveguides-related publications:

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Other Finite Element Codes primarily used for microwave waveguides

HFSS

Commercial software sold by Ansoft.

Concerto-Opera-Soprano

Commercial software sold by Vector Fields.

WaveSim

Commercial software sold by Field Precision.


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