
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
 Highperformance numerical algorithms
 Powerful postprocessing capabilities
 Extensive model libraries
 Optional applicationspecific addons
 Bidirectional interface to Matlab® & Simulink®
 RF Module developed for RF, microwave and optical structures engineering that can be easily combined with other modules
Waveguidesrelated applications:
 Optical fibers and waveguides
 Photonic crystal waveguides
 Microwave and optical components
 Plasmonics
 Surface plasmon resonance
Waveguidesrelated publications:
 S.K. Kim et al., "Metalslotted 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 Tshaped 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 ultrafast 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 finiteelement 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
 Timedomain analyses are performed using an explicit timeintegration technique that avoids the difficulties of manipulating large assembled matrices for the model. This approach restricts the computational timestep to satisfy the Courant stability criteria
 EMFlex uses cartesian isoparametric finite elements to model a continuum
 2D models use 4noded quadrilateral elements, 3D models use 8noded 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 problemsize are obtained by integrating to steady state in the time domain, then extracting amplitude and phase quantities via a discrete Fourier transform
Waveguidesrelated applications:
 Integrated optics
 Waveguides
 Grating couplers
 Resonators
Waveguidesrelated publications:
 L. C. Westet al., Ultra High Confinement Waveguides for Very Large Scale Integrated Optics (VLSIO) with Three Dimensional Packaging, Opt. Soc. Am. Integrated Photonics Research Technical Digest (1996).
 D. Chaudhari et al., "Highly Compact Optical Waveguides with a Novel Pedestal Geometry," IEEE Photon. Technol. Lett. 7, 526 (1995).
 L. C. West et al., Non Uniform Grating Couplers for Coupling of Gaussian Beams to Compact Waveguides, Opt. Soc. Am. Integrated Photonics Research Technical Digest (1994).
 G. Wojcik, J. Mould Jr., and L. C. West, TimeDomain Finite Element Modeling of 3D Integrated Optical Devices, Opt. Soc. Am. Technical Digest (1993).
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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 nonuniform mesh.
Simulation Technology and Capabilities:
 FemSIM is based on a fullvector implementation of the finite element method on a nonuniform mesh
 Fullvectorial 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/antisymmetric boundary conditions
 Determination of propagating, leaky, and cavity modes
 Higher order modes can be found with minimal additional computational expense
Waveguidesrelated 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
 Siliconbased devices
 Polarization rotators
 Air or solid core photonic fibers
 Laser and PBG defect cavities
Waveguidesrelated publications:
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FIMMWAVEFEMSolver^{*}
Commercial software sold by Photon Design.
FIMMWAVEFEMSolver 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 electromagnetic 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 refractiveindex, confinement factor versus core thickness etc.
 Fully integrated with the FIMMPROP (propagation tool), so that it may be used to generate the basisset modes of a FIMMPROP simulation.
Waveguidesrelated applications:
 Holey fibers
 Elliptical fibers
 Oddshaped 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 nanooptical devices.
Simulation Technology and Capabilities:
 The rigorous physical model for all three main modules JCMharmony , JCMmode and JCMresonance are the timeharmonic 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 MultiGrid 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 IndexContrast Structures
 Polarization Effects, Gain and Loss
 Anisotropic Materials
 Inhomogeneous Exterior Domains
Waveguidesrelated applications:
 Integrated Optics
 Gratings, Coatings
 FibertoChip Coupling
 Transmission and Reflection of Waveguides,
 Microlenses, Micromirrors
 Meta Materials, NanoOptics
 Optical Fibers, Photonic Crystal Fibers
 Integrated Optical Waveguides
 Plasmonic Waveguides
 Microcavities, Microlaser Modes, VCSEL
 Photonic Bandgap Structures
Waveguidesrelated 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 hollowcore photonic crystal fiber design using the finite element method," JEOSRapid 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, timedependent, steadystate 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 builtin graphics, a MATLAB mfile, or other graphics programs
Waveguidesrelated applications:
 Birefringent optical fibers
 Nonlinear optical fibers and waveguides
 Strongly guiding structures
 Gain/loss effects in photonic devices
 Integrated optical resonators
Waveguidesrelated 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, "Crossphase Modulation Phenomena in Strongly Guiding Waveguides: A Theoretical Approach Revisited," J. Opt. Soc. Am. B15, 964 (1998).
 M. Fontaine, "Theoretical Approach to Investigating Crossphase 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 FiniteElement 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 PolySi Thermistor," J. Lightwave Technol. 14, 2260 (1996).
 V. Tzolov et al., "Nonlinear Modal Parameters of Optical Fibers: A FullVectorial Approach," J. Opt. Soc. Am B12, 1933 (1995).
 V. Tzolov and M. Fontaine, "Theoretical Analysis of Birefringence and FormInduced Polarization Mode Dispersion in Birefringent Optical Fibers: a FullVectorial 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 NonLinear 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 threedimensional finite element modeling codes that can be used to analyze simple 3dimensional 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 easeofuse, modest resource requirements, and accurate modeling of simple threedimensional configurations over a wide range of frequencies.
Simulation Technology and Capabilities:
 EMAP1 is based on a variational formulation
 EMAP2 uses the Galerkin finite element formulation
 Both EMAP1 and EMAP2 are scalar (nodebased) 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 fullwave 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 noncomplexelement vector FEM codes
Waveguidesrelated publications:
 G. L. Maile, "Threedimensional 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 3D, finite element modeling code for analyzing timevarying electromagnetic fields," Journal of the Applied Computational Electromagnetics Society 8 (1993).
 T. H. Hubing and M. W. Ali, "EMC Applications of EMAP2: 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, divcurl systems, diffusion problems, Helmholtz equations, wave equations, etc.
 Designed primarily for MPIbased distributed memory supercomputers
 EMSolve code suite can be made available to external users
Waveguidesrelated 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 reedit and rerun repeatedly without leaving the FlexPDE application environment.
 FlexPDE has no predefined 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 threedimensional Cartesian geometry, or in axisymmetric twodimensional geometry.
 The system may be steadystate or timedependent, or alternatively FlexPDE can solve eigenvalue problems. Steadystate and timedependent 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 NewtonRaphson 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
Waveguidesrelated 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 DeepEtched 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 JacquesLouis 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 multivariables, multiequations, bidimensional (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 quadtreebased 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 postprocessing 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
Waveguidesrelated applications:
Waveguidesrelated publications:
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Other Finite Element Codes primarily used for microwave waveguides
HFSS
Commercial software sold by Ansoft.
ConcertoOperaSoprano
Commercial software sold by Vector Fields.
WaveSim
Commercial software sold by Field Precision.
