
BeamPROP Mode Solvers
Commercial software (part of BeamPROP) sold by RSoft.
BeamPROP includes two fully functional mode solvers based on (1) the iterative method and (2) the correlation method. Both of these methods are based on the Beam Propagation Method (BPM).
Capabilities:
 Can solve for the propagating modes of a structure with an arbitrary two or threedimensional index cross section
 Calculates mode spectrum
 Mode profiles
 Imaginary distance BPM method is faster; it is the default choice and is recommended for most standard waveguide problems
 Correlation method is slower, but more general, e.g. it can be applied to problems that cannot be handled by the Imaginary distance BPM, such as antiguiding, leaky, lossy, or radiating modes, or when large numbers of modes need to be calculated.
Related publications:
 P. Bienstman et al., "Modelling leaky photonic wires: A mode solver comparison," Opt. and Quantum Electron. 38, 731 (2006).
 W. Zhao et al., "Effect of mask thickness on the nanoscale sidewall roughness and optical scattering losses of deepetched InP/InGaAsP high mesa waveguides," J. Vac. Sci. Technol. B 23, 2041 (2005).
 A. Abeeluck et al., Analysis of spectral characteristics of photonic bandgap waveguides, Opt. Express 10, 13201333 (2002)
 R.S. Fan and R. B. Hooker, "Tapered polymer singlemode waveguides for mode transformation," J. Lightwave Technol. 17, 466 (1999).
 G.R. Hadley and R.E. Smith, "Fullvector waveguide modeling using an iterative finitedifference method with transparent boundary conditions," J. Quantum Electron. (1995).
 S. Jungling and J.C. Chen, "A study and optimization of eigenmode calculations using the imaginarydistance beampropagation method," J. Quantum Electron. 30, 2098 (1994).
 D. Yevick and Witold Bardyszewski, "Correspondence of variational finitedifference (relaxation) and imaginarydistance propagation methods for modal analysis", Opt. Lett. 17, 329 (1992).
 D. Yevick and B. Hermansson, "New formulations for the Beam Propagation Method: Application to Rib Waveguides," J. Quantum Electron. 25, 221 (1989).
 M. D. Feit and J. A. Fleck, "Computation of Mode Properties in Optical Fiber Waveguides by a Propagating Beam Method," Appl. Opt. 19, 1154 (1980).
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FIMMWAVE Mode Solvers
Commercial software sold by Photon Design.
FIMMWAVE is a generic, robust, fully vectorial mode finder for 2D waveguide structures, which contains a variety of robust and computationally efficient solvers optimized for a particular geometry.
Capabilities:
 FMM Solver
 Based on the mode matching method
 Optimized for rectangular waveguide structures
 Fully vectorial solver
 Generic version capable of solving structures with complex refractive index (such as metallic components and waveguides with gain)
 A version optimized for real structures only
 The mode matching method models an arbitrary waveguide by a list of vertical slices, each uniform laterally, but composed vertically of a number of layers. A 3D mode is built up from the TE and TM 2D modes of each slice.
 The method is theoretically exact for an infinite number of 2D modes.
 The modeled area may be bound by either perfect metallic or magnetic walls or with periodic boundary conditions.
 The method handles modes near cutoff in the lateral direction, without loss of accuracy or an increase in computation time.
 General Fiber Solver
 Fully vectorial solver for generic circular waveguides with arbitrary refractive index
 Metallic or transparent boundaries.
 Exploits the circular symmetry, thus making it extremely fast.
 A scalar version is also available.
 Gaussian Mode Fiber Solver
 Quick utility for getting the fundamental mode using the gaussian approximation
 The user simply specifies the effective index and the spot size of the desired mode  useful where the fiber profile is not known.
 Finiteelement method based solver (detailed description can be found in the FEM section)
Applications:
 Silicon on insulator structures
 Polymer and etched GaAs/AlGaAs waveguides
 Single and multicore fibers
Related publications:
 Q. Liu et al., "Dual resonance in a longperiod waveguide grating," Appl. Phys. B 86, 147 (2007).
 M. Nordström et al., "SingleMode Waveguides With SU8 Polymer Core and Cladding for MOEMS Applications," J. Lightwave Technol. 25, 1284 (2007).
 R. Halir et al., "Fabrication Tolerance Analysis of Bent SingleMode Rib Waveguides on SOI," Opt. and Quantum Electron. 38, 921 (2006).
 F. Xia et al., Mode conversion losses in silicononinsulator photonic wire based racetrack resonators, Opt. Express 14, 3872 (2006),
 S.K. Kim et al., "Electrooptic phase modulator using metaldefined polymer optical waveguide," Appl. Phys. Lett. 87, 011107 (2005).
 D. Yin et al., "Integrated optical waveguides with liquid cores," Appl. Phys. Lett. 85, 3477 (2004).
 D. Yin et al., Waveguide loss optimization in hollowcore ARROW waveguides, Opt. Express 13, 9331 (2005).
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Commercial software sold by Lumerical.
MODE Solutions is an accurate and flexible mode solver technology for the design and analysis of guidedwave optical devices.
Capabilities:
 Fully vectorial finitedifference analysis
 Handles arbitrary waveguide geometries
 Efficient eigenvalue search algorithm
 Tracks specific modes during frequency sweeps
 Macrobending loss
 Coupling efficiency calculator
 Waveguide definition: supports basic, customized, parameterized and imported (from SEM or other image) primitives
 Comprehensive material management: supports dielectric, lossy, conductive Lorentz, Drude, Debye, Sellmeier and anisotropic materials; supports spatiallyvarying material distributions
 Boundary conditions: speed calculation and improve accuracy through choice of absorbing (PML), periodic, symmetric, asymmetric, and metal boundary conditions
 Modal analysis: complex propagation constants and polarization state for guided and leaky modes visualization tools for modal field profiles, Poynting vector data for power flow; customized integration of field data; near to farfield projections
 Frequencydomain analysis: analyze dispersion, group velocity, group index, propagation loss, effective refractive index as a function of frequency/wavelength
 Data import/export: import/export to Breault's raytracing package ASAP; export to MATLAB or textfiles for postprocessing
Applications:
 Traditional fiber
 Rib waveguides
 Photonic crystal fiber
 Coaxial Bragg fiber
 Slopingwall ridge waveguides
 Spatiallyvarying refractive index distributions
Related publications:
 J.H. Lin et al., "Supercontinuum generation in a microstructured optical fiber by picosecond self Qswitched modelocked Nd:GdVO4 laser," Laser Phys. Lett. 4, 413 (2007).
 Z. Yang et al., Enhanced secondharmonic generation in AlGaAs microring resonators, Opt. Lett. 32, 826 (2007).
 Ch. Deneke and O. G. Schmidt, "Structural characterization and potential xray waveguiding of a small rolledup nanotube with a large number of windings," Appl. Phys. Lett. 89, 123121 (2006).
 D. J. Sirbuly et al., "Optical routing and sensing with nanowire assemblies," PNAS 102, 7800 (2005).
 R. Gordon and A. Brolo, Increased cutoff wavelength for a subwavelength hole in a real metal, Opt. Express 13, 1933 (2005).
 L. Shah et al., Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate, Opt. Express 13, 1999 (2005).
 Z. Zhu and T. G. Brown, Fullvectorial finitedifference analysis of microstructured optical fibers, Opt. Express 10, 853 (2002).
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Commercial software sold by C2V.
Effective Index Method and Marcatili Method are approximate twodimensional solvers that can be used for performing fast initial estimates, followed by calculations using more accurate mode solving techniques such as finite difference based method and film mode matching method. OlympIOs offers a choice basic and more advanced mode solvers.
Capabilities:
 Mode solver basic:
 1D mode solvers
 Approximate 2D solvers: (Effective Index Method, Marcatili Method)
 Semivectorial Finite Difference solver
 Gradedindex profiles
 Overlap, farfield, confinement and Gaussfit calculations
 Mode solver advanced:
 Fullvectorial solvers (Finite Difference and Film Mode Matchingbased)
 Adaptive grids for thin layers
 Bend and leaky mode solver
 Reliable higher order modes solvers
 Generic simulation features:
 Extensive parameterization capabilities
 Vary runs
 Material library
Related publications:
 C. Herzog et al., "Epitaxial K1xNaxTa0.66Nb0.34O3 thin films for optical waveguiding applications," J. Opt. Soc. Am. B24, 829 (2007).
 H. Ou et al., "Deep glass etched microring resonators based on silicaonsilicon technology," Electron. Lett. 42, 581 (2006).
 H. Tazawa et al., "Ring ResonatorBased Electrooptic Polymer TravelingWave Modulator," J. Lightwave Technol. 24, 3514 (2006).
 Y. Ruan t al., Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching, Opt. Express 12, 5140 (2004),
 D. J. W. Klunder et al., A Normalized Approach for Designing Cylindrical Microresonators, J. Lightwave Technol. 21, 1405 (2003),
 D. J. W. Klunder et al., Experimental and Numerical Study of SiON Microresonators With Air and Polymer Cladding, J. Lightwave Technol. 21, 1099 (2003),
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Commercial software sold by Optiwave.
OptiFiber uses numerical mode solvers and other models specialized to fibers for calculating dispersion, losses, birefringence, and PMD.
Capabilities:
 Meshless Mode Solvers for LP and Vector Modes: OptiFiber 2.0 mode solvers find an exact solution based on matching boundary conditions at layer boundaries instead of relying on meshes to approximate the structure.
 Advanced mode solvers that are especially useful for multimode fiber calculations, where there are many modes in the spectrum.
 Another advantage of the meshless mode solver is the calculation of fields far from the fiber.
 Meshing introduces finite difference errors of a certain level, and fields weaker than the differencing error cannot be calculated. The meshless mode solvers, on the other hand, have the correct asymptotic behavior far from the fiber, and can calculate fields of magnitude 1015 or less.
 OptiFiber allows users to decompose an arbitrary field into the modes of a multimode fiber.
 Calculates the complex coefficients of the modes for the arbitrary field.
 Given the amplitude of a set of modes, OptiFiber can display the sum (composition of modes).
 OptiFiber 2.0 can also calculate this multimode field after propagating down the fiber by a specified distance.
 Assess parameters, sensitivities, and tolerances
 Fiber mode solving of LP or Vector modes by Finite Difference or by Transfer Matrix Methods
 Visualization of multimode interference patterns with propagation
 Automatic parameter scanning
Applications:
 Analysis of measured fiber profiles from instruments
 Single mode fiber designs, dispersion flattened or dispersionshifted fibers
 Multimode fiber design
 Fiber Sensor design
 Birefringence and PMD
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Free software developed by Dr. Manfred Hammer (University of Osnabrück).
WMM is a quasianalytic mode solver for rectangular dielectric integrated optical waveguide channels (threedimensional configurations with twodimensional cross sections), based on the wave matching method.
Capabilities:
 Downloadable, commented C++ sources, accompanied by several application examples are provided
 The WMM explicitly and accurately yields semianalytical mode field representations which are defined on the entire plane of the waveguide cross section, including the dielectric discontinuities.
 Implemented for semivectorial and fullyvectorial mode analysis
 The piecewise defined trial fields are well suited to deal with field discontinuities or discontinuous derivatives
 At the corners of dielectric waveguides, the method yields correct qualitative features of the divergent field behavior
 A number of C++ library files is available
 For a new application, a C++ program including the main() procedure should be written, or one of the supplied application examples for can be edited
 The program structure obviously requires a basic knowledge of the C++ programming language and a working C++ compiler
 Code runs under MSDOS / Windows or Linux
 Free GNU Compiler Collection is available
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RP Fiber Power is commercial software sold by RP Photonics Consulting GmbH. It includes a numerical mode solver for optical fibers, calculating LP modes for radially symmetric refractive index profiles. It also calculates optical powers in fiber amplifiers and lasers.
Capabilities:
 Calculates all guided modes (LP modes) for arbitrary refractive index profiles, defined via formulas, tabulated values, or in other forms
 Refractive index profiles can be wavelengthdependent (e.g., via Sellmeier equations)
 For each mode, calculates the amplitude and intensity profile, propagation constant, group velocity, group velocity dispersion (from material and waveguide dispersion), and the fraction of the power propagating within the fiber core
 Can use calculated mode profiles for further models, calculating the propagation of optical powers and fiber amplifiers, fiber lasers and ASE sources
 Can handle freely defined level schemes of laseractive ions
 Dynamic calculations for timedependent powers, e.g., in pulse amplification or Qswitched lasers
 Powerful script language can be used to access all mode properties, calculated optical powers in devices, etc., freely define diagrams, generate output files, etc.
 Numerical optimization features allow one, for example, to optimize index profiles for certain dispersion properties, by minimizing a freely defined figureofmerit function
 Comprehensive documentation, online help, and large set of demo files
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RP Fiber Calculator is a software distributed by RP Photonics Consulting GmbH without charge. It can be used even for commercial purposes. An improved version "RP Fiber Calculator PRO" is expected to appear soon, and licenses for that will be sold.
Capabilities:
 Calculates all guided modes for a given radially symmetric refractive index profile, defined via a graphical user interface
 Displays a table with mode properties such as phase constant, effective index, effective area, fraction of power within the fiber core, and cutoff wavelength
 Displays mode profiles
 Simulates launching a Gaussian laser beam into the fiber, also with misalignment
 Simulates propagation of guided modes in the fiber and after exiting the fiber in the far field
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