Optical Waveguides: Numerical Modeling
 

Other Mode Solvers

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 three-dimensional 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 deep-etched 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, 1320-1333 (2002)
  • R.S. Fan and R. B. Hooker, "Tapered polymer single-mode waveguides for mode transformation," J. Lightwave Technol. 17, 466 (1999).
  • G.R. Hadley and R.E. Smith, "Full-vector waveguide modeling using an iterative finite-difference method with transparent boundary conditions," J. Quantum Electron. (1995).
  • S. Jungling and J.C. Chen, "A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method," J. Quantum Electron. 30, 2098 (1994).
  • D. Yevick and Witold Bardyszewski, "Correspondence of variational finite-difference (relaxation) and imaginary-distance 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.
  • Finite-element 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 long-period waveguide grating," Appl. Phys. B 86, 147 (2007).
  • M. Nordström et al., "Single-Mode Waveguides With SU-8 Polymer Core and Cladding for MOEMS Applications," J. Lightwave Technol. 25, 1284 (2007).
  • R. Halir et al., "Fabrication Tolerance Analysis of Bent Single-Mode Rib Waveguides on SOI," Opt. and Quantum Electron. 38, 921 (2006).
  • F. Xia et al., Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators, Opt. Express 14, 3872 (2006),
  • S.-K. Kim et al., "Electro-optic phase modulator using metal-defined 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 hollow-core ARROW waveguides, Opt. Express 13, 9331 (2005).

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MODE Solutions

Commercial software sold by Lumerical.

MODE Solutions is an accurate and flexible mode solver technology for the design and analysis of guided-wave optical devices.

Capabilities:

  • Fully vectorial finite-difference 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 spatially-varying 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 far-field projections
  • Frequency-domain 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 ray-tracing package ASAP; export to MATLAB or text-files for post-processing

Applications:

  • Traditional fiber
  • Rib waveguides
  • Photonic crystal fiber
  • Coaxial Bragg fiber
  • Sloping-wall ridge waveguides
  • Spatially-varying refractive index distributions

Related publications:

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OlympIOs Mode Solver Modules

Commercial software sold by C2V.

Effective Index Method and Marcatili Method are approximate two-dimensional 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:
    • 1-D mode solvers
    • Approximate 2D solvers: (Effective Index Method, Marcatili Method)
    • Semi-vectorial Finite Difference solver
    • Graded-index profiles
    • Overlap, far-field, confinement and Gauss-fit calculations
  • Mode solver advanced:
    • Full-vectorial solvers (Finite Difference and Film Mode Matching-based)
    • 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:

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OptiFIBER

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 10-15 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 dispersion-shifted fibers
  • Multimode fiber design
  • Fiber Sensor design
  • Birefringence and PMD

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WMM

Free software developed by Dr. Manfred Hammer (University of Osnabrück).

WMM is a quasi-analytic mode solver for rectangular dielectric integrated optical waveguide channels (three-dimensional configurations with two-dimensional 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 semi-analytical mode field representations which are defined on the entire plane of the waveguide cross section, including the dielectric discontinuities.
  • Implemented for semi-vectorial and fully-vectorial 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 MS-DOS / Windows or Linux
  • Free GNU Compiler Collection is available

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RP Fiber Power

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 wavelength-dependent (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 laser-active ions
  • Dynamic calculations for time-dependent powers, e.g., in pulse amplification or Q-switched 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 figure-of-merit function
  • Comprehensive documentation, online help, and large set of demo files

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RP Fiber Calculator

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 cut-off 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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