Optical Waveguides: Numerical Modeling
 

Plane-Wave Expansion Method (PEM): Software

BandSOLVE

Commercial software sold by RSoft.

BandSOLVE is a design tool to automate and simplify the modeling and the calculation of photonic band structures for all photonic crystal devices.

Capabilities:

  • BandSOLVE employs a powerful Plane Wave Expansion algorithm for the solution of one-, two, and three-dimensional photonic bandgap devices.
  • BandSOLVE includes several advanced simulation features that allow for more efficient band computations.
  • For many types of devices, the inversion symmetry can be enforced leading up to a 40% increase in speed.
  • Mode seeding can be utilized to dramatically increase the speed of the calculations.
  • In 3D calculations, parity can be included for the separation of even and odd modes.

Applications:

  • BandSOLVE can be used to optimize the band structure of new photonic crystal geometries before fabricating the device and to determine the performance of existing components.
  • Two-dimensional and three-dimensional PC slab and waveguides
  • Two-dimensional and three-dimensional cavity problems
  • Photonic Crystal Fibers, both band-gap guiding and conventional guiding
  • Defect modes of non-strictly periodic structure
  • Metallic and anisotropic structures

Related publications:

  • A. Martinez and J. Marti, "Positive phase evolution of waves propagating along a photonic crystal with negative index of refraction," Opt. Express14, 9805 (2006).
  • R. Gajic et al., "All-angle left-handed negative refraction in Kagome and Honeycomb lattice photonic crystals," Physical Review B 73, 1 (2006).
  • Y. Tanaka et al., "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron. 41, 76 (2005).
  • I. Celanovic et al., "Resonant-cavity enhanced thermal emission," Phys. Rev. B 72, 075127 (2005).
  • K. K. Tsia and A. W. Poon, "Dispersion-guided resonances in two-dimensional photonic-crystal-embedded microcavities," Opt. Express 12, 5711 (2004).
  • Y. K. Lize et al., "Microstructured optical fiber photonic wires with subwavelength core diameter" Opt. Express 12, 3209 (2004).
  • J. Zarbakhsh et al., "Arbitrary angle waveguiding applications of 2D curvilinear-lattice photonic crystals," Appl. Phys. Lett. 84, 4687 (2004).
  • E. C. Magi et al., "Tapered photonic crystal fibers" Opt. Express 12, 776 (2004).
  • J. C. Baggett et al., "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317 (2003).

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Band Structure Analyzer

Commercial software (part of CrystalWAVE) sold by Photon Design.

The Band Structure Analyzer computes the Bloch (periodic) modes of a photonic crystal lattice with two or three dimensional periodicity. It automatically identifies the band gaps and evaluates the Bloch mode profiles at any point.

Capabilities:

  • Plane wave expansion based engine for best computation in the frequency domain
  • Two- and three-dimensional simulation modes
  • Generates w/k band diagrams for TE-like and TM-like polarizations
  • Brillouin-zone constant-omega contour plots.
  • Easily plot the Bloch modes from any point on the w/k band diagram
  • Full integration with the CrystalWave framework
  • Simple graphical specification of Cartesian and non-Cartesian unit cells
  • Supports all lattices definable in the CrystalWave layout editor - rectangular, hexagonal lattices, with square, elliptical or arbitrary shaped "atoms"
  • Automatic detection of band gaps
  • Real and lossy materials
  • Calculate effective index, group index and dispersion of the Bloch mode
  • Automatic scanners for generation of "band maps" e.g. against lattice period or hole size
  • Speed optimized calculation engine takes advantage of any symmetries

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MIT Photonic-Bands (MPB)

Free software developed by MIT group.

MPB is a free program for computing the band structures (dispersion relations) and electromagnetic modes of periodic dielectric structures, on both serial and parallel computers.

Capabilities:

  • Computes definite-frequency eigenstates (harmonic modes) of Maxwell’s equations in periodic dielectric structures for arbitrary wavevectors
  • Fully-vectorial and three-dimensional methods are implemented
  • Preconditioned block-iterative eigensolvers in a planewave basis are used
  • Sharp material discontinuities can be handled and convergence proportional to the square of the spatial resolution can be achieved even for sharply discontinuous anisotropic dielectric structures

Applications:

  • Photonic crystals
  • Optical waveguides and resonator systems
  • Waveguides with arbitrary cross-sections
  • Anisotropic or magnetic materials

Related publications:

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Waveguide Mode Solver

Free software.

A waveguide mode solver is based on a two-dimensional plane-wave expansion method which includes gain and losses.

Capabilities:

  • The first version employs analytical integration while the second version uses a numerical integration. It is limited to not too complex situation, because of the complexity of the analytical integration of piecewise defined functions.
  • The numerical version is capable to treat reasonable large scale problems.

Related publications:

  • U. T. Schwarz and B. Witzigmann, Optical properties of edge-emitting lasers: measurement and simulation, invited chapter in Nitride Semiconductor Devices, edited by J. Piprek, Wiley-VCH (2007) ISBN-10: 3-527-40667-0.
  • U. T. Schwarz et al., "Influence of ridge geometry on lateral mode stability of (In/Al)GaN laser diodes," Phys. Stat. Sol. (a) 202, 261 (2005).
  • T. Herrle et al., "T-shaped waveguides for quantum-wire intersubband lasers," Phys. Rev. B 72, 035316 (2005).

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