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MODE Solutions can be used to obtain accurate results for a wide range of problems. The following results show the comparison between analytic and simulated results for a series of reference test structures.
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Step-index and graded-index optical fiber
Step-index (left) and graded-index (right) fiber geometries and index profiles. The step-index fiber was tested at a wavelength of 1.55 µm, while the graded-index fiber was tested at a wavelength of 1 µm.
STEP-INDEX FIBER: Magnitude of error of MODE Solutions calculation for TM modes of a step-index fiber, compared to analytic result at a wavelength of 1.55 µm. The x-axis denotes the number of grid points per side of the calculation region.
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GRADED-INDEX FIBER: Magnitude of error of MODE Solutions calculation for TE modes of a graded-index fiber, compared to analytic result at an operating wavelength of 1 µm. The x-axis is the number of grid points per side of the calculation region.
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GRADED-INDEX FIBER: Dispersion of TE01 mode in graded-index fiber calculated by MODE Solutions (o) compared to the analytic solution (solid line). 80 grid points per side were used in this calculation.
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GRADED-INDEX FIBER: Magnitude of error of MODE Solutions calculation for dispersion of TE01 mode of a graded-index fiber, compared to analytic result. 80 grid points per side were used in this calculation.
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Hollow metal waveguide
Dimensions of the hollow metal waveguide. The metals walls are perfectly conducting, and the waveguide is tested over a frequency range of 5 to 25GHz to compare with analytic results. The region is discretized such that the grid spacing is the same in both the x and y directions.
Propagation wavevector as a function of frequency for hollow metal waveguide. Dispersive characteristics of the first three modes are shown for frequencies ranging from 5 to 25 GHz. The solid lines show the analytic response, while the symbols (o) show the results calculated with MODE Solutions.
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Error amplitude of MODE Solutions calculation for hollow metal waveguide modes at a frequency of 20 GHz compared to the analytic response. The x-axis shows the number of grid points along the long side of the hollow metal waveguide.
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Asymmetric slab dielectric waveguide
Dimensions and refractive indices of three-layer asymmetric dielectric slab waveguide. Numerical results calculated with MODE Solutions are compared with the analytic results at a wavelength of 1.55µm.
Effective index values for TE (red) and TM (blue) modes as calculated via MODE Solutions (o) and via analytic relations (lines) for three-layer, asymmetric slab waveguide. The x-axis shows the convergence of MODE Solutions on the correct answer as the number of grid points is increased.
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Magnitude of error of MODE Solutions calculation for three-layer asymmetric slab waveguide at a wavelength of 1.55µm. The x-axis shows the number of grid points in the one-dimensional calculation region.
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Exponential index profile slab waveguide
Dielectric slab waveguide with exponential refractive index profile. The refractive index of the slab decays exponentially from a value of 2.47 at the air/core interface surface into the substrate such that n(z) = 5.928X10-2 exp(-z/2.5) + 2.47, where z represents the depth below the surface measured in microns. Calculations performed with MODE Solutions are compared to the analytic response at a wavelength of 633nm.
Effective index values for TE (red) and TM (blue) modes as calculated via MODE Solutions (o) and via analytic relations (lines) for slab waveguide with exponential refractive index profile. The x-axis shows the convergence of MODE Solutions.
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Error amplitude of MODE Solutions calculation for slab waveguide with exponential refractive index profile. The x-axis shows the number of grid points in the one-dimensional calculation region.
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Surface plasmon modes
Structure and physical constants of air/gold interface. The gold layer is many wavelengths thick, with a refractive index of 0.238+3.385i at a wavelength of 632.8nm.
Effective index (red) and propagation loss (blue) calculations for air/gold interface at a wavelength of 632.8nm. The symbols (o) denote the MODE Solutions calculations, and the horizontal lines show the analytic results. The x axis shows the number of grid points used in the calculation.
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Error amplitude of MODE Solutions calculation for fundamental surface plasmon mode of air/gold interface at a wavelength of 632.8 nm. The x-axis is the number of grid points in the one-dimensional calculation region.
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Error amplitude of MODE Solutions calculation of effective index using a uniform mesh (red) and graded mesh (blue). For this calculation, the graded mesh achieves similar levels of accuracy as the uniform mesh using approximately 20 times less grid points.
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ARROW slab waveguide
Geometry and refractive indices of the multilayer dielectric ARROW slab waveguide at a wavelength of 632.8nm. Comparison results are taken from E. Anemogiannis et al., Determination of Guided and Leaky Modes in Lossless and Lossy Planar Multilayer Optical Waveguides: Reflection Pole Method and Wavevector Density Method, IEEE Journal of Quantum Electronics, vol. 17, pp. 929-941, 1999.
Effective index (red) and loss (blue) calculations for TE mode of ARROW waveguide at 632.8nm. The symbols (o) denote MODE Solutions calculations, and the lines show the comparison results.
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Error amplitude of MODE Solutions calculation for ARROW waveguide TE mode at a wavelength of 632.8 nm. The x-axis is the number of grid points in the calculation region.
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See how easily MODE Solutions can assist you with your design efforts! Download a free 30 day trial and request that a technical expert contact you.
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