Mode Solving Arbitrary Waveguides
Question:
When solving an isotropic waveguide in OptiMode there are two main numerical methods (excluding fibers) for calculating the modes, the Alternating Direction Implicit and the Implicitly Restarted Arnoldi Method mode solvers. Could you explain the advantages and disadvantages of both?
Furthermore, when solving a waveguide with a large core I found that the ADI method would calculate results slightly differently for various starting fields.
Responses (3):
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Question:
When solving an isotropic waveguide in OptiMode there are two main numerical methods (excluding fibers) for calculating the modes, the Alternating Direction Implicit and the Implicitly Restarted Arnoldi Method mode solvers. Could you explain the advantages and disadvantages of both?
Furthermore, when solving a waveguide with a large core I found that the ADI method would calculate results slightly differently for various starting fields.
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Answer:
There are subtle differences between the ADI and IRAM solvers. The IRAM solver is used for more general waveguide problems and it can resolve the discrete modes of a larger waveguide easily. The ADI on the other hand is better suited for small waveguides with less modes, which it can solve swiftly.
In your particular case the large core of your waveguide is making it difficult for the ADI method to resolve the different modes. If there are many modes, then the solver might not be able to distinguish between them. The calculated mode would actually be a linear superposition of different modes. Different starting fields could affect which modes would be included in this superposition and change the results.
A waveguide could support 100’s of modes and in this case a mode solver is probably not the best technique for solving the problem. The V number, often used in fiber optics, is a good tool for estimating the number of modes in waveguide. The V number is given by:
V = ( 2π/ λ) * a * sqrt( n1^2 – n2^2 )
The core of the waveguide is given by n1 and the cladding by n2. The radius and wavelength are represented by a and λ. The number of modes is calculated by 0.5*V^2. This tool can be used regardless of the waveguide shape to roughly find how many modes there are.
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Thanks a lot. During working on the mode solver by using ADI and FD. I found it much better work for small cross section by using the FD ( 500 nm – 900 nm).
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why more people are working with FD? and what is them main cause?
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