Finite-element method analyzes waveguides
Courtesy O plus E magazine, Tokyo
SAPPORO--Masanori Koshiba and colleagues at the Division of Electronics and Information Engineering at Hokkaido University are developing software that analyzes guided modes and beam transmission in optical and microwave waveguides. The Expert Lightwave Modeling (ELM) system is based on the finite-element method of numerically solving partial differential equations. The object in question is separated into a finite number of elements (triangular), the nodes assigned to each of the elements are given values, and the partial differential equation is converted into a system of linear equations to be simultaneously solved.
The ELM system comprises three components: the preprocessor, which supports the input of information necessary for the calculations such as the shape of the waveguide and the index of refraction of each component; the solver, which performs the numerical calculations; and the postprocessor, which writes out the output or converts it into a visual format. In the main solver, there is a solver to analyze the guided modes and one to analyze the transmission of beams. There are also solvers designed to analyze static electric fields, resilience and warping, surface acoustic waves, and heat. By using all of these solvers together, devices that analyze optical effects due to electricity, acoustics, and heat can be developed.
The quality of the solutions using the finite-element method is highly dependent on how the components are separated. Accuracy is increased when the number of elements is increased, but the problem becomes more computationally intensive. Therefore, it is necessary to determine how to partition the elements on a case-by-case basis. It is difficult for researchers to separate the elements so that highest efficiency is reached, but the ELM system separates the elements roughly at first and then makes finer partitions by weighting each element based on the initial results. This method allows appropriate separation of elements to be achieved. Methods for solving simultaneous linear equations also have been developed for speed and reliability.
The results achieved by calculating the characteristics of an optical switch that uses a heat effect (a thin-film heater attached to a polymer Y-branched waveguide) agree with experimental values. In addition, the transmission of a light pulse (with slight reflection) through a perpendicular waveguide in a photonic crystal has been calculated using this method (see figure). Results with the same degree of accuracy as conventional finite-difference time-domain calculation can be attained using about two-orders-of-magnitude less computation time.
This software is made for the UNIX operating system. The source code has not been publicly released, but the program can be used under certain conditions, such as collaborative research.