• Nuclear Engineering and Technology
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• v.49 no.1
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• pp.17-28
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• 2017

The modified power method has been studied by many researchers to calculate the higher eigenmodes and accelerate the convergence of the fundamental mode. Its application to multidimensional problems may be unstable due to degenerated or near-degenerated eigenmodes. Complex eigenmode solutions are occasionally encountered in such cases, and the shapes of the corresponding eigenvectors may change during the simulation. These issues must be addressed for the successful implementation of the modified power method. Complex components are examined and an approximation method to eliminate the usage of the complex numbers is provided. A technique to fix the eigenvector shapes is also provided. The performance of the methods for dealing with those aforementioned problems is demonstrated with two dimensional one group and three dimensional one group homogeneous diffusion problems.

• Korean Journal of Optics and Photonics
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• v.4 no.3
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• pp.309-316
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• 1993

We find the vectorial solution of the optical waveguide with semicircular cross-section by expanding the electromagnetic fields of the waveguide into the series of trigonometric and Bessel funtions and by applying the boundary conditions at the finitely selected points on the interface of the core and the cladding. We find also the propagation constants and the energy distributions of the eigenmodes and discuss its properties. As a result of computation, we find that the electromagnetic fields of the even modes about the symmetric axis of the semircular shape are nearly the same as those of the odd modes except that E and H of the odd modes are replaced by -H and E and that the even and odd modes are degenerated as the ratio of refractive index of the core and cladding approaches to 1.