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Publication Detail
Invited Author: Computational Modeling of Bound and Radiation Mode Optical Electromagnetic Fields in Multimode Dielectric Waveguides
  • Publication Type:
  • Authors:
    Selviah DR, Papakonstantinou I
  • Publication date:
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  • Name of conference:
    Progress In Electromagnetics Research Symposium PIERS 2008 in Cambridge, USA, 2-6 July, 2008
The bound modes of optical multimode rectangular buried step index waveguides, in which the core has a uniform refractive index and the cladding has another lower refractive index, are usually calculated using an approximation that the wave equation is separable along two orthogonal axes, so that the modes can be considered to be a combination of modes in two orthogonal slab waveguides. This is useful as multimode waveguides can have many modes so the calculation of modes in a one dimensional slab waveguide is faster to calculate. A more accurate model is now needed to calculate both the bound modes and the radiation modes of multimode waveguides having uniform and non-uniform refractive index profiles within the guide. Non-uniform refractive index profiles are of interest for graded refractive index guides and photonic band gap guides but also because the modes in waveguide bends can be analyzed by performing a conformal transformation to another domain in which the waveguides become straight but in which their refractive index becomes non-uniform, asymmetric and graded. Radiation modes are needed to fully describe wave propagation in waveguides where coupling between modes occurs, for example, in practical waveguides suffering from sidewall roughness. Coupling of bound to radiation modes can be one of the main reasons for propagation loss in such guides. Analytical solutions for radiation modes do not exist for all waveguide geometries of interest and especially for ones in which the wave equation is not separable. For example, radiation modes have not been presented before for multimode rectangular dielectric waveguides. In this paper, we present for the first time, a semi-analytical method for constructing the radiation modes in buried channel multimode waveguides in the weakly guiding limit. Our method relies on a non-linear transformation, which maps the infinite –xy Cartesian space into an infinite set of periodically arranged sub-spaces. Due to the periodicity of the transformation, fields can be represented by a discrete Fourier series in the new domain. Each radiation mode is next separated into a free-space mode traveling in the cladding and a response or perturbation component, triggered by the particular free-space mode, due to the presence of the waveguide. With this method, the calculation of the radiation mode is simplified to be the solution of a simple system of linear first order equations. In addition, the normalization of the entire radiation mode follows from the normalization of the free-space part. Radiation modes can include high spatial frequencies and, therefore, the Fourier series may need to contain a large number of terms. This in turn results in an increased number of calculations, which cannot be handled by only one processor for highly multimode waveguides so we used a parallel computing cluster of 16 - 900 MHz processors. Each radiation mode of a 50 μm  50 μm waveguide required ~17 min to calculate. Although presented for rectangular waveguides our method is applicable to other arbitrary waveguide geometries if they are approximated by a number of thin rectangles and so will find use more widely in graded index optical fibers and photonic band gap fibers. The authors thank Dr Richard James for aid in parallelizing the computation.
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