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Following recent successes with semivectorial polarised £ field solutions for rib, channel, embedded, and buried waveguides a method is presented for the determination of corresponding polarised H field modes for similar and other rectangular waveguide structures which may contain any arbitrary distribution of horizontal and vertical dielectric discontinuities. The new finite difference schemes take full account of the discontinuities in the normal gradients of magnetic field components across all internal dielectric interfaces. The polarised H field results, which are presented for various rib and embedded waveguide structures, are found to be in excellent agreement with the corresponding polarised £ field modes. Application of the zero divergence constraint prevents the occurrence of spurious modes.

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