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Approximate solutions for the complex propagation constant in semiconductor loaded waveguides are obtained by expansion of the fields in terms of a finite number of the empty waveguide modes. Solutions are obtained for the case of partial loading in the narrow dimension of the guide, which explicitly exhibit the non-reciprocal effects observed in the presence of a transverse magnetic field. Coupling between the TE10 and TM11 empty waveguide modes is shown to explain qualitatively the observed experimental effects. Good quantitative agreement with experiments using Si samples is obtained.