Z independent nonuniformities,

When the modal fields and propagation constants for one waveguide are known, we can use the reciprocity theorem to determine the modal fields and propagation constants of modes on any other waveguide. The second waveguide is equivalent to the first waveguide with a translationally invariant, or z-independent, nonuniformity. The relationships derived below are exact, and form the basis for the perturbation analysis in Section 31-10 when the waveguides are similar. 

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