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Field transformers having irregular scattering elements in a rectangular waveguide are introduced as a means to achieve frequency-dependent mode conversion, mode-selective reflection, multiple mode conversion, and phase shifting. A stepwise wall profile provides for a large number of degrees of freedom and also induces large evanescent field content. A multiresolution optimization strategy allows good convergence during synthesis. The resulting structures are compact, with dimension of a few wavelengths, and can have functionality not achievable through periodic means. In some cases, more than one solution can be found that have different spectral characteristics, a result of the large number of degrees of freedom and the constraint set. This structure class may prove useful in microwave sources where multiple or higher order modes are excited, in waveguide transitions, in frequency-dependent switching, and as phase-shifting elements.