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A full-wave numerical approach is proposed for analyzing rectangular waveguides with periodic slots. The approach is based on an aperture magnetic field integral equation in one unit cell. The presented technique can analyze both bound and leaky modes on rectangular waveguides with periodic slots that have a rather arbitrary shape on either the broad or narrow wall. Besides, the method can be used for a uniformly slit rectangular waveguide by taking the limit of the period. Using the proposed method, it is found that an air-filled rectangular waveguide with periodic longitudinal slots supports a leaky waveguide mode but no slot mode, while a uniformly slit rectangular waveguide (air-filled) can support a leaky waveguide mode as well as a slot mode. It is also found that an air-filled rectangular waveguide with cross slots supports a surface-wave mode in addition to a leaky waveguide mode.