We present an analysis of the diffractional properties of dual-period apodizing gratings. In a previous paper we used these components to obtain single-lateral-mode and dual-longitudinal-mode emission from a broad-area diode laser. We now calculate the diffracted field for a monochromatic beam incident on the grating by using an analytical model. Predictions of the model are compared with experimental measurements made with several dual-period gratings. We also discuss the situation in which a dual-period grating is used as an external coupler of a diode laser in a two-wavelength emission regime.