Anti-phase-type complex-coupled, surface-emitting distributed feedback CC-SE-DFB) diode lasers are analyzed for the first time. For certain design parameters, both loss-coupled as well as gain-coupled structures are shown to select lasing in the symmetric mode (i.e. orthonormal emission in a single-lobe pattern). For loss-coupled structures we analyze a relatively simple configuration: a metallic second-order grating placed atop a diode-laser structure. This type of SE-CC-DFB structure can simply be fabricated by a lift-off and evaporation process; can operate in a single-lobed, orthonormal beam with a rather uniform near-field intensity pattern, and external differential quantum efficiency, eta(d), values in excess of 30%. Gain-coupled devices consist of a semiconductor-based 2(nd)-order grating placed at the metal-semiconductor p-side interface. By comparison to loss-coupled devices the threshold gain is reduced by a factor of 2 to 3. A design for realizing 2-D single-lobe, surface-emitting sources is discussed.