The angular dependence of the radiation-zone output power and electric polarization of stimulated terahertz amplified radiation (STAR) emitted from a dc voltage applied across cylindrical and rectangular stacks of intrinsic Josephson junctions is calculated. The boundary conditions are obtained from Love's equivalence principles. During coherent emission, a spatially uniform ac Josephson current density in the stack acts as a surface electric current density antenna source, leading to a harmonic radiation frequency spectrum, as in experiment, but absent in all cavity models of cylindrical mesas. Spatial fluctuations of the ac Josephson current allow its fundamental mode to lock onto the lowest finite energy cylindrical cavity mode, causing it to resonate, leading to a non-uniform magnetic surface current density radiation source, and a non-trivial combined fundamental frequency output power with linear polarization for general radiation directions, which may be fully or partially coherent. The higher ac Josephson harmonics do not excite other cylindrical cavity modes. For rectangular mesas, the lowest energy modes are empirically not excited, but the non-uniform ac Josephson current can excite the harmonic sequence of modes with spatial variation across the rectangular widths, leading to combined radiation outputs both for the fundamental and the higher harmonics, which combinations also may be either fully or partially coherent. The superconducting substrate is modeled as a perfect magnetic conductor, greatly reducing the STAR emitter power and modifying its angular dependence, especially parallel to the substrate. Based upon this substrate model, existing Bi(2)Sr(2)CaCu(2)O(8 + δ) crystals atop perfect electric conductors could have STAR emitter power in excess of 5 mW, acceptable for many device applications.