  We calculate the angular dependence of the power of stimulated terahertz
amplified radiation (STAR) emitted from a $dc$ voltage applied across a stack
of intrinsic Josephson junctions. During coherent emission, we assume a
spatially uniform $ac$ Josephson current density in the stack acts as a surface
electric current density antenna source, and the cavity features of the stack
are contained in a magnetic surface current density source. A superconducting
substrate acts as a perfect magnetic conductor with $H_{||,ac}=0$ on its
surface. The combined results agree very well with recent experimental
observations. Existing Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ crystals atop perfect
electric conductors could have Josephson STAR-emitter power in excess of 5 mW,
acceptable for many device applications.
