Angular dependence of the radiation power of a Josephson STAR-emitter

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.