  In order to enhance the radiation power in terahertz band based on the
intrinsic Josephson junctions of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ single
crystal, we investigate a long cylindrical sample embedded in a dielectric
material. Tuning the dielectric constant, the radiation power has a maximum
which is achieved when it equals the dissipation caused by Josephson plasma.
This yields the optimal dielectric constant of wrapping material in terms of
the properties of BSCCO single crystal. The maximal radiation power is found
proportional to the product of the typical superconducting current squared and
the typical normal resistance, or the gap energy squared divided by the typical
normal resistance, which offers a guideline for choosing superconductor as a
source of strong radiation. By introducing an anti-reflection layer, we can
build a compact device with the BSCCO cylinder and two wrapping dielectric
layers with finite thicknesses.
