Radiation from a single Josephson junction into free space due to Josephson oscillations

We consider electromagnetic emission from a Josephson junction (JJ) in a resistive state in an external magnetic field and derive the radiation power from the dielectric layer inside a JJ directly into outside dielectric media. Matching the electric and magnetic fields at the JJ edges, we find dynamic boundary conditions for the phase difference in JJ. We find that the fraction of the power transformed into radiation is determined by the dissipation inside the JJ. It tends to unity as dissipation vanishes independently of the mismatch of the junction and dielectric media impedances.