Superradiant emission stimulated by vortex-antivortex pair production in layered superconductors

We report numerical simulations of coupled sine-Gordon and heat diffusion equations describing dynamic states stimulated by a trapped vortex driven by dc current in a stack of up to $N=321$ Josephson junctions. It is shown that the Cherenkov wake behind the vortex shuttle trapped in the stack can trigger proliferation of counterpropagating vortices and antivortices which get synchronized and form large-amplitude standing electromagnetic waves. This happens if the dc current density $J$ exceeds a threshold value ${J}_{s}$ which can be well below the Josephson interlayer critical current density ${J}_{c}$ for underdamped junctions. The cavity modes stimulated by the vortex-antivortex pair production cause peaks in the radiated power ${P}_{N}(J)$ with a nearly monochromatic spectrum at discrete values of $J$ corresponding to the zero-field Fiske resonances. The power ${P}_{N}(J)$ was evaluated for small rectangular stacks in the magnetodipole approximation and for large stacks in a single mode state. For small stacks, the highest peak in ${P}_{N}(J)$ increases rapidly, ${P}_{N}\ensuremath{\propto}{N}^{6}$, with the number of junctions at $N\ensuremath{\le}81$ and gradually slows down to ${P}_{N}\ensuremath{\propto}{N}^{2}$ at $161\ensuremath{\le}N\ensuremath{\le}321$. For stacks larger than the radiation wavelength, we obtained ${P}_{N}\ensuremath{\propto}{N}^{5}$ at $N\ensuremath{\lesssim}200--300$ and ${P}_{N}\ensuremath{\propto}{N}^{2}$ at larger $N$. At $N\ensuremath{\le}321$ and representative parameters of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$, we observed moderate overheating and no hotspots. The vortex-antivortex pair production can amplify THz radiation from ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ mesas for which trapping Josephson vortices could be used to stimulate THz emission at subcritical currents and optimize the radiation output.