Wavelength-dependent power-law Josephson photoresponse of a ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ thin film

The Josephson photoresponse of a current biased granular ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ thin film has been measured at 4.2 K for radiation frequencies ω in the range 20–111 ${\mathrm{cm}}^{\mathrm{-}1}$. The resulting photosignal s depends nonlinearly on the incident power P satisfying the relationship s=K(ω)${\mathit{P}}^{\mathrm{\alpha }\left(\mathrm{\omega }\right)}$, where K is a frequency-dependent constant. The value of α increases monotonically from 0.5 at 20.2 ${\mathrm{cm}}^{\mathrm{-}1}$ to 0.9 at 111 ${\mathrm{cm}}^{\mathrm{-}1}$. At 20.2 ${\mathrm{cm}}^{\mathrm{-}1}$ this power law is valid for incident powers between 5 mW and 1 kW, a range of more than ${10}^5$. These limits are imposed by experimental constraints and not by deviations from the power-law behavior. As the frequency increases, the responsivity of the film drops strongly, K(ω) decreasing approximately as ${\mathrm{\omega }}^{\mathrm{-}3}$, so that the power-law validity is established over three orders of magnitude at 111 ${\mathrm{cm}}^{\mathrm{-}1}$. Such a behavior of the Josephson photoresponse has been previously observed, albeit over reduced dynamic ranges, in granular superconducting films of other materials. Thus we believe it to be an inherent characteristic of the random arrays of Josephson junctions contained in such films.