We present a theoretical study of the quantitative response of a superconducting film driven out of equilibrium by modulated laser irradiation. A numerical solution of the time-dependent coupled equations is performed, the quasiparticle distribution being represented by a Fermi-Dirac distribution with an effective temperature $T^{*}$. The time evolution of a typical Sn film is first studied at a drive frequency $f=1\mathrm{}$ GHz. The film response is then analyzed as a function of the drive frequency. It is shown that, in Sn, it is limited by the energy transfer from the quasiparticles to the phonon system. Although the film response depends on the phonon escape time and on the intrinsic times of the quasiparticle-phonon system, none of these times is shown to determine alone the time behavior. The characteristic times of the response also depend on the specific-heat ratios of the phonon and quasiparticle systems. Results are presented for the modulation depths and phase shifts of the quasiparticle temperature and of the power transferred to the phonon for different specific-heat ratios, intrinsic times, and phonon escape times. A comparison with the results obtained from a simple analytic model is done. We have also briefly discussed the situation for some other superconducting materials.

• Received 12 July 1982

DOI:https://doi.org/10.1103/PhysRevB.28.5150