Nonlinear dynamics in superconducting films

The theory of Halperin and Nelson describes the linear response of a superconducting film close to the Kosterlitz-Thouless transition to an ac field. We have extended this theory so as to describe the non-linear response in lowest order in the driving field. Two effects are predicted: the response at the driving frequency becomes non-linear, and odd harmonics are generated. We calculate explicitly the size and temperature dependence of these effects when the response is generated and detected by an identical pair of coils placed symmetrically either side of the film.