  The dynamical response of the Abrikosov vortex lattice in the presence of an
oscillating driving field is calculated by constructing an analytical solution
of the time-dependent Ginzburg-Landau equation. The solution is steady-state,
and work done by the input signal is dissipated through vortex cores, mainly by
scattering with phonons. The response is nonlinear in the input signal, and is
verified for consistency within the theory. The existence of well-defined
parameters to control nonlinear effects is important for any practical
application in electronics, and a normalised distance from the
normal-superconducting phase-transition boundary is found to be such a
parameter to which the response is sensitive. Favourable comparison with NbN
experimental data in the optical region is made, where the effect is in the
linear regime. Predictions are put forward regarding the suppression of heating
and also the lattice configuration at high frequency.
