  The in-plane infrared response of the high-Tc cuprate superconductors was
studied using the spin-fermion model, where charged quasiparticles of the
copper-oxygen planes are coupled to spin fluctuations. First, we analyzed
structures of the superconducting-state conductivity reflecting the coupling of
the quasiparticles to the resonance mode observed by neutron scattering. The
conductivity computed with the input spin susceptibility in the simple form of
the mode exhibits two prominent features: an onset of the real part of the
conductivity starting around the frequency of the mode omega_{0} and a maximum
of a related function W(omega), roughly proportional to the second derivative
of the scattering rate, centered approximately at
omega=omega_{0}+Delta_{0}/hbar, where Delta_{0} is the maximum value of the
superconducting gap. The two structures are well known from earlier studies.
Their physical meaning, however, has not been sufficiently elucidated thus far.
Our analysis involving quasiparticle spectral functions provides a clear
interpretation. Second, we explored the role played by the spin-fluctuation
continuum. Third, we investigated the temperature dependence of the
conductivity, of the intraband spectral weight, and of the effective kinetic
energy. The changes of the latter two quantities below Tc are determined by the
formation of the gap, by a feedback effect of the spin fluctuations on the
quasiparticles, and by a significant shift of the chemical potential.
