  The interaction of a cavity with an external field is symmetric under time
reversal. Thus, coupling to a resonator is most efficient when the incident
light is the time reversed version of a free cavity decay, i.e. when it has a
rising exponential shape matching the cavity lifetime. For light entering the
cavity from only one side, the maximally achievable coupling efficiency is
limited by the choice of the cavity mirrors' reflectivities. Such an
empty-cavity experiment serves also as a model system for single-photon
single-atom absorption dynamics. We present experiments coupling exponentially
rising pulses to a cavity system which allows for high coupling efficiencies.
The influence of the time constant of the rising exponential is investigated as
well as the effect of a finite pulse duration. We demonstrate coupling 94% of
the incident TEM00 mode into the resonator.
