  It has recently been discovered that the optical analogue of a gradient echo
in an optically thick material could form the basis of a optical memory that is
both completely efficient and noise free. Here we present analytical
calculation showing this is the case. There is close analogy between the
operation of the memory and an optical system with two beam splitters. We can
use this analogy to calculate efficiencies as a function of optical depth for a
number of quantum memory schemes based on controlled inhomogeneous broadening.
In particular we show that multiple switching leads to a net 100% retrieval
efficiency for the optical gradient echo even in the optically thin case.
