Recent experiments on N'-N-S junctions with high-temperature cuprate s
uperconductors have shown that superconductivity can be induced in the
adjacent, normal metal at distances many times greater than the few h
undred Angstroms range of the conventional proximity effect. We show t
hat this arises in the particular geometry used in these experiments t
hrough the constructive interference of the tails of the de Gennes-Sai
nt-James bound and quasi-bound states of the normal metal N that penet
rate into the third metal, N'. This constructive interference results
in the re-appearance of a pair amplitude in this metal which is analog
ous to the ''spin echo'' of NMR and which we name a ''pair echo.''