  Phonon-assisted 2-magnon absorption is studied at T=4 K in the spin-1/2
two-leg ladders of Ca_14-x La_x Cu_24 O_41 (x=5 and 4) for polarization of the
electrical field parallel to the legs and the rungs, respectively. Two peaks at
about 2140 and 2800 1/cm reflect van-Hove singularities in the density of
states of the strongly dispersing 2-magnon singlet bound state, and a broad
peak at about 4000 1/cm is identified with the 2-magnon continuum. Two
different theoretical approaches (Jordan-Wigner fermions and perturbation
theory) describe the data very well for J_parallel = 1050 - 1100 1/cm and
J_parallel / J_perp = 1 - 1.1. A striking similarity of the high-energy
continuum absorption of the ladders and of the undoped high T_c cuprates is
observed.
