We study the optical properties of rare-earth-ion-doped inorganic crys
tals with an emphasis on the dependence of two-pulse photon echoes on
the excitation density in the system. The experimental investigations
concentrate on Pr3+: Nd3+: Eu3+ codoped Y2SiO5 and YAlO3 crystals at l
ow temperatures. With two pulses of one laser the echo is induced in o
ne ion species and with a third, ''scrambler'' pulse of a second laser
another species is excited. These scrambler excitations lead to a dep
hasing and thus to an echo attenuation which depends on the strength,
frequency, and time of the scrambler pulse. The spectral sensitivity o
f the echo attenuation is used for a spectroscopic technique: ''photon
-echo attenuation spectroscopy.'' As a function of the delay time t(s)
between the scrambler pulse and the onset of the two-pulse echo seque
nce the attenuation shows a very specific behavior dictated by the exc
itation-induced frequency shifts (EFS's). For t(s) between the two ech
o-inducing pulses the echo intensity is partially regained by the ''de
phasing-rephasing balancing'' of the reversible EFS's. For the theoret
ical description a stochastic model is introduced and the dephasing by
excitation-induced lattice vibrations and by EFS's are analyzed in de
tail. The present results are discussed in the light of previous exper
imental and theoretical investigations.