Photon-echo attenuation in rare-earth-ion-doped crystals

We study the optical properties of rare-earth-ion-doped inorganic crystals 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 low temperatures. With two pulses of one laser the echo is induced in one ion species and with a third, ''scrambler'' pulse of a second laser another species is excited. These scrambler excitations lead to a dephasing and thus to an echo attenuation which depends on the strength, frequency, and time of the scrambler pulse. The spectral sensitivity of 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 sequence the attenuation shows a very specific behavior dictated by the excitation-induced frequency shifts (EFS's). For t(s) between the two echo-inducing pulses the echo intensity is partially regained by the ''dephasing-rephasing balancing'' of the reversible EFS's. For the theoretical description a stochastic model is introduced and the dephasing by excitation-induced lattice vibrations and by EFS's are analyzed in detail. The present results are discussed in the light of previous experimental and theoretical investigations.